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.

No abstract