Solutal Marangoni Effect Research Articles

Dynamics of a falling film with solutal Marangoni effect

We investigate the dynamics of a thin liquid film on an inclined planar substrate in the presence of an insoluble surfactant on its free surface. We consider both the linear and nonlinear regimes. The linear regime is examined through the Orr-Sommerfeld eigenvalue problem of the full Navier-Stokes and concentration equations and wall and free-surface boundary conditions. The nonlinear regime is investigated through two different models. The first one is obtained from the classical long-wave expansion and the second one through an integral-boundary-layer approximation combined with a simple Galerkin projection. Although accurate close to the instability threshold, the first model fails to describe the dynamics of the system far from criticality. On the other hand, the second model not only captures accurately the behavior close to the instability threshold, but is also valid far from criticality. Analytical and numerical results on the role of the surfactant on the free-surface dynamics are presented. In the linear regime, the Marangoni stresses induced by the surfactant reduce the domain of instability for the base flow. In the nonlinear regime, the system evolves into solitary pulses for both the free surface and surfactant concentration. The amplitude and velocity of these pulses decrease as the Marangoni effect becomes stronger.

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.

Characterization of Marangoni effect in non-isothermal falling liquid films of binary mixtures

The flow characteristics and heat transfer were investigated for the liquid films of water, ethanol aqueous solution, glycerol aqueous solution and aqueous Na 2SO 4 solution. By using a sensitive thermal imaging system, the temperature and liquid distributions of the film could be carefully studied to reveal the influence of Marangoni effect on the heat transfer and flow of the binary mixture films. Since the surface tension gradient and surface tension counteracted on the film, a surface tension factor was presented to describe the surface tension effect in the films and help designing the experiments. It was concluded to be the thermal Marangoni effect that caused the cooled films expanded and the heated films contracted. A novel expansion was found for the heated ethanol aqueous film, due to the concentration variation and so-caused solutal Marangoni flow that overcame the thermal Marangoni flow in the lateral direction of the film. Theoretical analysis also indicated that the solutal Marangoni effect was more effective than the thermal Marangoni effect. Furthermore, viscosity has a complex influence on the Marangoni flow. Larger viscosity generally caused greater temperature gradient, and thus enhanced surface tension gradient (Marangoni flow), meanwhile, all the liquid flow (including Marangoni flow) were retarded due to the more significant viscous resistance.

Marangoni effect of cracked liquid film of an aqueous electrolyte flowing over a vertical heated plate

An experimental investigation was performed on Marangoni effect of cracked liquid film of aqueous Na2SO4 flowing over a vertical heated plate by using a sensitive infrared imaging technique. The results show that the thermal and solutal Marangoni effects, which result from the non-uniform distributions of surface temperature and concentration of the film, respectively, occur in the streamwise and transverse directions of the film, generating different influences on the film heat transfer. Taking account of the Marangoni number (Ma) and the solution concentration (c 0), a correlation of the Nusselt number (Nu) for the cracked liquid film is proposed.

Self-assembly and characterization of Marangoni microfluidic actuators

We present a no moving parts fluidic actuator based on a solutal Marangoni effect which propels fluid in toroidal patterns. We show how to position the actuators at prescribed substrate locations by self-assembly and present experimental observations of the actuators in operation. We demonstrate how the actuators can be used to extend the range of capillary forces acting on a collection of submerged microfabricated parts leading to their self-assembly into larger structures. With one collection of microparts, a 250 µm radius actuator induced flow velocities of 5 mm s−1 in a water–ethanol solution. To explain and perform the predictive design of the actuators, we have developed a finite element model and obtained a good qualitative agreement with experimental observations. We calculated maximum non-dimensional velocities for Marangoni numbers (Ma) between 150 and 100 000, and found the velocities to follow a Ma0.695 power law, independent of Pr numbers between 530 and 1680. Both results agree with previous studies. These calculations allowed surface tension gradients in a particular experiment to be quantified, which led to the conclusion that the Marangoni actuators were equivalent to a 200 °C cm−1 thermocapillary effect operating at room temperature.

Change in the Mode of Spontaneous Motion of an Alcohol Droplet Caused by a Temperature Change

An alcohol (pentanol) droplet exhibits spontaneous motion on an aqueous solution, driven by a solutal Marangoni effect. We found that the mode of such droplet motion changes depending on the temperature of the aqueous phase. When the temperature of the aqueous phase is 20 °C, a droplet with a volume of 1 µl exhibits vectorial motion, whereas when the temperature is 25 °C, the droplet exhibits irregular motion. We discuss the mode change in relation to the solubility of pentanol in water.

Mode selection in the spontaneous motion of an alcohol droplet

An alcohol (pentanol) droplet exhibits spontaneous motion on an aqueous solution, driven by a solutal Marangoni effect. We found that the droplets mode of motion is controlled by its volume. A droplet with a volume of less than 0.1 microl shows irregular translational motion, whereas intermediate-sized droplets of 0.1-200 microl show vectorial motion. When the volume is above 300 microl, the droplet splits into smaller drops. These experimental results regarding mode selection are interpreted in terms of the wave-number selection depending on the droplet volume.

On Marangoni convective patterns driven by an exothermic chemical reaction in two-layer systems

This article is devoted to the investigation of Marangoni-driven pattern formation at the interface between two immiscible fluids filling a Hele-Shaw cell, each of them containing a reactant of an exothermic neutralization reaction. In such a system, convective patterns arise when one reactant diffuses through the interface to react with the other chemical species in one of the fluids. A chemo-hydrodynamical pattern appears due to Marangoni instabilities taking place because of heat and solutal driven changes of the surface tension. The mathematical model we develop consists in a set of reaction-diffusion-advection equations ruling the evolution of concentrations and temperature coupled to Navier–Stokes equation, written in a Hele-Shaw approximation. In our analysis, the time-dependent convectionless reaction-diffusion base state is first obtained and studied in detail. Next, we perform a linear stability analysis of this base state with regard to thermal and solutal Marangoni effects to determine the parameter values beyond which convection occurs. Finally, we perform numerical simulations of the fully nonlinear system and study the influence of the different parameters on pattern formation.

Thermal Marangoni Effects on Gas Bubbles Are Generally Accompanied by Solutal Marangoni Effects

The thermal Marangoni force on a bubble, as originally predicted and experimentally verified by Young et al., has been measured by at least three later investigators. In each of the later cases, the measurements were complicated by oscillations in the size of the bubbles, which produced vertical oscillatory motion of the bubble in the combined thermal and gravitational fields. The authors ascribed this motion to the variable solubility of air in the working liquid as the bubble moved in the temperature gradient. It is pointed out here that this variable solubility implies a second, solutal Marangoni effect, which reduces the thermal forces. Since the solubilities of all gases are a function of temperature, solutal forces will generally accompany thermal forces on gas bubbles.

Effect of surface tension on convection in a binary fluid layer under a zero gravity environment

The Marangoni flows in a horizontal layer of a binary mixture with an undeformable free upper surface are studied analytically and numerically. The system is heated and cooled by constant heat fluxes. The surface tension is assumed to vary linearly with temperature and solute concentration. Both double diffusive convection and Soret induced convection, in a zero gravity level, are considered. The governing parameters of the problem are the thermal Marangoni number Ma T, the solutal Marangoni number Ma S, the Prandtl and the Lewis numbers Pr and Le, the aspect ratio A and the parameter a defining the mechanism responsible for the occurrence of the solutal gradients (double diffusion or Soret effect). An approximate analytical solution, based on the parallel flow approximation, is proposed. Bifurcation diagrams are presented for the cases in which the solutal Marangoni effect acts in the same direction or competes with the thermal Marangoni effect. The stability of the parallel flow solution is studied numerically and the threshold for Hopf bifurcation determined. The validity of the analytical model is tested against the results obtained by solving numerically the full governing equations.

Marangoni and Stability Studies on Fiber-Supported Methanol Droplets Evaporating in Reduced Gravity

Support fibers are commonly employed in microgravity droplet evaporation and combustion studies. and it is of interest to develop models of fiber-supported droplets. In this paper, a numerical study of the Marangoni forces on a methanol droplet supported by a fiber has been carried out for an evaporating methanol droplet in both dry air and humid air environments, with the focus being the development of instabilities that form early in the lifetime of a droplet. The thermal Marangoni effect has a stabilizing effect, and it is always driving the droplet surface toward an isothermal condition. The solutal Marangoni effect (from water absorption) is much larger in magnitude, and it tends to concentrate water on the surface. This tendency to concentrate water leads to surface waves and instabilities, which are relieved by diffusion of the water into the droplet interior. For large droplets (initial radii of 0.5 mm) the surface forces have generated liquid Reynolds numbers greater than one hundred, Smaller droplets (initial radii of 0.005 mm) give qualitatively similar results, however the Reynolds numbers are reduced by size and diffusion damping influences. The numerical simulations are sensitive to droplet and supporting fiber size, and it appears that experimental verification and comprehensive numerical studies should be fully three-dimensional. It also appears that the solutal Marangoni flows are unstable to very small wavelengths, as has been suggested by previous linearized stability analyses.

Spreading and Instabilities Induced by a Solutal Marangoni Effect

We study the spreading of liquid films driven by surface tension gradients induced by evaporation from a two-component mixture. The films climb from a macroscopic reservoir on a plane tilted surface and their length L is found to depend linearly on the square root of time t: L(t) = (Dt)0.5. We develop a semiquantitative analysis that shows which parameters control the value of D for ideal mixtures and for nonideal ones. We report also experimental results about the time evolution and the spatiotemporal behavior of the interfacial instability that develops at the meniscus between the reservoir and the film. Results agree well with previous experimental and theoretical studies.

Nonlinear instabilities of falling films on a heated vertical plane with gas absorption

AbstractThe nonlinear instability and dynamics of nonisothermal falling films with simultaneous absorption from a gas phase are studied theoretically. The study is based on a long wave analysis of equations of motion, energy and mass. The resulting long wave evolution equation describing the film thickness is solved by a Fourier collocation technique. The effects and interactions of flows resulting from gravity, surface tension, thermocapillarity and solutal Marangoni effect are elucidated by considering the following cases: (1) isothermal film; (2) nonisothermal film with purely conductive heat transfer, as well as combined conductive and convective heat transfer; and (3) nonisothermal film with solute absorption. Conditions are identified for equilibration of the wave, wave breaking and for the formation of dry spots. Also, phase diagrams representing the stable and unstable regions are presented for the above cases.

Marangoni instability of bi-component droplet gasification

Simplified analyses using a linear stability approach are developed to predict influences of thermal and solutal Marangoni effects on hydrodynamic stability of bi-component droplets evaporating in a spherically-symmetrical manner in hot environments. It is predicted that with zeotropic mixtures and for ∂σ/∂T<0 and ∂σ/∂y<0 (where σ is surface tension, T temperature, and y the surface mass fraction of the more volatile droplet component), the thermal and solutal Marangoni effects oppose each other in that the thermal effect is stabilizing and the concentration effect is destabilizing. The model is applied to alkane/alkane and alcohol/water mixture droplets. The alkane mixture droplets were predicted to be hydrodynamically stable. For alcohol/water mixtures, the results suggest that critical radii for marginal stability exist; when a droplet is initially pure methanol which subsequently absorbs water from the ambient, the critical radius is predicted to depend upon the relative humidity of the environment.

Solutal Marangoni effect: I. Pure interfacial transfer

The motion of a nitroethane lens located at the surface of an aqueous solution of dodecyltrimethylammonium bromide is analyzed. This motion is generated by a solutal Marangoni effect, or soluto—capillary instability, induced by the transfer of the surfactant from one phase to the second one, both solvents being mutually saturated; its quasi-periodic character is demonstrated by a statistical and spectral analysis, and its characteristics, amplitude, and frequency are discussed as a function of the physicochemical conditions. The enhancement of the interfacial transfer by the Marangoni effect is evaluated. It is shown that none of the available models of linear stability analysis can account for the present results.