David J. Fairhurst

Drying and deposition of poly(ethylene oxide) droplets determined by Péclet number

We report results of a detailed experimental investigation into the drying of sessile droplets of aqueous poly(ethylene oxide) (PEO) polymer solutions under various experimental conditions. Samples are prepared with a range of initial concentrations c0 and are filtered to remove traces of undissolved PEO clusters. In typical experiments, droplets with initial volumes between 5 μL and 50 μL are left to evaporate while temperature and relative humidity are monitored. Droplets either form a disk-like solid “puddle” or a tall conical “pillar”. The droplet mass is monitored using a microbalance and the droplet profile is recorded regularly using a digital camera. Subsequent processing of the data allows values of droplet volume V, surface area A, base radius R, contact angle θ and height h to be determined throughout drying. From these data we identify four stages during pillar formation: pinned drying; pseudo-dewetting; bootstrap building; solid contraction and propose physical models to explain key aspects of each stage and to predict the transition from each stage to the next. The experimental parameters of relative humidity, temperature, pressure, droplet volume and initial contact angle are all systematically varied and observed to influence the drying process and consequently whether the droplet forms a pillar or a puddle. We combine these parameters into a dimensionless Peclet number Pe, which compares the relative effects of evaporation and diffusion, and show that the drying behaviour is only dependent on c0 and Pe.

Imaging internal flows in a drying sessile polymer dispersion drop using Spectral Radar Optical Coherence Tomography (SR-OCT)

In this work, we present the visualization of the internal flows in a drying sessile polymer dispersion drop on hydrophilic and hydrophobic surfaces with Spectral Radar Optical Coherence Tomography (SR-OCT). We have found that surface features such as the initial contact angle and pinning of the contact line, play a crucial role on the flow direction and final shape of the dried drop. Moreover, imaging through selection of vertical slices using optical coherence tomography offers a feasible alternative compared to imaging through selection of narrow horizontal slices using confocal microscopy for turbid, barely transparent fluids.

Three-dimensional structure and growth of myelins

After contact with water, surfactant lamellar phases (L(α)) can show spectacular interface instabilities: multibilayer tubules, so-called myelins, grow from the L(α)/water interface into the water. We have studied the shape, size, and growth of myelins in aqueous solutions of the nonionic surfactant C(12)E(3) (triethylene glycol monododecyl ether) during dissolution. We used a combination of different imaging techniques: optical microscopy providing 2-D projections of the sample and confocal microscopy offering a complete 3-D reconstruction. These techniques provide quantitative information on the shape and growth of myelins, such as their width, length, and depth profile as a function of time. The growth rate of myelins, characterized by a swelling or diffusion coefficient, was found to increase with surfactant mass fraction and, seemingly, with sample thickness. We demonstrate that myelin creaming due to buoyancy can explain the apparent dependence on sample thickness. Our experiments furthermore suggest that myelin growth is controlled by an interplay between the water mobility in the lamellar phase and the osmotic pressure difference between the lamellar phase and the contacting water.

Flexible conformable hydrophobized surfaces for turbulent flow drag reduction

In recent years extensive work has been focused onto using superhydrophobic surfaces for drag reduction applications. Superhydrophobic surfaces retain a gas layer, called a plastron, when submerged underwater in the Cassie-Baxter state with water in contact with the tops of surface roughness features. In this state the plastron allows slip to occur across the surface which results in a drag reduction. In this work we report flexible and relatively large area superhydrophobic surfaces produced using two different methods: Large roughness features were created by electrodeposition on copper meshes; Small roughness features were created by embedding carbon nanoparticles (soot) into Polydimethylsiloxane (PDMS). Both samples were made into cylinders with a diameter under 12 mm. To characterize the samples, scanning electron microscope (SEM) images and confocal microscope images were taken. The confocal microscope images were taken with each sample submerged in water to show the extent of the plastron. The hydrophobized electrodeposited copper mesh cylinders showed drag reductions of up to 32% when comparing the superhydrophobic state with a wetted out state. The soot covered cylinders achieved a 30% drag reduction when comparing the superhydrophobic state to a plain cylinder. These results were obtained for turbulent flows with Reynolds numbers 10,000 to 32,500.

Robust spatially resolved pressure measurements using MRI with novel buoyant advection-free preparations of stable microbubbles in polysaccharide gels

MRI of fluids containing lipid coated microbubbles has been shown to be an effective tool for measuring the local fluid pressure. However, the intrinsically buoyant nature of these microbubbles precludes lengthy measurements due to their vertical migration under gravity and pressure-induced coalescence. A novel preparation is presented which is shown to minimize both these effects for at least 25 min. By using a 2% polysaccharide gel base with a small concentration of glycerol and 1,2-distearoyl-sn-glycero-3-phosphocholine coated gas microbubbles, MR measurements are made for pressures between 0.95 and 1.44 bar. The signal drifts due to migration and amalgamation are shown to be minimized for such an experiment whilst yielding very high NMR sensitivities up to 38% signal change per bar.

Investigation of the drag reducing effect of hydrophobized sand on cylinders

Superhydrophobic surfaces show strong potential for drag reducing applications. If such a surface supports a Cassie–Baxter state with low solid surface fraction and when immersed it retains a plastron air layer, large slip can occur across its surface as well as a consequent reduction in drag. In this work we report a facile method for creating hydrophobic cylinders and hydrophobic flat surfaces with varying surface roughness able to support a Cassie–Baxter state. Cylinders of 12 mm diameter were coated in hydrophobized sand with grain sizes in the ranges of 50–100, 212–300, 425–600 and 600–710 µm to produce the varying degrees of roughness. A laser Doppler anemometer was used to measure the velocity profile of the water across their wake in a large water circulating flow chamber. The hydrophobic cylinders in the Cassie–Baxter state show drag reductions of up to 28% compared to the same sample in the Wenzel state for flows with Reynolds numbers of 10 000 to 40 000. These drag reduction results, in combination with confocal microscopy images of the plastron air layer and feature height, show that the thickness of the plastron and the protrusion height of the features combine to give a drag reduction or drag increase depending on the ratio of the two.

Controlling and characterising the deposits from polymer droplets containing microparticles and salt

Abstract.A coffee ring-stain is left behind when droplets containing a wide range of different suspended particles evaporate, caused by a pinned contact line generating a strong outwards capillary flow. Conversely, in the very peculiar case of evaporating droplets of poly(ethylene oxide) solutions, tall pillars are deposited in the centre of the droplet following a boot-strapping process in which the contact line recedes quickly, driven by a constricting collar of polymer crystallisation: no other polymer has been reported to produce these central pillars. Here we map out the phase behaviour seen when the specific pillar-forming polymer is combined with spherical microparticles, illustrating a range of final deposit shapes, including the standard particle ring-stain, polymer pillars and also flat deposits. The topologies of the deposits are measured using profile images and stylus profilometery, and characterised using the skewness of the profile as a simple analytic method for quantifying the shapes: pillars produce positive skew, flat deposits have zero skew and ring-stains have a negative value. We also demonstrate that pillar formation is even more effectively disrupted using potassium sulphate salt solutions, which change the water from a good solvent to a theta-point solvent, consequently reducing the size and configuration of the polymer coils. This inhibits polymer crystallisation, interfering with the bootstrap process and ultimately prevents pillars from forming. Again, the deposit shapes are quantified using the skew parameter.Graphical abstract

Swelling and shrinking kinetics of a lamellar gel phase

We investigate the swelling and shrinking of Lβ lamellar gel phases composed of surfactant and fatty alcohol after contact with aqueous poly(ethyleneglycol) solutions. The height change Δh(t) is diffusionlike with a swelling coefficient S: Δh=St. On increasing polymer concentration, we observe sequentially slower swelling, absence of swelling, and finally shrinking of the lamellar phase. This behavior is summarized in a nonequilibrium diagram and the composition dependence of S quantitatively described by a generic model. We find a diffusion coefficient, the only free parameter, consistent with previous measurements.

Phase equilibria of polydisperse colloids

A set of colloidal particles (be they sterically or charge-stabilized) can never be made truly identical. They are polydisperse in their sizes (or charges), and their interactions are a function of that property. A truly polydisperse system, in the thermodynamic limit, contains infinitely many species. Therefore, calculations of phase equilibria involve infinitely many coexistence constraints (a difficulty not encountered when determining single-phase properties such as structure factors). This hampers the mathematics, and typically engenders arbitrary, uncontrolled approximations and cumbersome, system-specific results. We construct a formalism which is equally applicable to monodisperse and polydisperse systems, and use it to define a controlled expansion for slightly polydisperse colloids (i.e. those with a narrow size/charge distribution). Thus we provide a complete description of their phase equilibria. The resulting universal law of fractionation is surprisingly concise. For quantitative comparison with a real system, we have performed measurements on a colloid-polymer mixture, using both light scattering and extensive counting of transmission electron micrographs to obtain particle size distributions in coexisting phases.

Droplets of ionic solutions

Of all the types of liquid droplets, ionic solutions are probably the most abundant: soluble salts are present all over Earth as well as on other planets, so they appear in any naturally occurring droplets. One of the most visually arresting consequences of droplets is the rainbow, the angular size of which is altered by the presence of dissolved salts. Similar optical effects on Venus caused by aerosol droplets have been analyzed to determine the composition of our neighboring planet’s atmosphere. On Earth, aerosols containing salt constitute a large fraction of the atmosphere, influence the greenhouse effect, and have an important role in determining global climate. When aerosols dry, either in the atmosphere or in industrial applications such as spray drying, various particle morphologies are observed, determined by the solute and the drying conditions. On the ground, evaporating saltwater droplets can damage rocks, although the extent of the damage depends subtly on the dissolved species and its crystallization morphology and wettability. When deposited on an inert substrate, electrolyte droplets exhibit interesting behaviors: evaporation-induced crystallization can be used to grow metastable crystal polymorphs, and drying droplets will “creep” across surfaces and even out of containers, escaping the constraints of the initial droplet.