Effect of nonionic surfactant on wetting behavior of an evaporating drop under a reduced pressure environment

The evaporation of sessile drops at reduced pressure is investigated. The evaporation of water droplets on aluminum and PTFE surfaces at reduced pressure was compared. It was found that water droplets on an aluminum surface exhibit a 'depinning jump' at subatmospheric pressures. This is when a pinned droplet suddenly depins, with an increase in contact angle and a simultaneous decrease in the base width. The evaporation of sessile water droplets with a nonionic surfactant (Triton X-100) added to an aluminum surface was then studied. The initial contact angle exhibited a minimum at 0.001 wt% Triton X-100. A maximum in the evaporation rate was also observed at the same concentration. Droplets with low surfactant concentrations are found to exhibit the 'depinning jump.' It is thought that the local concentration of the surfactant causes a gradient of surface tension. The balance at the contact angle is dictated by complex phenomena, including surfactant diffusion and adsorption processes at interfaces. Due to the strong evaporation near the triple line, an accumulation of the surfactant will lead to a surface tension gradient along the interface. The gradient of surface tension will influence the wetting behavior (Marangoni effect). At low surfactant concentrations the contact line depins under the strong effect of surface tension gradient that develops spontaneously over the droplet interface due to surfactant accumulation near the triple line. The maximum evaporation rate corresponds to a minimum contact angle for a pinned droplet.     

Evaporation and Marangoni driven convection in small heated water droplets

Evaporation dynamics of small sessile water droplets under microgravity conditions is investigated numerically. The water-air interface is free, and the surrounding air is assumed to be quasisteady. The droplet is described by Navier-Stokes and heat equations and its surrounding water/air gaseous phase with Laplace equation. In the thermodynamic conditions of the simulations presented herein, the evaporative mass flow is nonlinear. It shows a minimum that indicates the existence of qualitative changes in the evaporative regimes although the droplet is sessile. Due to temperature gradients on the free interface, Marangoni motion occurs and generates inside the droplet convection cells that furthermore exhibit small fluctuating motion as evaporation goes on.     

Evaporation of two solution droplets and a droplet located near a flat liquid surface

The mutual influence of two moderate-sized droplets of a dilute nonvolatile substance solution on the processes of their evaporation or condensation is theoretically analyzed under the assumption of a uniform concentration distribution inside the droplets. The conditions for the applicability of this approach are revealed. The evaporation or condensation of a droplet near a flat liquid surface is considered as a limiting case. The fluxes of water molecules to and from the surface of aqueous glycerol solution droplets occurring in air are numerically estimated depending on the droplet radii, distances between their surfaces, and air humidity. Analogous estimates are obtained for an aqueous glycerol solution droplet growing near a flat water surface.     

Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet

We study the effects of Marangoni stresses on the flow in an evaporating sessile droplet, by extending a lubrication analysis and a finite element solution of the flow field in a drying droplet, developed earlier. The temperature distribution within the droplet is obtained from a solution of Laplace's equation, where quasi-steadiness and neglect of convection terms in the heat equation can be justified for small, slowly evaporating droplets. The evaporation flux and temperature profiles along the droplet surface are approximated by simple analytical forms and used as boundary conditions to obtain an axisymmetric analytical flow field from the lubrication theory for relatively flat droplets. A finite element algorithm is also developed to solve simultaneously the vapor concentration, and the thermal and flow fields in the droplet, which shows that the lubrication solution with the Marangoni stress is accurate for contact angles as high as 40 degrees. From our analysis, we find that surfactant contamination, at a surface concentration as small as 300 molecules/microm(2), can almost entirely suppress the Marangoni flow in the evaporating droplet.     

Internal flow in polymer solution droplets deposited on a lyophobic surface during a receding process

When a polymer solution droplet is deposited on a lyophobic surface, the contact line is moved back to some degree and subsequently pinned. An experimental setup is constructed to investigate not only the receding process but also an internal flow of polystyrene-acetophenone and -anisole solutions. As a result, the time variation of the evaporation rate per unit area during receding does not strongly depend on the initial solute concentration. The average solute concentration at the pinning of the contact line increases as the initial solute concentration increases. A convective circulation flow that is upward at the axis of symmetry is observed. This flow pattern is different from those of pure liquids such as water, acetone, benzene, and so forth, which have been previously reported. Furthermore, the observed flow is enhanced as the initial solute concentration increases, contrary to an increase in the fluid viscosity. To resolve these discrepancies, the mechanism of the flow is numerically investigated using a hemispherical droplet model considering the density and surface tension distributions. The numerical results demonstrate that the circulation flow that is experimentally observed is actually caused. It is also found that the solutal Rayleigh effect initially induces the internal flow, and subsequently the solutal Marangoni effect dominates the flow. Both effects are enhanced as the initial concentration increases because of the evaporative mass balance at the free surface.     

Evaporation of water droplets on polymer surfaces

The evaporation of water droplets on polymer surfaces was investigated by using a digital image analysis technique. There were three distinct stages in the water evaporation process: a constant contact area mode, a constant contact angle mode, and a mixed mode that is independent of both the initial quantity of water droplets and the hydrophobic properties of the polymer surfaces. The physical factors influencing the first and second transitions in the evaporation process were found to be the attainment of the receding angle on the polymer surfaces and the Marangoni instability in the evaporating water droplets, which result from the concentration gradient of contaminants. This study also provides qualitative information about the microfluid flows inside the evaporating water droplets and the morphology of drying stains on polymer surfaces. The contaminants were found to be concentrated at the perimeter of the stains, in agreement with the observed outward microfluid flow in the mixed mode of the evaporation process.     

Flow development at the surfaces of bubbles and droplets in gradient solutions of a surfase-active liquid

The development of solutocapillary flows at the surfaces of air bubbles and chlorobenzene droplets was experimentally studied in nonuniform aqueous solutions of ethanol and isopropanol, which have a low surface tension and, hence, exhibit surface-active properties with respect to water. The experiments demonstrated the retardation of the onset of the development of the Marangoni concentration-induced convection relative to the moment of the contact between an inflowing surfactant (alcohol) and the surface. The critical concentration gradients (the Marangoni diffusion numbers) necessary for the initiation of mass transfer of a liquid along the interface were determined as dependent on the rate of inflow of a tongue of a more concentrated solution and the initial alcohol concentration around the bubble.     

Marangoni effect reverses coffee-ring depositions

We show here both experimentally and theoretically that the formation of "coffee-ring" deposits observed at the edge of drying water droplets requires not only a pinned contact line but also suppression of Marangoni flow. For simple organic fluids, deposition actually occurs preferentially at the center of the droplet, due to a recirculatory flow driven by surface-tension gradients produced by the latent heat of evaporation. The manipulation of this Marangoni flow in a drying droplet should allow one in principle to control and redirect evaporation-driven deposition and assembly of colloids and other materials.     

On the effect of marangoni flow on evaporation rates of heated water drops

In this letter we show that the Marangoni flow contribution to the evaporation rate of small heated water droplets resting on hot substrates is negligible. We compare data of evaporating droplet experiments with numerical results and assess the effect of Marangoni flow and its contribution to the evaporation process. We demonstrate that heat conduction inside these water droplets is sufficient to give an accurate estimate of evaporation rates. Although convection in evaporating water droplets remains an open problem, our aim in this study is to demonstrate that these effects can be neglected in the investigation of evaporation rate evaluation. It is worth noting that the presented results apply to volatile heated drops which might differ from spontaneously evaporating cases.     

Dependence of the structure of ring-shaped deposits resulting from evaporation of dispersion droplets on initial contact angle

Experiments have been performed on the formation of ding-shaped deposits upon the evaporation of dispersion droplets on different substrates accompanied by the coffee ring effect. The main attention has been focused on studying the structure of a formed deposit as depending on the initial contact angle of a droplet. It has been established that the deposit structure may vary from ring-shaped to disc-shaped with a decrease in the contact angle. For certain systems, as the initial contact angle is varied, the scenario of droplet evaporation may change and, in some cases, acquire a combined character. Before the onset of pinning, menisci of droplets that are evaporated on modified polymer substrates may initially move not only toward the droplet center, but also in the opposite direction.     

A novel method to quantify the amount of surfactant at the oil/water interface and to determine total interfacial area of emulsions

We present a methodology to quantitatively determine the fraction of sodium dodecyl sulfate (SDS) that partitions to the oil/water interface in oil-in-water macroemulsions and calculate the total interfacial area (TIA) through the novel use of filtration through nanoporous membranes. Ultrafiltration was carried out in centrifuge tubes having nanoporous filters with a 30,000 molecular weight cutoff (MWCO), so that emulsion droplets would not pass through, and only SDS (as monomers and micelles) that is in the bulk water phase (i.e., not at the interface) could pass through. The concentration of SDS in the filtrate was determined and used to calculate the TIA for each system. The mean droplet diameter of the emulsions was measured by light scattering. We analyzed the effects of total SDS concentration and oil chain length on the amount of SDS that partitions to the interface, the TIA, and the droplet diameter. The results showed that partitioning of SDS to the oil/water interface increases with increasing total SDS concentration in emulsion systems (i.e., the more SDS we add to the bulk solution, the more SDS partitions to the oil/water interface). However, the surface-to-bulk partition coefficient (i.e., the SDS concentration at the interface divided by the SDS concentration in the aqueous phase) remains the same over the entire concentration range (8-200 mM). The results showed a chain-length compatibility effect in that the minimum amount of SDS partitioned to the interface for C(12) oil. The droplet size measurements revealed a maximum size of droplets for C(12) oil. Penetration of oil molecules into SDS film at the interface has been proposed to account for the maximum droplet size and minimum partitioning of SDS at the oil/water interface for C(12) oil+SDS emulsion system. The TIA, as determined from our ultrafiltration method, was consistently two orders of magnitude greater than that calculated from the droplet size measured by light scattering. Possible explanations for this disparity are discussed.     

Surfactant-induced Marangoni eddies alter the coffee-rings of evaporating colloidal drops

The influence of the small ionic surfactant sodium dodecyl sulfate (SDS) on the evaporation of drying colloidal droplets is quantitatively investigated. The addition of SDS leads to a significantly more uniform deposition of colloidal particles after evaporation (i.e., the so-called "coffee-ring effect" is dramatically altered). We understand this phenomenon in the context of circulating radial Marangoni flows induced by the variation of SDS concentration along the air-water interface. Video microscopy permits the direct visualization of the colloidal particles involved in these flows, revealing a surprisingly stable "Marangoni eddy" that prevents particle deposition at the drop perimeter.     

Monitoring entering and spreading of emulsion droplets at an expanding air/water interface: a novel technique

The entering and spreading of emulsion droplets at quiescent and expanding air/water interfaces was studied using a new apparatus consisting of a modified Langmuir trough in which the air/water interface can be continuously expanded by means of rollers in the place of traditional barriers. When sodium caseinate and whey protein isolate-stabilized emulsion droplets were injected under the surface of sodium caseinate and whey protein isolate solutions, respectively, it appeared that the droplets entered the air/water interface only if the air/water surface pressure did not exceed a threshold value of approximately 15 mN/m. This condition was satisfied either under quiescent conditions for low protein concentrations or by continuous expansion of the interface at higher protein concentrations. According to equilibrium thermodynamics, entering of the droplets and the formation of lenses should occur for all the systems investigated, but this was not observed. At surface pressures higher than approximately 15 mN/m, immersed emulsion droplets were metastable. This is probably due to a kinetic barrier caused by the formation of a thin water film bounded by protein adsorption layers between the emulsion droplet and the air/water interface.     

Fast evaporation of spreading droplets of colloidal suspensions

When a coffee droplet dries on a countertop, a dark ring of coffee solute is left behind, a phenomenon often referred to as the coffee-ring effect. A closely related yet less-well-explored phenomenon is the formation of a layer of particles, or skin, at the surface of the droplet during drying. In this work, we explore the behavior of a mathematical model that can qualitatively describe both phenomena. We consider a thin axisymmetric droplet of a colloidal suspension on a horizontal substrate undergoing spreading and evaporation. In contrast to prior work, precursor films (rather than pinned contact lines) are present at the droplet edge, and evaporation is assumed to be limited by how quickly molecules can transfer out of the liquid phase (rather than by how quickly they can diffuse through the gas phase). The lubrication approximation is applied to simplify the mass and momentum conservation equations, and the colloidal particles are allowed to influence the droplet rheology through their effect on the viscosity. By describing the transport of the colloidal particles with the full convection-diffusion equation, we are able to capture depthwise gradients in particle concentration and thus describe skin formation, a feature neglected in prior models of droplet evaporation. The highly coupled model equations are solved for a range of problem parameters using a finite-difference scheme based on a moving overset grid. The presence of evaporation and a large particle Peclet number leads to the accumulation of particles at the liquid-air interface. Whereas capillarity creates a flow that drives particles to the droplet edge to produce a coffee ring, Marangoni flows can compete with this and promote skin formation. Increases in viscosity due to particle concentration slow down droplet dynamics and can lead to a reduction in the spreading rate.     

Analysis of droplet evaporation on a superhydrophobic surface

The evaporation process for small, 1-2-mm-diameter droplets of water from patterned polymer surfaces is followed and characterized. The surfaces consist of circular pillars (5-15 microm diameter) of SU-8 photoresist arranged in square lattice patterns such that the center-to-center separation between pillars is 20-30 microm. These types of surface provide superhydrophobic systems with theoretical initial Cassie-Baxter contact angles for water droplets of up to 140-167 degrees, which are significantly larger than can be achieved by smooth hydrophobic surfaces. Experiments show that on these SU-8 textured surfaces water droplets initially evaporate in a pinned contact line mode, before the contact line recedes in a stepwise fashion jumping from pillar to pillar. Provided the droplets of water are deposited without too much pressure from the needle, the initial state appears to correspond to a Cassie-Baxter one with the droplet sitting upon the tops of the pillars. In some cases, but not all, a collapse of the droplet into the pillar structure occurs abruptly. For these collapsed droplets, further evaporation occurs with a completely pinned contact area consistent with a Wenzel-type state. It is shown that a simple quantitative analysis based on the diffusion of water vapor into the surrounding atmosphere can be performed, and estimates of the product of the diffusion coefficient and the concentration difference (saturation minus ambient) are obtained.     

Elucidating the relationship between the spreading coefficient, surface-mediated partial coalescence and the whipping time of artificial cream

We studied the whipping of artificial creams composed of a blend of sunflower oil and hydrogenated palm fat stabilized by protein or a mixture or protein and low molecular weight (lmw) surfactant. It was found that an increased whipping speed, decreased protein concentration, and the addition of lmw surfactant leads to shorter whipping times. Further, shorter whipping times were observed for WPI-stabilized cream compared to cream stabilized by sodium caseinate. In all cases, the decrease in whipping time was due to a decrease in the length of the second stage of whipping, the stage characterized by the adhesion of fat droplets to the air bubble surface. The decrease in whipping time could be accounted for by considering the influence of the experimental variables on the fraction of bubble surface area at which fat droplet spreading is possible. The same changes in parameters that promote droplet spreading at the air/water interface cause a decrease in the whipping time of our model creams. Correlating the whipping time of cream with the spreading behavior of fat droplets at the air/water interface represents a new insight into the mechanisms involved in the whipping of cream.     

Airborne virus transmission via respiratory droplets: Effects of droplet evaporation and sedimentation

Airborne transmission is considered as an important route for the spread of infectious diseases, such as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), and is primarily determined by the droplet sedimentation time, that is, the time droplets spend in air before reaching the ground. Evaporation increases the sedimentation time by reducing the droplet mass. In fact, small droplets can, depending on their solute content, almost completely evaporate during their descent to the ground and remain airborne as so-called droplet nuclei for a long time. Considering that viruses possibly remain infectious in aerosols for hours, droplet nuclei formation can substantially increase the infectious viral air load. Accordingly, the physical-chemical factors that control droplet evaporation and sedimentation times and play important roles in determining the infection risk from airborne respiratory droplets are reviewed in this article.     

凹槽状PDMS基底上水滴的挥发及Cassie-Wenzel转变行为

通过在线跟踪水滴在凹槽状聚二甲基硅氧烷(PDMS)基底上的挥发行为, 研究了蒸馏水的挥发规律Cassie-Wenzel转变行为. 结果表明, 初始阶段, 水滴处于Cassie状态, 且在垂直于凹槽方向(V)和平行于凹槽方向(P)上存在显著的各向异性. 水滴的挥发过程依次表现出接触直径不变模式、 接触角不变模式及共同减小模式, 与平滑基底上水滴的挥发规律类似. 在挥发过程中, 发生了Cassie-Wenzel转变, 转变发生的时间与PDMS基底上突起部分的面积分数(即固相率)呈现良好的线性关系. 随着挥发的进行, 水滴的各向异性在接触角不变模式阶段消失, 即挥发导致水滴从开始的椭球缺状变为球缺状.     

Investigation of the interactions in emulsions stabilized by a polymeric surfactant and its mixtures with an anionic surfactant

 The interaction of a nonionic polymeric surfactant with an anionic surfactant at the oil–water interface has been studied by its effects on the droplet size, stability and rheology of emulsions. Oil-in-water (o/w) emulsions were prepared using isoparaffinic oil and mixtures of a nonionic polymeric surfactant with an anionic surfactant. The macro-molecular surfactant was a graft copolymer with a backbone of polymethyl methacrylate and grafted polyethylene oxide (a graft copolymer with PEO chains of MW=750). The anionic surfactant was sodium dodecyl sulfate (SDS). The stabiliza-tion of the emulsion droplets was found to be different when using one or the other surfactant. The mechanism of stabilization of emulsion droplets by the macro-molecular surfactant is of the steric type while the stabilization by anionic surfactant is of the electrostatic repulsion type. Emulsions stabilized with mixtures present both types of stabilization. Other effects on the preparation and stabilization of emulsions were found to be dependent on properties associated with the surfactant molecular weight such as the Marangoni effect and Gibbs elasticity. The initial droplet size of the emulsions showed a synergistic effect of the surfactant combination, showing a minimum for the mixtures compared to the pure components. Emulsion stability also shows a synergistic interaction of both surfactants. Rheological measurements allow for the estimation of the interparticle interaction when measured as a function of volume fraction. Most of the effects observed can be attributed to the differences in interfacial tension and droplet radius produced by both surfactants and their mixtures. The elastic moduli are well explained on the basis of droplet deformation. Ionic versus steric stabilization produce little difference in the observed rheology, the only important differences observed concerned the extent of the linear viscoelasticity region. Received: 22 November 1996 Accepted: 24 March 1997     

The role of the surfactant head group in the emulsification process: binary (nonionic-ionic) surfactant mixtures

Dilute emulsions of dodecane in water were prepared under constant flow rate conditions with binary surfactant systems. The droplet size distribution was measured as a function of the mixed surfactant composition in solution. The systems studied were (a) the mixture of anionic sodium dodecyl sulfate (SDS) with nonionic hexa(ethyleneglycol) mono n-dodecylether (C12E6) and (b) the mixture of cationic dodecyl pyridinium chloride (DPC) with C12E6. At a constant concentration of SDS or DPC surfactant in solution (below the CMC) the mean emulsion droplet size decreases with the increase in the amount of C12E6 added to the solution. However, a sharp break of this droplet size occurs at a critical concentration and beyond this point the mean droplet size did not significantly change upon further increase of the C12E6. This point was found to corresponded to the CMC of the mixed surfactant systems (as previously determined from microcalorimetry measurements) and this result suggested the mixed adsorption layer on the emulsion droplet was similar to the surfactant composition on the mixed micelles. The emulsion droplet size as a function of composition at the interface was also studied. The mean emulsion droplet size in SDS-C12E6 solution was found to be lower than that in DPC-C12E6 system at the equivalent mole fraction of ionic surfactant at interface. This was explained by the stronger interactions between sulphate and polyoxyethylene head groups at the interface, which facilitate the droplet break-up. Counterion binding parameter (beta) was also determined from zeta-potential of dodecane droplets under the same conditions and it was found that (beta) was independent of the type of the head group and the mole fraction of ionic surfactant at interface.