Influence of drying conditions on the stress and weight development of capillary suspensions
IInfluence of drying conditions on the stress and weightdevelopment of capillary suspensions
Steffen B. Fischer a , b , Erin Koos a , ∗ a KU Leuven, Soft Matter, Rheology and Technology, Department of Chemical Engineering,Celestijnenlaan 200f, 3001 Leuven, Belgium b Karlsruhe Institute of Technology, Institute for Mechanical Process Engineering andMechanics, Karlsruhe, Germany ∗ e-mail: [email protected] Abstract
Laser Position SensingDetector (PSD)
CoatingCantilever
T = const.RH = const.
Analytical scaleFixture Attachment mechanism ' Regularsuspension:Capillarysuspension:
Compressive forces F uniform F non-uniformStress measurement cantilever Cracking of suspensions during drying is a common problem. While additives,e.g. binders and surfactants, can mitigate this problem, some applications, such asprinting conductive pastes or sintering green bodies, do not lend themselves to theuse of additives. Capillary suspensions provide an alternative formulation withoutadditives. In this work, we use simultaneous stress and weight measurements to in-vestigate the influence of formulation and drying conditions. Capillary suspensionsdry more homogeneously and with lower peak stresses, leading to an increased ro-bustness against cracking compared. An increase in dry film porosity is not the keydriver for the stress reduction. Instead, the capillary bridges, which create strongparticle networks, resist the stress. Increasing the relative humidity enhances thiseffect, even for pure suspensions. While lower boiling point secondary liquids, e.g.water, persist for very long times during drying, higher boiling point liquids offerfurther potential to tune the the drying process.
Keywords : drying, particle coatings, capillary suspension, simultaneous stressmeasurement, cantilever deflection method
Stress growth during drying of paints, inks and coatings is an important measure for de-veloping defect free coatings. Stress is a direct measure of a film’s proneness to cracking.1 a r X i v : . [ c ond - m a t . s o f t ] N ov n nature, we find crack patterns in things like mud cracks [1]. Examples of technical im-portance include drying of ceramic tape cast films [2], as well as subsequent green bodybinder burn out, where internal stresses can build up and lead to cracking [3–5]. Anotherexample is represented by screen printing of conductive inks [6]. With increasing de-mand for low-cost solar cells and electronic gadgets, such as RFID tags, high throughputproduction is required [7]. The functional material is printed on flexible polymeric sub-strates with low glass transition temperatures. If drying of these electrically conductingcircuits lead to cracks, their function would be destroyed. In order to print the circuits,or apply pigments, the functional particles have to be suspended in a liquid, forming asuspension. Upon application, drying sets in. Initially, the suspension dries continuouslyas if there were no particles present for as long as the surface is covered with liquid. Thisdrying behavior is termed the constant rate period (CRP) [8]. Due to the evaporationof the liquid, the film shrinks and the solids density (particle volume fraction) increases.Generally, drying does not occur uniformly across the coating on narrow substrates orin droplet evaporation. In dilute systems, such as drying of a coffee droplet, this leadsto the coffee-ring effect in which particles are transported towards the edges. The causefor this phenomenon, capillary flows, was identified by Deegan et al. [9]. As the dropletstarts shrinking, the three phase contact line remains pinned at the substrate. Since thedroplet perimeter stays constant and evaporation continues, there must be flow carryingparticles towards the edges forming stains. The same phenomenon occurs during thedrying of more concentrated suspensions. As the film dries laterally, transporting parti-cles to the edges, particle depleted areas, or film defects, such as pinholes or trenches areleft behind [10–17]. When drying proceeds and a compact film forms, the CRP decreasesdue to imposed mass transport resistances. The liquid filled voids in the saturated andconsolidated particle coating represent pores and necks. Further evaporation pins thesurface liquid to the pore mouths, such that concave menisci start to develop. Thismenisci formation causes pressure differences across the interface, which is described bythe Young-Laplace equation for the capillary pressure p c : p c = 2 γ lv cos θr (1)Where the capillary pressure p c , depends on the liquid-vapor interfacial tension γ lv , thecontact angle θ , and the radius of a capillary tube inscribing the neck between particles r . Continued evaporation and pinning of the liquid causes the contact angle to decrease,which leads to a larger capillary pressure. This, in turn, compacts the surroundingparticles. If the coating is free to shrink in all directions, no stresses are observed.However, if the coating adheres to the substrate, which locally restricts the shrinkage,the strain mismatch can lead to severe cracking in hard particles or film formation forsoft particles [18–20]. In order to prevent film fracture, there are different possibilitiesto modify the suspension. Avoiding the formation of small pores and particle mobilityis achieved by addition of binders, which store the stresses and prevent delaminationbetween the film and substrate.Additionally, the flow properties of the suspension need to be adjusted for the appli-cation method. In many coatings, carboxymethyl cellulose (CMC) is used as thickening2gent. However, a study by Wedin et al. showed a dramatic increase in peak stressduring drying of a coating when CMC was added [21]. Furthermore, Equation 1 showsthe direct relationship between the capillary pressure and liquid-vapor interfacial ten-sion, which can be lowered through the addition of surfactants. In order to obtain anelectrically conductive circuit, these additives have to be removed, which is usually doneby heat treatment. However, on flexible, polymeric substrates with low glass transitiontemperatures, the treatment is restricted in terms of temperature. An alternative tosolid additives that need additional treatment is provided by capillary suspensions. Incapillary suspensions, the “binder” is a second liquid, immiscible with the bulk phase[22]. Upon the addition of a very small volume percent of this immiscible liquid, adramatic change in rheological properties is observed [23]. The obtained capillary sus-pension exhibits an increase in the yield stress by several orders of magnitude, whileshowing shear-thinning behavior averting the need for potentially stress-inducing CMC,making these suspensions ideally suited for various printing applications [24–26] or ce-ramic bodies [27]. This change in properties is caused by the sample spanning particlenetwork induced by capillary bridges of the secondary liquid. In our previous work, wefound these novel suspensions reduce cracking without addition of further additives [28].More recently, we found capillary suspensions form a uniform final coating after drying,devoid of pinholes and trenches despite initially present lateral drying [17].Since cracking is driven by stress build-up, stress measurements indicate the resilienceof a coating. Many previous studies have tracked the stress formation of coatings usingthe cantilever deflection method due to its simple concept [16, 18, 29–32]. Moreover,this method allows the cantilever to be placed in a controlled environmental chamber.Besides the temporal stress measurement, the change in mass over time, i.e. dryingrate, is another important factor in the coating’s drying behavior. However, this largelycomplicates the experimental setup. In several studies, the drying rate was obtained bycoating another substrate, which was then weighed inside the same chamber, while thestress was tracked on the other substrate [21, 33, 34]. This approach works well, as longas the drying conditions in the chamber are spatially homogeneous and, most impor-tantly, the coatings are identical. For capillary suspensions with their high yield stress,the sample application on the cantilever has proven to be challenging without introduc-ing misinterpretations. Ideally, the stress development and weight loss are measuredsimultaneously. Studies by Kiennemann et al. [35] and Fu et al. [36] overcame these lim-itations by placing the clamped cantilever directly on an analytical balance. However,since the balance cannot be placed inside a small chamber with uniform drying condi-tions, their experiments were carried out under ambient conditions that are difficult tocontrol. Our apparatus design, allows the simultaneous tracking of weight loss and stressdevelopment in the same coating inside a drying chamber under controlled conditions.This paper examines the differences in these quantities between a pure suspension and acapillary suspension with different types and amounts of secondary liquid under variousdrying conditions. 3able 1: Composition and coating parameters for each sample tested. φ solid sec. fluid φ sec /φ solid Gap height [ µ m] Coating speed [m/s]0.20 – 0 250 0.070.20 water 0.075 250 0.090.20 water 0.125 230 0.290.20 glycerol 0.125 330 0.170.25 – 0 320 0.070.25 water 0.124 170 0.290.25 glycerol 0.125 170 0.17 Alumina suspensions were prepared at different particle volume fractions and with avariation of secondary liquid to obtain different rheological properties. Alumina parti-cles ( α -Al O , CT3000SG, Almatis GmbH, Germany) with an average particle size ofd , = 0 . µ m according to the supplier were dried in an oven at 100 ° C overnight anddispersed in 1-heptanol ( > ∅ = 35 mm) toobtain smooth samples with particle volume fractions of φ solid = 0 . φ solid = 0 . φ H O . These fractions were chosen to keep the ratio of the volume of the secondary liq-uid bridges ( φ sec ) to the particle volume fraction ( φ solid ) constant, as shown in Table 1.For spectrometry measurements, we used heavy water (D O, 99.9 atom% deuterium,Sigma-Aldrich). Additionally, we prepared samples with glycerol ( > In order to repeatably and uniformly coat the cantilever, we manufactured the smallcoating rig shown in Figure 1a. At first, the stainless steel cantilever was clampedperpendicularly in the fixture between two sanded steel slabs such that the availablearea for the coating measures 6 mm wide and 40 mm long. The cantilever’s thickness is4 b Laser Position SensingDetector (PSD)
CoatingCantilever
T = const.RH = const.
Analytical scaleFixture Attachment mechanism ' Figure 1: ( a ) The steel coating rig with the clamped cantilever fixture placed in therecess of the rig. To maintain the cantilever’s position, it is supported from below. Uponsample deposition, a coating blade with preset gap height is moved between the greenrails along the cantilever with a constant coating velocity. ( b ) Schematic of the humidityand temperature controlled drying chamber. After coating, the fixture is inserted into thechamber, and attached to the analytical balance. During the measurement, the weightloss and cantilever deflection, tracked by the position sensing detector, are recorded.200 µ m. After clamping, the fixture was then placed in the recess of the coating rig, wherethe cantilever was supported to prevent bending while coating. This bending can lead toan inhomogeneous wet film thickness along the cantilever. Before use, the samples wereremixed at 3500 rpm for one minute, in order to have a well-mixed suspension beforeapplication. The pastes were deposited onto the cantilever and spread with a coatingknife (ZUA 2000, Zehntner GmbH, Sissach, Switzerland) by means of dragging the bladebetween the green rails along the cantilever, driven by a voltage regulated motor. Thehigh yield stress capillary suspension sample with ( φ H O = 0 . φ H O = 0 . µ m but different drying speeds. Both quantities aresummarized in Table 1 for each formulation. The dry film thickness was kept constantat 75 ± µ m. Our design of the stress measurement apparatus is shown in Figure 1b. The desireddrying temperature is set on the controller and allowed to equilibrate for at least onehour. The desired relative humidity is obtained by manually mixing water saturated air,5hich was passed through a bubbler, with dry air at a total air flow rate of ≤ ∼
30 seconds) after coating. After closing the chamber door, dataacquisition is started. Laser light is directed to the polished bottom surface two mm fromthe free cantilever end where it is reflected and subsequently captured by the positionsensing detector (PSD).As drying proceeds, film shrinkage confined by good adhesion of the film to thesubstrate causes stresses, which are captured as bending in the cantilever. This bentcantilever causes the deflected laser beam to travel on the PSD from point 1 to 1 (cid:48) . Beforethe actual measurement, the setup was calibrated to correlate the movement of the laseron the PSD with the deflection of the cantilever. This was done by deliberately deflectingthe cantilever a known distance with a micrometer screw while the entire fixture is in themeasurement position. The stress in the deformed substrate was derived by Stoney in1909 [38] for an uniaxial film stress, which was later corrected to a biaxial in plane stressdue to an influence of the cantilever width, which is larger than the coating height [39].Corcoran [40] later developed a correlation that takes the effect of substrate bending onthe developed coating stress into account and is now widely used for determining stressesin drying coatings. The stress σ within the coating is given by σ = d · E s t s t c L · ( t s + t c )(1 − ν s ) + d · E c ( t s + t c ) L · (1 − ν c ) (2)where subscripts s and c represent substrate and coating, respectively. The substrate(cantilever) thickness t s = 0 .
196 mm, the Young’s modulus E s = 210 GPa, Poisson’sratio ν s = 0 .
3, and the cantilever’s free length L = 40 mm.However, the correlation contains quantities that are difficult to obtain. The coatingthickness at the moment of drying t c is unknown and instead the dry film thicknessis used. Another unknown parameter is the coating’s Young’s modulus E c , which isdifficult to obtain in general and especially at different drying times. This drawbackcan be overcome if the experimental design is chosen such that the second term inEquation 2 can be neglected. In a similar study using alumina particles with addedbinders, the measured maximum Young’s modulus after drying was 8.5 GPa [36]. Thestainless steel cantilever in our study has a Young’s modulus of 210 GPa, which leadsto the first requirement for neglecting the second term: E s >> E c . With a dry coatingthickness t c < µ m, the induced error by neglecting the second term is expected tobe below 10% [36]. Moreover, several assumptions underlay Corcoran’s equation, such6s ideal adhesion of the coating on the substrate, isotropic elastic properties of coatingand substrate, a uniform biaxial stress in the coating, and small deflection, amongstothers [40]. We did not observe an effect of coating weight loss on the deflection, butexperiments at 40 ° C and 50 % RH required that the fixture be pre-heated before coatingto avoid condensation when inserted into the chamber. Given all of the assumptions,the result of the measurements will be in the correct order of magnitude, but shouldbe considered qualitatively and in a comparative manner within this study. Error inpeak stress measurements are calculated from the standard deviation of at least fivemeasurements.The dry film thickness ( t c ) was measured with a digital stylus micrometer indicator(ID-H530, Mitutoyo, Japan) with a precision of ± µ m. Since the dry films are verydelicate, special care had to be taken in carefully lowering the measuring stylus on thecoating to prevent excessive compression of the coating. The film thickness was measuredat more than 15 locations distributed along the length and off center of the film. Yield stress measurements, which provide a measure for a sample’s network strength,were performed with a vane geometry (FL100/6W/Q1, 6 vanes, 22 mm diameter, 16 mmheight) on a MCR 702 rheometer (Anton Paar GmbH, Germany). In order to investigatethe temperature dependence on the yield stress, the prepared and sealed samples wereplaced in a lab oven at a constant temperature of 30 ° C and 40 ° C, respectively, andallowed to equilibrate. Before measurement, the samples were quickly remixed for oneminute in the Speedmixer to account for any particle settling that may have occurredduring temperature equilibration. Subsequently, the sample still in the mixing cup isplaced in a modified temperature controlled cup holder. Upon lowering the vane intothe cup, the sample was allowed to rest for five minutes to relax any induced stresses.Afterwards, a stepwise stress ramp was applied until yield occurred. The resulting strainvs. stress curve was then analyzed with the tangent method to obtain the apparentyield stress of the sample. Reported errors are from the standard deviation of triplicatemeasurements.
The coating is assumed to be dry, once a weight change is no longer detected. However,depending of the medium to be dried, there is an isothermal sorption equilibrium betweenthe liquid in the coating and the ambient air. This equilibration depends on the relativehumidity (in case of water evaporation), but also mass transport resistances in the film.Depending on the liquid, it is often undesirable to have residual fluid left in a coating.In this work, we used two different instruments to determine the amount of liquid leftin the film prepared by different formulations. At first, we used a thermogravimetricanalyzer (TGA Q500, TA Instruments, USA). Less than 9 mg of the paste was weighedinto a crucible. The amount was chosen such that the film height within the cruciblewas comparable to the film thickness on the cantilever. After placing the sample in7able 2: TGA profile for measuring the residual fluid contentStage 1 Stage 2 Stage 3 φ solid Temperature Duration Ramp Temperature Duration0.20 30 ° C 500 min 50 ° C/min 500 ° C 60 min0.20 40 ° C 430 min 50 ° C/min 500 ° C 60 min0.25 30 ° C 220 min 50 ° C/min 500 ° C 60 min0.25 40 ° C 160 min 50 ° C/min 500 ° C 60 minthe crucible, it was gently tapped on the table with tweezers to achieve equal spreading.Afterwards, it was placed in a suspended weighing pan attached to the TGA. The furnacewas closed and the measurement started. The furnace and balance were always flushedwith nitrogen gas at flow rates of 60 ml/min and 40 ml/min, respectively. The sequentialstages followed the same principle. At first, the furnace was heated to the desired dryingtemperature where it was held until the sample was dry. Subsequently, the temperaturewas increased with a ramp of 50 ° C/min to a temperature of 500 ° C, where it was onceagain held constant. Afterwards, the residual fluid load was calculated as the differencein weight before the temperature ramp and the weight at the end of the high temperaturehold time divided by the weight at the end. The conditions varied for different sampleparticle volume fractions and are shown in Table 2.Later, we analyzed the headspace composition during drying of the capillary sus-pension samples at drying temperatures of 30 ° C and 40 ° C. In this experiment, we areinterested in the sequence in which the components evaporate. In order to save equip-ment time, we reduced the sample weight, i.e. film thickness. As before, the samples weredeposited in the crucible and gently tapped on the table for spreading. Afterwards, theywere analyzed in a TGA coupled with mass spectrometry (MS). Compared to the pre-vious instrument, this TGA (STA 449 F3 Jupiter, NETZSCH-Ger¨atebau GmbH, Selb,Germany) differed in the measuring system, where the crucible was placed on a carriersystem rather than being suspended. The drying gas was a mixture of 80 ml/min nitro-gen and 20 ml/min oxygen to mimic air. In this measurement, only the samples with φ solid = 0 . φ H O /φ solid = 0 .
125 were analyzed. The stage 1 profile used a shorterholding time of 100 minutes and 180 minutes for 30 ° C and 40 ° C, respectively. Thetemperature ramp in stage 2 was also lowered to 20 ° C/min.Following evaporation, the gas passes through the mass spectrometer (HPR-20 QIC,Hiden Analytical Ltd., UK) by means of the carrier gas mixture. The ionized and accel-erated molecules are detected by a multiple ion detection (MID) scan. The characteristicmass to charge (m/z) ratios were detected at 20 m/z for D O and 56 m/z for 1-heptanol.We chose heavy water because 1-heptanol has a fragment peak overlapping with nor-mal water at 18 m/z. After closing the furnace, the instrument was purged for severalminutes. The measurement was subsequently started and sampling on both instrumentswere triggered. The MS has a delay of a few minutes compared to the weight change inthe balance. 8 .4 -0.022MPa/min -0.016MPa/ min a cb d ef hg i j Ⅰ Ⅱ ⅢⅣ Ⅴ Ⅵ -0.011MPa/min i ii iii iv v viii iii ivv vi
Ⅱ ⅢⅣⅤ Ⅵ S t r e ss [ M P a ] S t r e ss [ M P a ] Load [ - ] Load [ - ] ϕ H2O = 0 ϕ H2O = 0.025 -0.010MPa/min
Figure 2: The results for simultaneous stress and weight measurement at a drying tem-perature of 40 ° C and 1% RH for ( a-e ) a pure suspension sample and ( f-j ) a capillarysuspension sample with 2.5 vol% added water, each at an initial solid volume fraction of0.2. The left most panel (a,f) shows the entire stress and load evolution over time. Themagnitude for the stress value can be found on the right y-axis and with its span beingdifferent in each column but the same for both panel rows. The magnitude of the loadis shown on the left y-axis in each panel, where it is shifted relative to the stress curvein each column for better visibility of trends. The load scale is the value shown on theleft of each panel (the stress scaling from the previous panel). Special points of interestare marked in each panel with capitalized roman numerals for the pure suspension andlower case roman numerals for the capillary suspension.
In Figure 2, the stress and weight development comparison during drying at 40 ° C anda relative humidity of 1% is shown for two representative samples. The pure suspensionof alumina dispersed in 1-heptanol is depicted in the upper row (Figure 2(a-e)), whileFigure 2(f-j) shows the φ solid = 0 . φ H O /φ solid = 0 . m ( t ) − m final m final = m liquid ( t ) m dry (3)with m ( t ), being the film mass measured at time t . The measured dry film thickness forthe pure and the capillary suspension were 71 ± µ m and 69 ± µ m, respectively. Theleftmost panels (a and f) show the entire stress and load curve with excerpts thereofshown in the other panels. While the x- and y-scales differ for each of the excerpts, theyare identical between the two samples (columns). The inset in each panel represents theentire stress curve with a box marking the magnified area depicted in the main panel. Wehave identified six key points, marked in the stress graphs with capital roman numeralsfor the pure suspension and lower case numerals (i-vi) for the capillary suspensionsaccording to the following observations:I start of the measurement;II the point where the stress deviates from an initial linear trend;III the rapid increase in stress preceding the stress peak;IV peak stress;V end of rapid stress decrease following the stress peak;VI stress trough before the residual stress value is reached.First, we will examine the findings of the pure suspension without added water( φ H O = 0) in conjunction with observations from a previous study [17]. Initially (I),there is a quick stress increase, quickly transitioning into a linear growth. In Figure 2b,the deviation of the stress from the linear growth (point II) coincides with increasingdivergence of the load from the constant rate period. Visual observation and profilemeasurements of the drying films reveal lateral drying [17]. Due to an increased dryingrate near the edges and pinning of the contact line between the coating and substrate,the film starts consolidating near the edges first, while the remainder of the coating isstill supersaturated [10–15, 17]. This gradual increase in stress changes when a criticalamount of menisci have formed, which leads to a more rapid increase in stress as thedrying front propagates from the edges inward. When reaching point III (Figure 2c),a very rapid stress increase towards the peak stress (IV) occurs. Images of the filmshow that in this period, the final supersaturated patch or region vanishes until a fullycompacted film forms at the peak stress, leaving a pinhole or trench [17]. Moreover,experiments with dyed heptanol suggest that the film is still completely saturated atthat time [17]. Following the peak stress, a two-step stress relaxation takes place (Fig-ure 2d). Stress release can have various superimposed causes. These causes range fromthe deformation and coalescence of soft particles [20], to undesirable crack formationand plastic deformation, such as particle rearrangement [41] often leading to unusablecoatings. Another reason for stress relaxation is the reduction of stress inducing factors,10.e. evaporation of the menisci. When air starts invading the coating after point IV, theamount of liquid filled pores and menisci are reduced, leading to a decrease in equivalentpore stresses [31, 42]. We can exclude the formation of cracks since all examined films inthis work were crack free. The reason for the two-step relaxation is not clear. However,a quick air invasion, i.e. menisci removal, along the edges of the entire cantilever couldexplain the fast decrease. Once the fractal drying front moves inward from all sides, theoverall measured stress release decelerates due to the decreased area, and in particular,the shorter length where the stress acts. Eventually, the stress reaches a local minimumat point VI, before increasing again and approaching a final residual stress value (Fig-ure 2e). At the local minimum, the film is nearly dry, however, due to capillarity andblob formation, small amounts of the final residual fluid occupies the smallest pores [43].When air starts invading the remaining small liquid filled pores, the capillary pressureonce again increases and, thus, the measured stress rises.The stress and load profile of a capillary suspension with φ H O /φ solid = 0 .
125 is shownin Figure 2f. After the start of the measurement (i), the stress increases with a transitionto a linear growth (Figure 2g). This transition occurs for the capillary suspension in asimilar fashion as the pure suspension due to their nearly identical bulk fluid volumes.Unlike the pure suspension, when the stress increase deviates from its linear trend inthe capillary suspension, the load still remains in the constant rate period. Despite thesimilar stress increase between point i and point ii, profile analysis shows significantdifferences between the two films. Initially, the capillary suspension also exhibits lateraldrying, but to a lesser extent [17]. The edges constantly dry but only partially con-solidate while retaining this critical height. We attribute this phenomenon to a locallyincreased yield strength that is larger than the compressive forces, i.e. capillary pressure.Capillary suspensions have a large yield stress immediately after formulation, due to thepresence of a sample spanning network [23]. In this type of pendular state suspension,the particles are connected by water bridges, forming flocs. Connections between thesepercolated flocs form a path (backbone) throughout the sample (sample spanning net-work) [44]. As drying begins, the larger pores between the flocs compact (yield) and storesome stresses. At the edges of the cantilever, where compaction has already occurred, theparticle flocs form more percolating paths, which locally increases the yield stress andprevents the film from shrinking further, until the now higher intermediate yield strengthis exceeded. While lateral evaporation persists, the denser packing near the edges wicksliquid from the surface supersaturated center of the cantilever until the yield strengthof the film in the surface layers is equal across the cantilever. It is important to notethat while the surface layers across the cantilever have compacted, the region below isstill supersaturated. At point ii, this surface consolidation has finished and no supersat-urated surface region is visible anymore [17]. As drying proceeds, the capillary pressureincreases beyond the intermediate yield strength, causing the film stress to grow muchfaster than its previously linear trend during further compaction. This rapid increaseoccurs much earlier for the capillary suspension than for the pure suspension ( t ii < t II ).Qualitatively comparing the slope of the stress increase, we see a faster increase in thestress for the capillary suspension sample. A study by Price et al. [31], where they used11 walled cantilever to suppress edge drying, showed the effect of lateral drying on thestress evolution. While lateral drying causes a generally slower stress increase towardsthe peak, the absence thereof results in a very rapid stress growth. That is, the capil-lary suspension with its faster stress increase dries more uniformly across the cantileverwithout using artificial walls. Shrinkage profile measurements support this observationof top-down drying after point ii [17]. While capillary suspension coatings exhibit largersuperelevations near the edges of the cantilever compared to the regular suspension, thisis due to coating application effects and are present already before drying. However, theyretain their shape during the evaporation process in contrast to the regular suspensionwhere particle accumulation (coffee-ring effect) is observed. The reason is the connectedparticle network and larger cluster structures compared to individually dispersed par-ticles in the regular suspension. This also explains the almost uniform stress increasebetween point iii towards the peak stress (point iv), as depicted in Figure 2h, which isfurther substantiated by the lack of drying defects such as pinholes or trench formationin the capillary suspension film.The point of maximum peak stress (iv) and, thus, the state of full film compactiondisplays several differences compared to the pure suspension. First, the peak is reachedat an earlier time ( t iv < t IV ). Second, the peak stress for the capillary suspension sampleis lower ( σ iv < σ IV ), which will be explored in more detail later on. Moreover, whilethe constant drying rate for the pure suspension has already ceased at point II, theconstant rate period for the capillary suspension persists even beyond full compaction.This implies that despite the early development of a consolidated surface, which usuallydecreases the drying rate, the drying continues unabated such that the surface must bekept sufficiently wet. We ascribe this phenomenon to corner flow [45, 46], as describedpreviously [17]. After the peak stress (point iv), the capillary suspension also shows atwo-step stress relaxation (Figure 2i). In the capillary suspension, however, the firstslope is clearly smaller in magnitude, i.e. displays a slower stress decay in the first stepafter the peak (-0.016 MPa/min) compared to the pure suspension (-0.022 MPa/min).Linking this first stress release to the drying rate and the fully compacted film, thisimplies capillary flow from inside the coating to the surface. This pore emptying throughflow (decrease in equivalent pore pressure) must therefore be a slower process than poreemptying through Haines jumps. Additionally, we have shown in our previous workwith dyed samples that point v corresponds to the appearance of the first dry areastransitioning to pore emptying by air invasion [17]. The second stress release step is onlymarginally, but consistently slower for capillary suspensions (-0.010 MPa/min versus -0.011 MPa/min). This may be caused by the capillary water bridges, which require alarger air invasion pressure than the bulk fluid. Heptanol covers these bridges, whichprotects them, and prevents sudden stress releases by air invasion into pores throughHaines jumps, as is the case for the pure suspension [47, 48]. As a result, the heptanolcluster in the coating remains connected and should dry more gradually. Finally, thestress reaches its local minimum at point vi (Figure 2j), before once again increasingtowards the final residual stress. The width of the trough (full width at half maximum)is wider for capillary suspensions (6.45 min) than for the pure suspension (5.66 min),12 ϕ H2O ϕ solid = 0.075 ϕ H2O ϕ solid = 0.125 ϕ H2O ϕ solid = 0.125 ϕ glycerol ϕ solid % RH % RH % RH % RH % RH % RH % RH % RH % RH % RH
30 °C 40 °C 30 °C 40 °C0.00.10.20.30.40.50.6 P ea k f il m s t r e ss , σ pea k [ M P a ] ϕ solid = 0.2 ϕ solid = 0.2530 °C 40 °C 30 °C 40 °C101001000 Y i e l d s t r e ss , σ y [ P a ] = 0 ϕ H2O ϕ solid = 0.075 ϕ H2O ϕ solid = 0.125 ϕ H2O ϕ solid = 0.125 ϕ glycerol ϕ solid ϕ solid = 0.2 ϕ solid = 0.25 a b Figure 3: ( a ) Yield stress measurements of samples with a variation in secondary fluidcontents and initial particle volume fraction, as measured at 30 ° C and 40 ° C. ( b ) Thecomparison in peak film stress for drying experiments with a variation in secondary fluidcontent and initial particle volume fraction performed at 30 ° C and 40 ° C as well asdifferent relative humidities.which could be explained by larger pores, formed by the initial network structure, filledwith remaining fluid. This should theoretically also lead to a lower residual stress. Thisresidual stress is very sensitive to film variations in terms of film height and lateraldrying, which made it difficult to identify a clear trend of residual stress dependencies.Capillary suspensions exhibit distinctly different stress development features com-pared to the pure suspension. For capillary suspensions, the stress increase is morerapid, indicating reduced lateral drying, whereas the stress decrease is more gradual.Moreover, the peak stress, which is an indicator for a film’s proneness to cracking, is re-duced in the capillary suspension. The differences and dependencies on drying conditionsare examined more detailed in the following section.
As observed in Figure 2, the measured peak stress is lower for the capillary suspensionwith φ H O /φ solid = 0 .
125 at φ solid = 0 . φ solid = 0 .
25 compared to the pure suspen-sion. Generally, a sample without particle yielding exhibits larger stresses with increasingelastic strain acting on the sample network. The yield strength is, therefore, a measure ofthe coating’s resistance to stresses. Because the yield stress of capillary suspensions canbe modified through addition of water, the yield stress for the different formulations atthe two temperatures is measured. The effect of a variation in secondary liquid volumeon the yield stress, σ y is marked with different colors (blue for the largest water addi-tion) and patterns, as shown in Figure 3a. At a particle volume fraction of φ solid = 0 . φ H O /φ solid = 0 . φ H O /φ solid = 0 . φ solid = 0 . φ glycerol /φ solid = 0 . φ solid = 0 .
25. An increase in temperature only has a small decreasing effect on the yieldstress.Naturally, the drying conditions will also influence the peak stress, as shown inFigure 3b. First, the drying temperature will influence the drying rate. At higherdrying rates, one expects a larger peak stress due to smaller contact angles of the pinnedmenisci, leading to larger capillary pressures. A temperature induced decrease of theinterfacial tension is not expected to balance the change in contact angle. Second, therelative humidity influences the drying of water while leaving the heptanol unchanged.The intention is to suppress drying of the capillary water bridges, such that the yieldstrength is maintained once the bridges are exposed to air. Exchanging water with thehigher boiling point glycerol should further that effect. The influence of the discussedformulation changes and drying parameters on the maximum drying stress ( σ peak ) isshown in Figure 3b. To understand these results, we will first only consider water asthe secondary liquid and a particle volume fraction of φ solid = 0 .
2. The black column(most left in each RH segment) represents the pure suspension. When evaporating intodry air (1% RH), an increase in water fraction results in a lower peak stress, both at30 ° C and 40 ° C. While an increase in humidity decreases the peak stress for no andlow amounts of added water, it has no effect on the sample with the highest wateraddition (blue, φ H O /φ solid = 0 . φ H O /φ solid = 0 . φ H O /φ solid = 0 .
125 and φ solid = 0 . ≤ .
07, i.e. the means aredifferent with a probability of more than 93 percent). From the small yield stress decrease(Figure 3a), one would have expected a larger peak stress in the absence of particlemigration. However, the bulk viscosity of heptanol is also temperature dependent. Itdecreases from 5.090 mPa · s at 30 ° C to 3.740 mPa · s at 40 ° C [49]. This reduction mayallow particle clusters that are not part of the sample spanning network, or have yieldedalready, to rearrange more easily resulting in a partial stress release. This rearrangementwould most likely occur in the lower layers, which are still uncompacted before the stresspeak. 14he pure samples show more pronounced lateral drying at higher temperatures [17].This more pronounced lateral drying leads to trench formation and causes more particlesto migrate, thus releasing the evolving stresses. Therefore, the maximum stress, whichis expected to be larger compared to a lower temperature cannot be independently mea-sured since the stress accumulation and stress relaxation through yielding and particlemigration are superimposed. Increasing the initial solid load to φ solid = 0 .
25 leads tosmaller liquid volume between the particles. In non-stabilized suspensions, this leadsto more particle-particle interactions upon lateral drying, with the result of restrictedparticle migration (reduced trench formation and pinholes) and, consequently, a largerstress formation due to the absence of stress relaxation through particle migration [11].Indeed, as shown in Figure 3b, the pure suspension at 1% RH displays a larger peakstress than at lower volume fraction. This trend holds for both drying temperatures.Interestingly, the capillary suspension ( φ H O /φ solid = 0 . φ solid = 0 . φ glycerol /φ solid =0 .
125 is much lower than when using water, especially at φ solid = 0 . ° C, which means it essentially does not evaporate under the examined conditionsand should remain completely in the film. As expected due to the only slightly largeryield stress for the glycerol capillary suspension at lower particle load, the reductionin peak stress compared to the pure suspension is small (Figure 3b). In contrast, thelarger σ y at higher initial solid content causes an immense reduction in peak stress ofapproximately 40%. This exceeds the reduction measured for the water sample at 1%RH despite the higher yield stress. This observation, along with the decrease in peakstress at 50% RH, suggests that water lowers the coating’s resilience against shrinkingstresses.We have shown that the peak stress can be reduced by using capillary suspensions indrying coatings. Changing the drying temperature did not generally lead to a change inthe peak stress. Interestingly, we found that an increase in humidity can lower the peakstress of the pure suspension and capillary suspension at high particle load (whereas nochange is observed at φ solid = 0 . .3 Film morphology at the peak: Residual fluid In the previous section, we observed the addition of a secondary fluid, which changes theiryield strength, decreases the peak stress. While non-stabilized suspensions can flocculatedue to van der Waals forces, a capillary suspension represents a highly flocculated systemwhere the capillary force (originating from the secondary fluid bridges), is much stronger[22, 23], leading to the yield stress increase as displayed in Figure 3a. However, thisnetwork formation may also result in a different microstructure of the coating. The filmdensity, that is the final packing volume of a coating, is a measure of its porosity. Thesimultaneous stress and weight measurement used in this study allows us to directlyestimate the final packing volume fraction in a reliable way based on a few simpleassumptions:1. For the systems with added glycerol, the glycerol is treated as inert and remainingcompletely in the film.2. For the systems with added water, the water volume in the capillary bridges istreated as heptanol (the densities are approximately equal and there is no differencein their distribution within the film).3. When the stress has approached its residual value, the film was considered dry(devoid of any volatile components). Due to small noise in the weight signal, thefinal dry mass m final is the averaged value over the last 100 recorded data points(50 seconds).4. The volatile liquid content of the dry film (isothermal sorption equilibrium) isnegligible (V final = V Al O or V final = V Al O + V glycerol ).5. The coating is fully saturated and the maximum final packing volume fraction isobtained when the peak stress σ peak is reached [11].The experiments were carried out until the residual stress approached its final value(assumption 3). This is sufficient since the weight change was already below the smallfluctuations of the balance a few minutes after point VI/vi. Glycerol with a boiling pointof 290 ° C will not evaporate in measurable amounts at 40 ° C (assumption 1). For thecases with added water, small amounts of water may remain in the final film. The errorinduced by assumption 2 is below 0.6% due to the low secondary fluid volume fractionsused in capillary suspensions. In a previous study with dyed 1-heptanol, we found thatthe film is saturated until the peak stress had occurred (assumption 5) [17]. Theseassumptions allow to calculate the final packing volume fraction φ solid , peak as follows:Water : φ solid , peak = V Al O V Al O + V heptanol = m final ρ Al2O3 m final ρ Al2O3 + m ( σ peak ) − m final ρ heptanol (4)Glycerol : φ solid , peak = V Al O V Al O + V glycerol + V heptanol = m final ρ Al2O3 +0 . ρ glycerol m final ρ Al2O3 +0 . ρ glycerol (1 + 0 . m ( σ peak ) − m final ρ heptanol (5)16 ϕ H2O ϕ solid = 0.075 ϕ H2O ϕ solid = 0.125 ϕ H2O ϕ solid = 0.125 ϕ glycerol ϕ solid % RH % RH % RH % RH % RH % RH % RH % RH % RH % RH
30 °C 40 °C 30 °C 40 °C0.00.10.20.30.40.50.6 M a x i m u m s o li d l oad i ng , ϕ s o li d , pea k [ - ] ϕ solid = 0.2 ϕ solid = 0.25 Figure 4: The average dry film particle volume fraction of the experiments obtainedfrom the particle volume fraction at the peaks for the aforementioned formulations anddrying conditions.with m ( σ peak ) indicating the mass at the stress peak and φ solid , peak denoting the finalvolume packing. Equation 4 is used for the samples with water, and Equation 5 showsthe equation for the samples with glycerol. The factor of 0.125 arises from the initialvolume fraction φ glycerol / φ Al O = 0 .
125 in these samples. The calculated particle volumefraction at the stress peak, φ solid , peak of our experiments is shown in Figure 4. In general,we see a decrease in particle volume fraction at the stress peak φ solid , peak with increasingwater content. That is, inducing a flocculated particle network increases the porosityof the sample. As can be seen in Equation 1, an increase in pore size results in lowercapillary stresses, which in turn leads to a lower peak stress for the same film height, orin other words, a higher critical cracking thickness. This observation is in accordancewith the findings of Guo and Lewis [11], and Singh et al. [50]. Singh et al. foundthat for a constant particle loading for alumina suspensions dispersed in water, the finalpacking volume of the coating decreased with increasing degree of flocculation, i.e. thefilm contained more pores [50]. Similarly, Guo and Lewis found the same decrease in dryfilm volume fraction for flocculation induced by salt addition to stabilized silica particles[11]. Additionally, their experiments indicated that an increase in initial particle volumefraction led to a larger dry film volume fraction, i.e. a more compact coating.Increasing the relative humidity tends to slightly decrease the dry film particle volumefraction in the capillary suspensions. Interestingly, an increase in relative humidity alsoincreases the dry film porosity (decreases φ solid , peak ) of coatings prepared from the puresuspension, coatings that were not intentionally flocculated. This effect appears to bemore evident at lower drying temperature. A temperature increase at the initial particlevolume fraction of 0.2 results in a denser film at each φ sec and relative humidity. This17nding supports our hypothesis of larger particle and cluster mobility at 40 ° C, whichallows some stress relaxation through particle migration. Increasing the initial particleload to 0.25 causes a less dense film for both temperatures compared to the lower initialload, a result that is in accordance with the larger measured yield stress (higher degreeof flocculation). The particle interactions suppress the particle mobility resulting inmore porous films. This result is in contrast to the results of Guo and Lewis [11].The discrepancy may arise from the use of partially stabilized silica particles versusunstabilized alumina, as well as the use here of irregularly shaped alumina particles.The link between the film porosity and stress peak should be established for cap-illary suspensions in order to elucidate the stress reduction potential caused by thesecondary capillary bridges rather than through a porosity increase. The samples withadded water both show a decrease in σ peak and φ solid , peak , as predicted. Recall that atlower initial solid load, there was no difference in peak stress with the capillary sus-pension ( φ H O /φ solid = 0 . φ sec /φ solid = 0 .
125 show almost identical porosities, while they differ inpeak stress. This clearly demonstrates that particle-particle interactions can dominatethe influence on the peak stress as opposed to the porosity of the coating.In this section, we have shown that capillary suspensions lead to more porous dryfilms than the pure suspension due to flocculation. However, increasing the relativehumidity can also increase the porosity, in particular for the pure suspension. More-over, we have demonstrated that the porosity increase in capillary suspensions are notresponsible for the reduction in peak stress. Instead, the particle interactions caused bythe secondary liquid capillary bridge determine the influence on the peak stress. Thissuggests that by choosing a secondary liquid with a higher boiling point than water andstronger interfacial tension than glycerol can further improve the formulation.
The observed temperature dependence of the secondary liquid on the dry film porosityraises the question whether the capillary water bridges persist until after drying or ifthey evaporate earlier, as would be predicted by the higher vapor pressure. If the waterbridges partially remain in the film, one would expect a larger residual fluid contentand longer influence of the bridges on the drying dynamics. In order to detect theserelatively low residual contents, a thermogravimetric analyzer with a resolution of 0.1 µ g was used. The samples were dried into a dry nitrogen atmosphere and a similar wetfilm thickness in the crucible as on the cantilever, as described in subsection 2.5. Figure 5shows the residual liquid in terms of the coating’s load m liquid /m dry (Equation 3) forfilms prepared with increasing water content at different initial solids load for both 30 ° Cand 40 ° C. All experiments show a residual load lower than the initial water load whenformulating the samples (3.2 % for φ H O /φ solid = 0 .
125 at φ solid = 0 . H2O ϕ solid = 0 = 0.075 ϕ H2O = 0.125 ϕ H2O
30 °C 40 °C 30 °C 40 °C ϕ solid = 0.2 ϕ solid = 0.250.00.20.40.60.8 R e s i dua l l oad [ % ] ϕ solid ϕ solid Figure 5: Residual fluid content for differently formulated suspensions with increasingwater content and initial particle load. The samples were dried at a constant temper-ature of 30 ° C and 40 ° C. Subsequent mass loss caused by heating was recorded witha thermogravimetric analyzer. The residual liquid load is normalized against the dryparticle weight.that at least 80% of the water has evaporated. At an initial solid fraction of φ solid = 0 . ° C. Atthe higher temperature, both the pure suspension and weak capillary suspension showan increase in the residual fluid fraction, while the capillary suspension exhibits a lowersaturation compared to 30 ° C. At higher initial solid fraction, the results contrast to thelower particle fraction; while the residual liquid content for the pure suspension is at alower level as for φ solid = 0 .
2, the capillary suspension displays a clear increase. Thismeans that more residual fluid, presumably water, remains in the capillary suspensionat φ solid = 0 . φ solid = 0 .
25 are in contrast to this theory. While the porosity of thecapillary suspension films at higher initial solid fraction are somewhat higher, the re-tained amount of liquid also increased. Further insight can be provided by researchusing porous media, especially in oil recovery, where three phase flow phenomena aremore common. When modeling the drying of a porous system, the rules of invasion per-colation (IP) and drainage flow can be applied [45, 51]. Drying of the pure suspensions19eads to phenomenon such as Haines jumps or meniscus snap-off (more dominant at im-bibition conditions) [51, 52]. These incidents lead to isolated blobs of heptanol that aredisconnected from the bulk. These droplets can remain trapped in the film as residualfluid. As mentioned in subsection 3.1 and shown in Figure 2, the water bridges, with ahigher capillary pressure than heptanol, allows the capillary suspension film to dry at aconstant rate even beyond close packing. The capillary bridges formed by the secondaryliquid obstruct the bulk fluid pathways so that snap-off events are reduced or even pre-vented. Furthermore, heptanol covers the water bridges, even in the presence of air [47].Thus, the bulk heptanol remains connected to a larger degree, leading to piston-like flow[52]. Continued drainage (drying) can even lead to reconnections between previouslydisconnected oil clusters [53]. In a recent micro-CT study by Scanziani et al., drainageexperiments with brine, oil, and gas showed that water is retained in the smallest necksand pores upon gas invasion in a porous carbonate rock [48]. Oil occupies the mediumsized pores and gas preferentially invades the larger pores. In porous media filled withoil and water, an increase in temperature additionally favors water retention leading topreferential oil drainage [54, 55].With this more complex behavior in mind, we can revisit the potential difference instructural particle arrangements for the capillary suspension at φ solid = 0 .
25 comparedto φ solid = 0 .
2. For granular materials, the coordination number z should be related tothe particle volume fraction by z = π/ (1 − φ solid ) [56]. Since the number and volume ofcapillary bridges are related through φ sec /φ solid = z / · V bridge / V particle the bridge vol-ume must be similar for the higher particle fraction sample since the φ sec /φ φ solid ratioremains constant [23, 57]. Of course, capillary suspensions are composed of dense flocsconnected by a sparse backbone [44] where the porosity of these networks is only weaklyrelated to the particle fraction [58]. In accordance with the porous rock/ particle bedfindings, this would lead to more residual liquid stemming from the similar capillarywater bridges. The increase in the number of connections would explain the observedincrease in yield stress, smaller peak stresses, similar porosity, and larger residual fluidcontent compared to the respective capillary suspension sample at lower initial particleload.We conclude that the residual fluid content for the pure suspension is mainly de-pendent on the porosity of the final dry film. For the capillary suspension on the otherhand, it appears to be an interplay of porosity and number of capillary water bridges.Blockage of pathways for air invasion leads to better drying of heptanol even fortifiedat elevated temperatures. This suggests that residual liquid in capillary suspensions ispredominantly water. The extent should be controlled by the total amount of waterbridges present in the sample. The following section will therefore examine if capillarywater bridges despite its higher vapor pressure persist longer than heptanol. In the previous section, we put forward a hypothesis that the water capillary bridgespersist through the late stages of drying. In order to directly elucidate the evaporationbehavior of the capillary water bridges, we coupled a mass spectrometer (MS) with20 .00.51.01.52.02.5 I n t en s i t y [ x - ] I n t en s i t y [ x - ] Time [min] R e l a t i v e w e i gh t [ % ] T e m pe r a t u r e [ ° C ] Time [min] R e l a t i v e w e i gh t [ % ] T e m pe r a t u r e [ ° C ] D O (20 m/z)Heptanol (56 m/z) ϕ solid = 0.230 °Cend of constant rate period start ramp start rampend of constant rate period D O (20 m/z)Heptanol (56 m/z) ϕ solid = 0.240 °C ba Figure 6: Results for thermogravimetrical analysis coupled with mass spectrometry overtime for drying of capillary suspensions with initial volumetric particle load of 0.2 anddried at ( a ) 30 ° C and ( b ) 40 ° C. The upper panel illustrates the intensity of the heptanolmeasured at a specific mass to charge ratio of 56 m/z (green line) and the intensity ofthe heavy water mass at 20 m/z (blue line). The lower panel shows the temperatureprofile (red line) and the relative weight change of the coating (dotted black line).thermogravimetrical analysis (TGA), as shown in Figure 6. This combination allowsus to set an accurate temperature, while obtaining the drying rate and analyzing theheadspace composition. The temperature for these measurements followed the profileshown in Table 2 where the sample was first dried at either 30 ℃ (Figure 6a) or 40 ℃ (Figure 6b) then, once the sample mass remained constant, increased to 500 ℃ .Since 1-heptanol (56 m/z) also has a fractional mass peak overlapping with water, wereplaced water with D O (20 m/z). Despite flushing, we observed a constant decrease forthe 20 m/z signal, the indicator for heavy water, even during the temperature increaseto 500 ° C. As this is highly unlikely to be D O, we hypothesize that the argon, whichis also present in trace amounts and also possesses a fractional peak at 20 m/z, couldbe the reason for the constant decline in that signal. Therefore, we used the lineardecrease after attaining a temperature of 500 ° C as a baseline for correction in theD O signal. Subsequently, the MS signals were smoothed. Figure 6 shows the resultsfor capillary suspensions at an initial solid load of 0.2 and φ H O /φ solid = 0 .
125 at thetwo temperatures. The green solid line represents the 56 m/z intensity over time forheptanol and the blue solid line shows the intensity of the 20 m/z signal detected forheavy water. After the start of the experiment for drying of the capillary suspensionat 30 ° C (Figure 6a), 1-heptanol constantly evaporates until the end of the constantrate period denoting the transition to the second drying period in which the headspaceconcentration drastically drops. When the film appears gravimetrically dry, the heptanol21n the gas phase swiftly decreases. Once the temperature is rapidly increased, the smallamount of residual heptanol evaporates.The evaporation of heavy water from the film is quite different. Over the courseof the constant rate period, the gas phase concentration of D O continually increases.In fact, it is still increasing at the end of the constant rate period when the heptanolconcentration starts to decrease. Once the heavy water concentration starts to decline,the rate of decrease is smaller than for the heptanol. Furthermore, water is still foundin the gas phase well after the film appears to be dry (mass reaches a constant value)and the temperature increase evaporates the leftover water. This clearly shows thatat 30 ° C, the capillary bridges dry much slower than heptanol despite the higher bulkvapor pressure. More importantly, the capillary bridges persist and are still drying whenheptanol has already reached its equilibrium.The drying of the capillary suspension at 40 ° C is shown in Figure 6b. As withthe drying at 30 ° C, heptanol dries with a fairly constant rate, although there is moregradual decrease before the end of the constant rate period. Due to the high sensitivityof the MS, the reason for this earlier drop could be inhomogeneities in coating thickness.This is also reflected in the TGA measurement where a rate change is observed in thefilm weight. Nevertheless, a sharp decrease is observed after entering the second dryingperiod. Again, the water concentration drop is delayed by several minutes, once againoccurring when the film has nearly reached its dry state. Surprisingly, this delay is longerat the higher temperature, supporting the results obtained from drainage experiments[54, 55] . When the heptanol concentration in the gas phase is approximately zero, thewater still has a high concentration in the gas phase. This concentration decays slowly,only reaching zero just before the temperature increase. Upon heating, the trappedheptanol evaporates, but water is not detected. This suggests that while persisting longerat elevated temperature, the water has completely evaporated before the temperaturerise.These results show that the capillary bridges, despite being formed of water with amuch lower boiling point than 1-heptanol, persist for long times during drying. While thecause for this delay should be determined, it does prove that even secondary fluids witha higher vapor pressure can persist in capillary suspension networks. The full potentialwill only be realized by replacing water with higher boiling point wetting liquids, suchas glycerol, to delay or even prevent bridge evaporation. The lower interfacial tension ofglycerol, however, tempers this potential. Thus, liquid combinations with high interfacialtension in addition to the desired high boiling point must be sought. One way of tailoringthe heptanol-water system used in this study is by adding salt to the water. Thisdecreases the vapor pressure and even increases the interfacial tension at the same time[59].The present research also points to a few unanswered questions. First, why a differ-ence between the evaporation dynamics is observed in the D O between 30 ° C and 40 ° C(Figure 6)? While the rate of the evaporation for the heptanol remains unchanged, theevaporation rate for the D O appears to be constant in time at the higher tempera-ture whereas it increases with time at the lowest temperature. We hypothesize that the22ifference may arise due to the small, but finite solubility of the D O in the heptanol.Thus, the change may be due to a varying miscibility of D O in heptanol. While theair-liquid interface at the surface may be depleted of D O at 30 ° C , the D O at theair-liquid interface is being constantly and more rapidly replenished from the bulk liquidat 40 ° C. This is caused by the larger solubility and thus concentration close to thecapillary bridges, leading to a larger gradient. Additionally, mass transport is increaseddue the higher temperature. The influence of particle size on the present results is alsoof interest. Previous research has shown that the yield stress depends on the reciprocalradius [60]. The structure of these systems, however, will differ networks created withlarger particles having a higher fractal dimension [44]. This also changes the averagesize of the flocs (relative to the particle size) and the strength of the inter-floc links. Theparticle size also has clear implication to the drying of these suspensions. The particlesize will change the capillary pressure (again, with a reciprocal dependence). Wouldthis change be balanced by the change in the yield stress? There is also a change inthe particle (or floc) mobility. Thus, the dependence of the particle size on the stressand structure of these drying capillary suspensions may be very interesting for furtherresearch.
In this paper, we investigated effects accompanying the drying of suspensions with andwithout capillary interactions. Enhancing a pure, oil-based suspension with only a fewdrops of water induces a network, transforming the suspension into an elastic paste.During drying, stresses caused by the capillary pressure within pores arise that are op-posed by the water bridges in the capillary suspensions. Therefore, we simultaneouslymeasured the evolving stresses and compared them with the drying rate. The capillarysuspensions exhibit a faster stress rise, an indication of more uniform drying, and havelower peak and residual stresses. The peak stress decreases with increasing amountsof water, such that films formed from capillary suspensions are less prone to cracking.Additionally, we found that drying into more humid air enhances the stress reduction,even for the pure suspension. An increased film porosity, caused by capillary suspen-sion networks, are only minor contributions to the observed stress reduction. Moreover,with reduced particle migration during drying, for example at higher initial solid loads,capillary suspensions show a greater potential. Lastly, we have shown that the capil-lary water bridges, despite having a lower bulk boiling point, persist into late stages ofdrying, after the heptanol has mostly evaporated. The partial evaporation of capillarybridges during drying is different at the two temperatures examined, which should beinvestigated further as well as the reason for the persistence of the bridges. Tuning thesuspension with a higher boiling point secondary liquid can further this potential. Insummary, the drying of capillary suspensions is a complex interplay between three phaseflow, interfacial tension, capillary pressure dependencies, vapor pressure and the result-ing yield strength. Understanding this interplay will help us tune the drying behaviorfor the desired applications. 23 cknowledgements
The authors would like to thank Almatis GmbH for the donation of alumina particles.Additionally, we thank Prof. Rob Ameloot and Dr. Min Tu for access and help withthe mass spectrometry measurements at the KU Leuven Centre for Membrane Sepa-rations, Adsorption, Catalysis, and Spectroscopy for Sustainable Solutions (cMACS),Belgium. Finally, we acknowledge financial support from the German Research Founda-tion, DFG under project number KO 4805/2-1 and the Research Foundation Flanders(FWO) Odysseus Program (grant agreement no. G0H9518N).
Conflicts of interest
The authors declare no conflicts of interests
References [1] L. Goehring, R. Conroy, A. Akhter, W. J. Clegg, A. F. Routh, Evolution of mud-crack patterns during repeated drying cycles, Soft Matter 6 (2010) 3562–3567.doi: .[2] D. Hotza, P. Greil, Review: Aqueous tape casting of ceramic powders, Materi-als Science and Engineering: A 202 (1995) 206–217. doi: .[3] D.-S. Tsai, Pressure buildup and internal stresses during binder burnout: Numericalanalysis, AIChE Journal 37 (1991) 547–554. doi: .[4] J. B¨ohnlein-Mauß, W. Sigmund, G. Wegner, W. H. Meyer, F. Heßel, K. Seitz,A. Roosen, The function of polymers in the tape casting of alumina, AdvancedMaterials 4 (1992) 73–81. doi: .[5] Z. Fu, A. Roosen, Shrinkage of tape cast products during binder burnout, Journalof the American Ceramic Society 98 (2015) 20–29.[6] A. Kamyshny, S. Magdassi, Conductive nanomaterials for printed electronics, Small10 (2014) 3515–3535. doi: .[7] S. E. Habas, H. A. S. Platt, M. F. A. M. van Hest, D. S. Ginley, Low-cost inorganicsolar cells: from ink to printed device, Chemical reviews 110 (2010) 6571–6594.doi: .[8] G. W. Scherer, Theory of drying, Journal of the American Ceramic Society 73(1990) 3–14. doi: .249] R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, T. A. Witten,Capillary flow as the cause of ring stains from dried liquid drops, Nature 389 (1997)827–829. doi: .[10] R. C. Chiu, M. J. Cima, Drying of granular ceramic films: Ii, drying stress andsaturation uniformity, Journal of the American Ceramic Society 76 (1993) 2769–2777. doi: .[11] J. J. Guo, J. A. Lewis, Aggregation effects on the compressive flow properties anddrying behavior of colloidal silica suspensions, Journal of the American CeramicSociety 82 (1999) 2345–2358. doi: .[12] D. M. Holmes, F. Tegeler, W. J. Clegg, Stresses and strains in colloidal filmsduring lateral drying, Journal of the European Ceramic Society 28 (2008) 1381–1387. doi: .[13] D. M. Holmes, R. Vasant Kumar, W. J. Clegg, Cracking during lateral drying ofalumina suspensions, Journal of the American Ceramic Society 89 (2006) 1908–1913. doi: .[14] Y. Ma, H. T. Davis, L. E. Scriven, Microstructure development in drying latexcoatings, Progress in Organic Coatings 52 (2005) 46–62. doi: .[15] A. F. Routh, W. B. Russel, Horizontal drying fronts during solvent evaporation fromlatex films, AIChE Journal 44 (1998) 2088–2098. doi: .[16] M. S. Tirumkudulu, W. B. Russel, Role of capillary stresses in film formation,Langmuir 20 (2004) 2947–2961. doi: .[17] S. B. Fischer, E. Koos, Using an added liquid to suppress drying defects in hardparticle coatings, Journal of Colloid and Interface Science 582 (2021) 1231–1242.doi: .[18] H. Lei, J. A. Payne, A. V. McCormick, L. F. Francis, W. W. Gerberich, L. E.Scriven, Stress development in drying coatings, Journal of Applied Polymer Science81 (2001) 1000–1013. doi: .[19] H. Lei, L. F. Francis, W. W. Gerberich, Le Scriven, Stress development in dryingcoatings after solidification, American Institute of Chemical Engineers. AIChEJournal 48 (2002) 437–451.[20] K. B. Singh, M. S. Tirumkudulu, Cracking in drying colloidal films, PhysicalReview Letters 98 (2007) 218302.[21] P. Wedin, C. J. Martinez, J. A. Lewis, J. Daicic, L. Bergstr¨om, Stress developmentduring drying of calcium carbonate suspensions containing carboxymethylcelluloseand latex particles, Journal of colloid and interface science 272 (2004) 1–9. doi: . 2522] E. Koos, N. Willenbacher, Capillary forces in suspension rheology, Science 331(2011) 897–900. doi: .[23] E. Koos, Capillary suspensions: Particle networks formed through the capillaryforce, Current Opinion in Colloid & Interface Science 19 (2014) 575–584. doi: .[24] J. Maurath, N. Willenbacher, 3d printing of open-porous cellular ceramics withhigh specific strength, Journal of the European Ceramic Society (2017). doi: .[25] M. Schneider, E. Koos, N. Willenbacher, Highly conductive, printable pastes fromcapillary suspensions, Scientific Reports 6 (2016) 31367. doi: .[26] C. Y¨uce, M. K¨onig, N. Willenbacher, Rheology and screen-printing performanceof model silver pastes for metallization of si-solar cells, Coatings 8 (2018) 406.doi: .[27] M. Weiß, J. Maurath, N. Willenbacher, E. Koos, Shrinkage and dimensional accu-racy of porous ceramics derived from capillary suspensions, Journal of the Euro-pean Ceramic Society 39 (2019) 1887–1892. doi: .[28] M. Schneider, J. Maurath, S. B. Fischer, M. Weiss, N. Willenbacher, E. Koos,Suppressing crack formation in particulate systems by utilizing capillary forces, ACSapplied materials & interfaces 9 (2017) 11095–11105. doi: .[29] J. A. Payne, A. V. McCormick, L. F. Francis, In situ stress measurement apparatusfor liquid applied coatings, Review of Scientific Instruments 68 (1997) 4564–4568.doi: .[30] S. Kim, J. H. Sung, K. H. Ahn, S. J. Lee, Drying of the silica/pva suspension: effectof suspension microstructure, Langmuir : the ACS journal of surfaces and colloids25 (2009) 6155–6161. doi: .[31] K. K. Price, Y. Wu, A. V. McCormick, L. F. Francis, G. Scherer, Stress developmentin hard particle coatings in the absence of lateral drying, Journal of the AmericanCeramic Society 98 (2015) 2214–2222. doi: .[32] A. F. Routh, Drying of thin colloidal films, Reports on progress in physics. PhysicalSociety (Great Britain) 76 (2013) 046603. doi: .[33] L. F. Francis, A. V. McCormick, D. M. Vaessen, J. A. Payne, Development andmeasurement of stress in polymer coatings, Journal of Materials Science 37 (2002)4717–4731. doi: .[34] C. J. Martinez, J. A. Lewis, Shape evolution and stress development dur-ing latex − silica film formation, Langmuir 18 (2002) 4689–4698. doi: . 2635] J. Kiennemann, T. Chartier, C. Pagnoux, J. F. Baumard, M. Huger, J. M.Lam´erant, Drying mechanisms and stress development in aqueous alumina tapecasting, Journal of the European Ceramic Society 25 (2005) 1551–1564. doi: .[36] Z. Fu, U. Eckstein, A. Dellert, A. Roosen, In situ study of mass loss, shrinkage andstress development during drying of cast colloidal films, Journal of the European Ce-ramic Society 35 (2015) 2883–2893. doi: .[37] E. Koos, W. Kannowade, N. Willenbacher, Restructuring and aging in a capillarysuspension, Rheologica Acta 53 (2014) 947–957. doi: .[38] G. G. Stoney, The tension of metallic films deposited by electrolysis, Proceedingsof the Royal Society of London. Series A, Containing Papers of a Mathematical andPhysical Character 82 (1909) 172–175. doi: .[39] G. Janssen, M. M. Abdalla, F. van Keulen, B. R. Pujada, B. van Venrooy, Cele-brating the 100th anniversary of the stoney equation for film stress: Developmentsfrom polycrystalline steel strips to single crystal silicon wafers, Thin Solid Films517 (2009) 1858–1867. doi: .[40] E. M. Corcoran, Determining stresses in organic coatings using plate beam deflec-tion, Journal of Paint Technology 41 (1969) 635–&.[41] L. Goehring, W. J. Clegg, A. F. Routh, Plasticity and fracture in drying colloidalfilms, Physical review letters 110 (2013) 024301. doi: .[42] O. Coussy, P. Dangla, T. Lassabat`ere, V. Baroghel-Bouny, The equivalent porepressure and the swelling and shrinkage of cement-based materials, Materials andStructures 37 (2004) 15–20. doi: .[43] A. Kharaghani, C. Kirsch, T. Metzger, E. Tsotsas, Micro-scale fluid model fordrying of highly porous particle aggregates, Computers & Chemical Engineering 52(2013) 46–54. doi: .[44] F. Bossler, J. Maurath, K. Dyhr, N. Willenbacher, E. Koos, Fractal approachesto characterize the structure of capillary suspensions using rheology and confocalmicroscopy, Journal of rheology 62 (2018) 183–196. doi: .[45] J. B. Laurindo, M. Prat, Numerical and experimental network study of evaporationin capillary porous media. drying rates, Chemical Engineering Science 53 (1998)2257–2269. doi: .[46] M. Prat, Pore network models of drying, contact angle, and film flows, ChemicalEngineering & Technology 34 (2011) 1029–1038. doi: .2747] M. J. Blunt, Flow in porous media — pore-network models and multiphase flow,Current Opinion in Colloid & Interface Science 6 (2001) 197–207. doi: .[48] A. Scanziani, K. Singh, T. Bultreys, B. Bijeljic, M. J. Blunt, In situ characterizationof immiscible three-phase flow at the pore scale for a water-wet carbonate rock, Ad-vances in Water Resources 121 (2018) 446–455. doi: .[49] A. Estrada-Baltazar, M. G. Bravo-Sanchez, G. A. Iglesias-Silva, J. F. J. Alvarado,E. O. Castrejon-Gonzalez, M. Ramos-Estrada, Densities and viscosities of binarymixtures of n-decane+1-pentanol, +1-hexanol, +1-heptanol at temperatures from293.15 to 363.15k and atmospheric pressure, Chinese Journal of Chemical Engi-neering 23 (2015) 559–571. doi: .[50] K. B. Singh, L. R. Bhosale, M. S. Tirumkudulu, Cracking in drying colloidal filmsof flocculated dispersions, Langmuir 25 (2009) 4284–4287. doi: .[51] L. A. Segura, P. G. Toledo, Pore-level modeling of isothermal drying of pore net-works, Chemical Engineering Journal 111 (2005) 237–252. doi: .[52] Joekar-Niasar, S. M. Hassanizadeh, Analysis of fundamentals of two-phase flowin porous media using dynamic pore-network models: A review, Critical Re-views in Environmental Science and Technology 42 (2012) 1895–1976. doi: .[53] R. T. Armstrong, M. L. Porter, D. Wildenschild, Linking pore-scale interfacial cur-vature to column-scale capillary pressure, Advances in Water Resources 46 (2012)55–62. doi: .[54] E. L. Davis, Effect of temperature and pore size on the hydraulic properties andflow of a hydrocarbon oil in the subsurface, Journal of Contaminant Hydrology 16(1994) 55–86. doi: .[55] H. Y. She, B. E. Sleep, The effect of temperature on capillary pressure-saturationrelationships for air-water and perchloroethylene-water systems, Water ResourcesResearch 34 (1998) 2587–2597. doi: .[56] W. Pietsch, H. Rumpf, Haftkraft, kapillardruck, fl¨ussigkeitsvolumen und gren-zwinkel einer fl¨ussigkeitsbr¨ucke zwischen zwei kugeln, Chemie Ingenieur Technik 39(1967) 885–893. doi: .[57] S. J. Heidlebaugh, T. Domenech, S. V. Iasella, S. S. Velankar, Aggregation and sepa-ration in ternary particle/oil/water systems with fully wettable particles, Langmuir30 (2014) 63–74. doi: .2858] J. Dittmann, E. Koos, N. Willenbacher, Ceramic capillary suspensions: Novel pro-cessing route for macroporous ceramic materials, Journal of the American CeramicSociety 96 (2013) 391–397. doi: .[59] C. Zhang, P. Carloni, Salt effects on water/hydrophobic liquid interfaces: a molecu-lar dynamics study, Journal of physics. Condensed matter : an Institute of Physicsjournal 24 (2012) 124109. doi: .[60] E. Koos, J. Johannsmeier, L. Schwebler, N. Willenbacher, Tuning suspensionrheology using capillary forces, Soft Matter 8 (2012) 6620–6628. doi:10.1039/C2SM25681A