Pendant drop tensiometry enhanced by video-image digitization is shown to be a useful tool for the experimental measurement of the relaxation in interfacial tension due to the adsorption of surfactant at a fluid interface. Using this method, profiles of the relaxation in surface tension of a diffusion-controlled, nonionic polyethoxy surfactant were measured. A diffusion coefficient was computed by comparing these profiles with numerical solutions of the bulk surfactant diffusion equation and a Frumkin equilibrium adsorption isotherm. This comparison was made for the entire relaxation period. This method establishes a more reproducible diffusion coefficient than current techniques that utilize only the short-or long-time parts of the relaxation spectrum. In addition, lower bounds on the kinetic constants for the sorption process are inferred for the polyethoxy surfactant used by comparing numerical solutions of mixed diffusion and surface kinetic transfer with the diffusion-limited result.

Self-propelled, chemically powered colloidal locomotors are swimmers designed to transverse small scale landscapes in a range of applications involving micropumping, sensing, and cargo transport. Although applications can require precise navigation and onboard steering mechanisms, here we examine by calculation how locomotors through their hydrodynamic interaction can navigate along a boundary. We adopt an engine model consisting of a spherical Janus colloid coated with a symmetrical catalyst cap, which converts fuel into a product solute. The solute is repelled from the colloid through a repulsive interaction, which occurs over a distance much smaller than the swimmer radius. Within this thin interaction layer, a concentration difference develops along the surface, which generates a pressure gradient as pressure balances the interaction force of the solute with the surface. The pressure gradient drives a slip flow towards the high concentration, which propels the particle oppositely, away from product accumulation (self-diffusiophoresis). To study boundary guidance, the motion near an infinite no-slip planar wall that does not adsorb solute is obtained by analytical solution of the solute conservation and the Stokes equations using bispherical coordinates. Several regimes of boundary interaction unfold: When the colloid is oriented with its cap axisymmetrically facing the wall, it is repelled by the accumulation of solute in the gap between the swimmer and the wall. With the cap opposite to the wall, the swimmer moves towards the wall by the repulsion from the solute accumulating on the cap side, but very large caps accumulate solute in the gap, and the motor stops. For oblique approach with the cap opposite to the wall and small cap sizes, the swimmer is driven to the wall by accumulation on the cap side, but rotates as it approaches the wall, and eventually scatters as the cap reorients and faces the wall. For a swimmer approaching obliquely with a larger cap (again facing away from the wall), boundary navigation results as the accumulation of product in the gap suppresses rotation and provides a normal force, which directs the swimmer to skim along the surface at a fixed distance and orientation or to become stationary. We also demonstrate how gravity can force transitions between skimming and stationary states.

The relaxation in surface tension due to the adsorption of bulk-soluble, unbranched, long chain surfactants with small polar groups at the air-water interface is often characterized by an initial induction period in which the surface tension relaxes very slowly. In this study, the origin of this induction in the surface tension relaxation is attributed to intermolecular cohesive forces among the adsorbed surfactant molecules which develop as the surface coverage increases. Surfactant molecules with long, slender hydrocarbon chains and small polar groups are subject to strong, attractive van der Waals forces when surface crowding causes interchain contact. Two models are constructed to account for this cohesion. In the first, intermolecular attraction leads to the formation of a liquid phase from a gaseous state. The induction period arises as the liquid state is forming, and addition of further molecules by diffusion is not accompanied by a change in the surface pressure. In the second model, the intermolecular attraction causes a cooperative adsorption as the activation energy for desorption increases faster with surface coverage than for adsorption. The induction period arises as the presence of cohesion lowers the surface pressure, offsetting the effect of the large increase in surface concentration due to the cooperative adsorption. Equations of state and adsorption isotherms necessary to describe this cooperative adsorption/ phase transition behavior are developed, and theoretical solutions of the diffusion limited mass transfer to a fresh surface coupled with these isotherms are presented. Experimental verification of these ideas is obtained by studying the adsorption of aqueous solutions of l-decanol at the air-water interface. Surface tension relaxation profiles for l-decanol are obtained by using pendant bubble tensiometry enhanced by video digitization, and these profiles compare favorably with the numerical solutions obtained by using the developed models.

In this paper the weakly nonlinear stability of two-phase core-annular film flows in the limit of small film thickness and in the presence of both viscosity stratification and interfacial tension is examined. Rational asymptotic expansions are used to derive some novel nonlinear evolution equations for the interface between the phases. The novel feature of the equations is that they include a coupling between core and film dynamics thus enabling a study of its effect on the nonlinear evolution of the interface. The nonlinear interfacial evolution is governed by modified Kuramoto–Sivashinsky equations in the cases of slow and moderate flow [the former also developed by Frenkel, Sixth Symposium on Energy Engineering Sciences (Argonne Lab. Pub. CONF-8805106, 1988), p.100, using different asymptotic methods], which include new nonlocal terms that reflect core dynamics. These equations are solved numerically for given initial conditions and a range of parameters. Some interesting behavior results, such as transition (in parameter space) of chaotic solutions into traveling-wave pulses with more than one characteristic length scale.

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The buoyant motion of a bubble rising through a continuous liquid phase can be retarded by the adsorption onto the bubble surface of surfactant dissolved in the liquid phase. The reason for this retardation is that adsorbed surfactant is swept to the trailing pole of the bubble where it accumulates and lowers the surface tension relative to the front end. The difference in tension creates a Marangoni force which opposes the surface flow, rigidifies the interface and increases the drag coefficient. Surfactant molecules adsorb onto the bubble surface by diffusing from the bulk to the sublayer of liquid adjoining the surface, and kinetically adsorbing from the sublayer onto the surface. The surface surfactant distribution which defines the Marangoni force is determined by the rate of kinetic adsorption and bulk diffusion relative to the rate of surface convection. In the limit in which the rate of either kinetic or diffusive transport of surfactant to the bubble surface is slow relative to surface convection and surface diffusion is also slow, surfactant collects in a stagnant cap at the back end of the bubble while the front end is stress free and mobile. The size of the cap and correspondingly the drag coefficient increases with the bulk concentration of surfactant until the cap covers the entire surface and the drag coefficient is that of a bubble with a completely tangentially immobile surface. Previous theoretical research on the stagnant cap regime has not studied in detail the competing roles of bulk diffusion and kinetic adsorption in determining the size of the stagnant cap angle, and there have been only a few studies which have attempted to quantitatively correlate simulations with measurements.This paper provides a more complete theoretical study of and a validating set of experiments on the stagnant cap regime. We solve numerically for the cap angle and drag coefficient as a function of the bulk concentration of surfactant for a spherical bubble rising steadily with inertia in a Newtonian fluid, including both bulk diffusion and kinetic adsorption. For the case of diffusion-limited transport (infinite adsorption kinetics), we show clearly that very small bulk concentrations can immobilize the entire surface, and we calculate the critical concentrations which immobilize the surface as a function of the surfactant parameters. We demonstrate that the effect of kinetics is to reduce the cap angle (hence reduce the drag coefficient) for a given bulk concentration of surfactant. We also present experimental results on the drag of a bubble rising in a glycerol–water mixture, as a function of the dissolved concentration of a polyethoxylated non-ionic surfactant whose bulk diffusion coefficient and a lower bound on the kinetic rate constants have been obtained separately by measuring the reduction in dynamic tension as surfactant adsorbs onto a clean interface. For low concentrations of surfactant, the experiments measure drag coefficients which are intermediate between the drag coefficient of a bubble whose surf...

Thermodynamics of anisotropic surfactant micelles. I. The influence of curvature free energy on the micellar size and shape