Electrostatic precipitation of exhaled particles for tensiometric examination of pulmonary surfactant
Andrey Shmyrov, Alexey Mizev, Irina Mizeva, Anastasia Shmyrova
11 2 a r X i v : . [ q - b i o . T O ] A p r lectrostatic precipitation of exhaled particles fortensiometric examination of pulmonary surfactant Andrey Shmyrov, Alexey Mizev, Irina Mizeva and Anastasia ShmyrovaApril 6, 2020
Abstract
Objective:
Collecting exhaled particles that represent smalldroplets of the alveolar lining fluid shows great promise as atool for pulmonary surfactant (PS) sampling. For this purpose,we present a setup consisting of two modules, namely, a modulefor droplet collecting, called an electrostatic aerosol trapping(ESAT) system, and a measurement module for studying PSproperties. We suggest the way how to extract numerical valuesfrom the experimental data associated with PS properties.
Methods:
The operating principle of ESAT is based on theelectrostatic precipitation of exhaled particles. The native ma-terial was collected directly on the water surface, where an ac-cumulated adsorbed film of PS was examined with tensiometricmethod. The modified capillary waves method adapted to studysmall volume samples was utilized. The efficiency of the setupwas verified in the experiments with healthy subjects.
Conclusion:
The accumulation of PS components on the wa-ter surface in an amount sufficient for tensiometric study wasreported. It was shown how to extract the numerical valuesfrom the experimental data characterizing PS properties.
Significance:
The idea underlying the new concept used inthis study may give impetus to further development of point-of-care facilities for collecting PS samples and for their expressanalysis.
Human breathing is accompanied by the formation of small droplets of the alve-olar lining fluid (ALF), which are emitted from the lungs with exhaled air in ∗ This study was supported Russian Foundation for Basic Research under project No. 17-41-590095. † A. Shmyrov, A. Mizev, I. Mizeva and A. Shmyrova are with the Institute of ContinuousMedia Mechanics, Perm, Russia (correspondence e-mail: [email protected]).
The schematic diagram of the ESAT system is shown in Fig.1. The exhaled airmoves through a silicone tube of 1.2 cm inner diameter. A thin stainless steel4eedle with 20 µ m tip is installed along the centerline of the tube just beforeits outlet in such a way that the needle tip is 0.5 cm below the tube edge. Theneedle is connected to a negative electrode of the high voltage power supply ,which results in inducing a corona discharge ionizing the air molecules near theneedle tip. The aerosol droplets emerged from the tube collide with the ionizedair molecules, thus becoming electrically charged, and then they are transportedby the electrostatic force toward the grounded collecting electrode . The latteris placed at the bottom of the cylindrical glass cuvette of 1.6 cm in diameterand 0.05 cm in depth. Before each experiment the cuvette was thoroughlycleaned and filled with high purity water up to its edge. The electrode is a thinstainless tube (the outer diameter is 0.07 cm) connected to a syringe to varythe water volume in the cuvette (with accuracy 0.1 µ L), which compensatesthe volume loss of the water due to evaporation. The droplets moving towardthe collecting electrode coalesce with the water surface and accumulate therein the form of an adsorbed film. Further, the surface-active properties of thefilm were investigated by the tensiometric method. The ESAT system wasisolated from the environment by a cylindrical plastic box , which preventedcontamination of a sample. The box has a hole for the air outlet.Figure 1: Scheme of the ESAT system (left panel) and an overview of thecuvette (right panel). Numbers indicate parts of the setup: - silicone tube, - thin stainless steel needle, - high voltage power supply , - groundedcollecting electrode, - cylindrical glass cuvette, - syringe, - water surface, - cylindrical plastic box, - hole for the air outlet.The efficiency of droplet trapping by the ESAT system may depend on thepotential difference between the electrodes, interelectrode distance, number andgeometry of the electrodes, and the air flow rate. To optimize the configurationof the ESAT system and to find the regime with maximal trapping efficiency,additional experiments with a model aerosol were performed.5 .2 Optimization of the ESAT system in the experimentswith a model aerosol The model aerosol was generated by the nebulizer (Omron-NE-U17, OMRONCorporation, Japan) which produced the droplets with a mass median diam-eter of 4.4 µ m at a nebulization rate up to 3 mL/min. The peristaltic pump(see Fig. 2) pushed the constant air flow through the nebulizer container. Theconcentrated air-droplet mixture, coming from the nebulizer container, was sup-plied through a T-joint into a silicone tube, where it was mixed with the airflux, forming thus the model aerosol, which entered the ESAT system. Theconstant air flow rate was provided by the compressed air cylinder connectedto the silicone tube through a pressure reducer. Such design allowed us to varyseparately the aerosol concentration and its flow rate through the ESAT systemby changing the nebulizing rate and the rate of the air flow from the compressedair cylinder. To prevent contamination of the model aerosol from the outsideenvironment, the air, coming from the peristaltic pump and the compressed aircylinder, was infiltrated with HEPA filters.Figure 2: Scheme of the experimental setup used for optimization of the ESATparameters using the model aerosol.A 10%-by-mass aqueous solution of sodium chloride was used to produce amodel aerosol. The saline solution allows us to perform accurate control overthe amount of trapped droplets by measuring the conductivity of water in thecuvette. The cuvette, used in the experiments with the model aerosol, differs ina depth (being 50 mm deep) from that for the exhaled aerosol.For conductivity measurements, the sensor of the conductometer (LR01V,WTW, Germany), having the measuring range 0.001-200 µ S/cm, was placedin the water sample after each experiment. During the collecting procedure,the sensor was taken out and the grounded electrode was put inside the waterthrough the bottom so that its tip was approximately 1 mm below the liquidsurface.As a measure of the effectiveness of the ESAT system, the ratio of the salinemass m tr , trapped in the cuvette, and its total mass m tot , delivered to the air6ow from a nebulizer during the collecting procedure, was used K = m tr m tot · m tot was defined as m tot = M t , where t is the experiment durationand M is the saline mass rate which depends on both the nebulizer capacityand the flow rate provided by the peristaltic pump. The M values were pre-liminary measured for each regime by means of weighing the nebulizer reservoirbefore and after a longtime experiment. The saline mass m tr , trapped in the cu-vette during the experiment, was calculated from the measured values of waterconductivity obtained at the end of each experiment.The experimental procedure was as follows. The cuvette was filled with purewater and the conductivity was measured to check the purity of the trappingsystem. The grounded electrode was set into the water. The nebulizer, theperistaltic pump and the air delivery from the compressed air cylinder wereswitched on. After the aerosol filled completely the tube from T-joint to ESAT,the high voltage power supply was switched on. From this moment the experi-ment duration time was counted. Upon completion of the trapping procedure,the high voltage power supply was switched off, the aerosol delivery was stoppedand the grounded electrode was taken out of the cuvette. After that the liq-uid in the cuvette was mixed by a magnetic stirrer for 2 minutes, and then itsconductivity and temperature were measured. Each experiment was repeated 5times to estimate an experimental error. During the experiments we had beenmeasuring the aerosol trapping effectiveness depending on the system configu-ration, namely, on the distance D between the tube edge and the liquid surface,the air flow rate Q , the saline mass flow M produced by a nebulizer and thepotential difference U between the electrodes. The variations of the parame-ters were made relative to the so called base configuration which was as follow: D = 4 . cm , Q = 0 . L/s , M = 250 µg/s , U = 5 . kV .First, we found that the droplet trapping is extremely inefficient withoutuse of the electric field. In the base configuration and at U = 0 kV , the effec-tiveness was only K = (0 . ± . . kV raises the effectiveness to the order up to 0 . U = 20 kV , itbecomes already K = 2 . D up to 2 cmincreases the effectiveness twice. Further reduction of the distance results instrong perturbations of the water surface with the air jet which may lead tosplashing the water out of the cuvette even at low air flow rates. The flow ratevariation has the most profound effect on the efficiency. The reduction of this7arameter from 0 . L/s to 0 . L/s increases K from 0 .
5% to 5 . M = 25 µg/s had no effect on theeffectiveness of the ESAT system. In our opinion, this fact offers the possibil-ity of extending the results obtained with the model aerosol to the case of theexhaled aerosol where the mass flow is still four orders of magnitude lower.Thus, the optimal set of parameters obtained in the experiments with themodel aerosol is as follows: D = 2 . cm , Q = 0 . L/s , U = 20 . kV . The effec-tiveness of the ESAT system was found to be near 30% under these conditions,and it may increase still more at lower values of the air flow rate. However,the maintenance of such low exhalation rate is complicated for a subject andreduces significantly the exhaled particle concentration [2]. On the other hand,use of the flow rate of 1 . L/s , corresponding to normal breathing, leads to aconsiderable reduction of the trapping effectiveness. To handle this problem,an intermediate flexible reservoir was installed into the setup construction (seeFig. 2 and Fig. 3).A subject makes a normal breathing into this reservoir through automatic2-way valve. When an exhalation is finished the exhaled air is pressed out witha slow flow rate into ESAT tract by applying a load to the reservoir. The use ofthe additional reservoir for intermediate storage has certain disadvantage. Someof the particles are inevitably lost due to settling on the walls of the reservoir,which decreases the effectiveness of the trapping process. Nevertheless, the gainin effectiveness caused by the reduction of the air flow rate turns out to be higher.The experiments with the model aerosol have shown that the use of reservoirreduces the effectiveness three times, whereas the decrease of the air flow ratefrom 1 . L/s to 0 . L/s increases the effectiveness twenty times. Finally, thefollowing set of parameters was selected for further experiments with exhaledair: D = 2 . cm , Q = 0 . L/s (here, Q is the air flow rate provided taking intoaccount the application of the intermediate reservoir), U = 20 . kV . Underthese conditions, the effectiveness was about 10%. The setup for trapping native aerosol particles from exhaled air is presentedin Fig. 3. The design of the collecting module is similar to that used in theexperiments with the model aerosol. After the cuvette in the ESAT system(position A in Fig. 3) was filled with water and the high voltage power supply wasswitched on, a subject made one full expiration at the flow rate approximately1 . L/s through the tube (see Fig. 3). To avoid any contamination of theinhaled air from the environment, the subject inhaled filtered, particle-free roomair through a filter. The exhaled air came through the automatic 2-way valve into the intermediate storage reservoir . After the exhalation was finished,the air was pressed out from the reservoir into the ESAT tract with the slowflow rate of 0 . L/s . When the air completely came out from the reservoir, thesubject made next expiration.After the required number of exhalations was made, the high voltage powersupply was switched off, and the cuvette was shifted to position B (see Fig. 3)8igure 3: Scheme of a setup for collecting and analyzing the exhaled particles.The collecting module includes: - subject, - silicone tube, - reservoir, - automatic 2-way valve, - high voltage power supply, - cuvette. Themeasurement module includes: - syringe, - speaker, - laser, - referenceglass plate, - video camera. A and B are the positions of the cuvette duringthe collecting and measuring procedures, respectively.so that the water surface containing a collected material can be analyzed usinga capillary waves method. We used the modified version of the capillary waves method which was describedin detail in Ref. [38]. The capillary wave was excited by periodical pressurepulsations in the gas phase near the interface. For this purpose, the acousticwave generated by the miniature speaker , connected to the AC generator, wasdirected to the water surface through the thin steel tube (0 . cm in diameterand 2 . cm length) used as a waveguide. The face of the tube was parallel tothe liquid surface and situated at a distance of 0 . cm . The frequency rangewas from 0.5 to 2.5 kHz.Optical interferometry was used to register the interface relief. On the con-trary to the optical scheme described in [38], we applied the Michelson schemewhich is more suitable in the considered case. The interference pattern resultingfrom the addition of two collimated laser beams reflected from the surface ofthe liquid and the reference glass plate was observed using a video camera (TXG50, Baumer, Germany). The view field of the camera is 2 cm, andthe matrix resolution is 2500 × µ m/pixel. The reference plate and the unperturbed liquid interface form theangle of approximately 30 (cid:48) , which allows us to observe the interface deforma-tion in the interference fringes of constant thickness. This approach makes itpossible to apply the spatial phase shifting technique for precise reconstructionof the interface relief. 9 .5 Data processing Each interferogram were processed in three steps. First, a 3D interface profilewas reconstructed from the interferogram by means of the spatial phase shiftingmethod using the IntelliWave (ESDI, USA) software. From the 3D profile, wefiltered only deformations associated with small-scale capillary waves, as it wasdescribed in detail in [38]. The profile thus obtained was approximated by thedamped cylindrical wave equation: z ( (cid:126)r ) = A (cid:112) | (cid:126)r | e − β | (cid:126)r | (cid:60) (cid:16) e − i ( ωt − (cid:126)k(cid:126)r ) (cid:17) + z , (1)where A is the wave amplitude, ω = 2 πν is the excitation frequency, t isthe time, (cid:126)r is the radius vector from the point of wave excitation, (cid:126)k is the wavevector, and β is the attenuation coefficient. This model well describes a capillarywave away from the source (beyond about three wavelengths) with an accuracyof 0 . σ and the attenuation coefficient β ,calculated as described in Ref. [38], were used to characterize the properties ofthe adsorbed film occurring on the water surface during the trapping of exhaledparticles. Typical capillary wave profiles observed at the pure water surface (Fig. 4 a) andat the water surface obtained after 14 (Fig. 4 b) and 40 (Fig. 4 c) exhalations ofa subject are presented in Fig. 4. The form of the wave changes as the numberof exhalations increases. The changes become more evident from the analysisof the vertical cross sections of presented profiles (Fig. 4 d). The reduction ofthe wavelength and, consequently, the surface tension, as far as an increase inthe attenuation coefficient, clearly indicate the accumulation of surface-activesubstances on the water surface. It is evident that these substances, constituentto the PS complex, accumulate on the water surface during the trapping process.To make sure that the collected material comes to the water surface from theexhaled air rather than from the environment, we performed some additionalexperiments. In the first experiment, we used the filtered air coming to theESAT system instead of the exhaled air. The water surface in the cuvetteremained clean even after 20 min of the experiment. In the second test, we alsoused the filtered air instead of the exhaled air, but additionally we removed theplastic box covering the ESAT system. A noticeable reduction in the surfacetension was found already in 3 minutes, which indicates pollution of the watersurface with some inclusions trapped from the surrounding air by an electrostaticfield. These tests show that the covering plastic box safely protects the ESATsystem from outward contamination.Figure 5 illustrates the dependence of the surface pressure Π on the numberof exhalations obtained at three different values of potential difference. The10igure 4: 3D profiles of the capillary waves observed at pure water (a) and thewater surface obtained after 14 (b) and 40 (c) exhalations of the subject. (d) -vertical cross sections of the profiles (a), (b) and (c).surface pressure was defined as Π = σ − σ (here σ and σ is the surface tensionof a clean water surface and the water surface containing an adsorbed film,respectively); it is equal to zero at clean interface.The growth of the surface pressure is clear evidence of the accumulation ofthe surface-active substances contained in the exhaled particles on the free watersurface. Under the assumption that approximately the same amount of thenative material comes with every exhalation, the plot in Fig. 5 may be consideredas the dependence of the surface pressure Π on the surface concentration Γ ofthe surfactant adsorbed at the water surface, which is called the surface pressureisotherm.The form of the curves presented in Fig. 5 is typical for the isotherm of anysurfactant. At the initial segment of the curve, when the surface concentration islow, the surfactant molecules are in gaseous phase state and, therefore, interactweakly. As the surface concentration increases, the surface pressure in suchrarefied layer grows slowly and only slightly differs from zero. At higher surface11 ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ●● ● ● ● ● ● ● ● ● ● ● ▲▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ Π , d y n / c m Figure 5: Variation of the surface pressure Π with the number of exhalationsfor different voltage on the electrodes 1 - 8 kV, 2 - 10 kV, 3 - 15 kV.concentration, when the molecules begin to interact, the film is in a liquid-expanded phase state, which is characterized by a higher growth rate of surfacepressure as the surfactant content at the interface increases. The form of theΠ(Γ) curve is a unique characteristic of any surfactant. Three curves in Fig. 5plotted for different values of the potential difference between the electrodes inthe ESAT system are similar because they reflect accumulation of the same PSbut at different rate.In contrast to the experiments with the model aerosol, we have found thenonmonotonic dependence of the efficiency of the trapping process on the volt-age applied. At values below 15 kV, the surface pressure, measured on thewater surface after a fixed number of exhalations, grows almost linearly as thepotential difference increases (see Fig. 5). However, further increase of the volt-age up to 17 kV leads to unexpected result, namely, we found that the surfacepressure remains equal to zero after any quantity of exhalations. Moreover, thenative material, collected ,e.g., at 15 kV, disappears from the interface in a fewseconds after we increase the potential difference to 17 kV. In our opinion, thisphenomenon can be caused by ozone production in the corona discharge at highenough voltage. The characteristic smell of this substance begins to be felt atvoltages above 15 kV. Being strong oxidizer, ozone breaks the organic moleculesthat are constituents of the PS complex, cleaning thus the water surface. Takingthis fact into account, the maximal value of the potential difference, used in thefurther experiments, did not exceed 13 kV.12 ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ●● ● ● ● ● ● ● ● ● ● ● ▲▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ Π , d y n / c m Figure 6: Variation of the surface pressure Π with a number of exhalations.To check the possibility of producing the PS saturated monolayer and toestimate an absolute amount of the collecting material, we examined the Πvariations during the long-term collection. To this end, we made measurementsafter every ten-twenty exhalations. The results of this experiment are presentedin Fig. 6. It is seen that the Π does not reach saturation, continuing to growaccording to logarithmic law (see inset in Fig. 6) even after three hundred ex-halations.For most surfactants, the surface concentration value at which the phasetransition occurs in the film from the gas to the liquid-expanded state is Γ / Γ e =(0 . − . e is the surface concentration in a saturated film. Takinginto account the fact that in our experiments the phase transition in the ad-sorbed film is observed near the fifteenth exhalation (at 15 kV ), one can expectthe saturation starting with approximately 40-60 th exhalations. The resultspresented in Fig. 6 show the surface pressure increases slower compared to theexpected value, which indicates that the ESAT system effectiveness decreasesduring the collection procedure. On the contrary, this was not observed in theexperiments with the model aerosol, in which the efficiency remained constantover time. It is obvious that this should be somehow related to the propertiesof the material being collected.In our opinion, the most probable cause of a reduction in the trapping ef-ficiency is a deterioration of coalescence conditions due to the formation of anadsorbed film. The PS which covers both particle and water surfaces preventstheir approaching at the distance at which coalescence occurs. Moreover, this13ffect reinforces as the surfactant accumulates. A similar situation is knownto arise in emulsions, the stability of which against aggregation is achieved byforming a surfactant film on the droplet surface.For the correct analysis of the PS surface properties, it is necessary to inves-tigate the relationship between the surface pressure and the surfactant surfaceconcentration Γ, which should be obtained from the analysis of the dependenceof Π on the number of exhalations (see, e.g., Fig. 6). However, as the quantityof the collected material is nonlinearly related to the amount of exhaled airpassed through the system, this procedure is not evident. In addition, it is notconvenient for the subject to be interrupted for periodic measurements duringthe collection process. Therefore, we changed the sequence of actions to solvethe above problems.Initially, the material is accumulated on the water surface during the se-quential 50 exhalations of the subject. Further, the work is done by an operatorin the absence of a subject. The operator inserts the cuvette into the partof the experimental setup where the capillary wave technique is realized andthen measures the wavelength and the attenuation coefficient of the wave at3-5 frequencies. After that, the operator removes some amount of an adsorbedsubstance from the surface using a sampler. The sampler is a thin-walled metaltube with an inner diameter of 2.0 mm, the inner and outer surfaces of whichare coated with an anti-wetting agent. A small lenticular drop of liquid coatedwith a surfactant remains on the tip of the sampler after each touching, re-ducing thereby the surface concentration of the surfactant in the cuvette. Inour experiments, the ratio of the surface area of the droplet to be removed andthe water surface in the cell was such that half of the adsorbed material wasremoved after 25 touches of the sampler. The wave profiles were measured aftereach change in the surface concentration.The surface pressure calculated using the wavelength measurements and theattenuation coefficient of the capillary wave are presented in Fig. 7. Note thatboth values were determined for each surface concentration obtained by themethod described above. The surface concentration was measured in relativeunits Γ / Γ ∗ , being normalized to the value of the surface concentration Γ ∗ atwhich a phase transition in the surfactant film from the gaseous phase state tothe liquid-expanded state was observed. The attenuation coefficient is measuredas β − β , where β is the attenuation coefficient taken at Γ = 0, i.e. on the freesurface of water, and occurred due to the volumetric viscosity of water.A comparison of the two dependencies shows that the attenuation coefficientis more sensitive to the presence of the collected material on the surface. Thisparameter begins to increase noticeably already at small values of the surfaceconcentration, whereas the surface pressure begins to increase only after thetransition of the adsorbed layer into a liquid-expanded state. It is worth notingthat, in contrast to the Π(Γ) dependence, the β (Γ) one is nonmonotic andexhibits a maximum associated with resonance effects. The excitation of acapillary wave on the water surface containing a surfactant is accompanied bythe appearance of a dilatation wave associated with stretching and compressionof the surfactant film. This additional dissipative mechanism amplifies wave14ttenuation. It is known that the local maximum of the attenuation coefficientof the capillary wave is observed when its frequency coincides with the naturalfrequency of the dilatation wave [39]. Varying the capillary wave frequency(see Fig. 7) causes the local maximum of this dependence to shift because thenatural frequency of the dilatation wave is the function of the surface surfactantconcentration. In this paper we demonstrate the possibility of using electrostatic forces to trapaerosol particles containing in the exhaled air on a gas-liquid surface. The PScomponents containing in the particles accumulate on the liquid surface in theform of an adsorbed film, the surface-active and rheological properties of whichcan be investigated by the tensiometric method. The high efficiency of theESAT system proposed in this paper, as well as the small liquid surface arearequired for the implementation of the modified method of capillary waves, makeit possible to collect native material in an amount sufficient for tensiometricstudy during only 30-50 exhalations of the subject. The modified capillary wavesmethod allows studying the dependence of the surface pressure and attenuationcoefficient on the relative surface concentration of PS. The shape of both curvesdepends on the composition of the adsorbed layer and is its unique characteristic.PS is a complex of a few surface-active substances and each componentmakes its own contribution to the surface properties of the adsorbed layer [22,23, 24, 25, 26]. Variations in the components ratio or their quantity causedby the presence of a pulmonary disease are able to vary the shape of bothΠ(Γ) and β (Γ) dependencies, which can be used as the markers of a PS systemdysfunction. For comparative analysis of PS samples in healthy subjects andpatients with pulmonary diseases, the following quantitative characteristics canbe utilized:1. Γ total which indicates the surface concentration (expressed in relativeunits) achieved after completion of the total number of exhalations and can beapplied to assess the PS concentration in exhaled air.2. d Π /d Γ which is measured at Γ >
1, i.e., on the part of the Π (Γ) curvewhere the adsorbed film is in the liquid-expanded phase state. This value reflectsthe surface activity of PS, i.e., it shows how quickly the surface tension decreaseswith increasing surface concentration.3. β max and Γ max which are the coordinates of the extremum on the β (Γ)curve.4. β (Γ = 1) which denotes the value of the attenuation coefficient at thephase transition point.5. d Γ max /dν and dβ max /dν which reflect the shift of the extremum positionwith changing the frequency of the wave excitation.The key feature of the proposed facility is the ability of point of care test-ing PS functional state. The sample of PS can be nonivasively collected andimmediately examined. In some groups of subjects, such elder people, children,15atients with distress syndrome this method can be the only alternative to col-lect lung native material. Moreover, there is a possibility to connect the ESATsystem to a artificial lungs ventilation machine to control PS state even in in-tensive care. Both modules of the complex, ESAT and measurment part, canbe fully automatized. References [1] K. Haslbeck, K. Schwarz, J. M. Hohlfeld, J. R. Seume, and W. Koch, “Sub-micron droplet formation in the human lung,”
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Γ Γ Π , d y n c m Γ T o t a l Γ ◆ ◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆ ●●●●●●●●●●●●●●●●●●●●● ■■■■■■■■■■■■■■■■■■■■■■■■ ▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲ ■■▲▲●●◆◆ Γ Γ β - β , / c m Figure 7: Upper panel - dependence of the surface pressure Π on the surfactantconcentration Γ / Γ ∗ . Lower panel - dependence of β − β on Γ / Γ ∗ for differentfrequencies of wave excitation - 2.5 kHz, - 2 kHz, - 1 kHz, - 0.7 kHz.Red dash-dotted line indicates Γ ∗ at which a phase transition in the surfactantfilm from the gaseous phase state to the liquid-expanded state was observed.Black dashed line denotes Γ totaltotal