ABSTRACT
Spreading of aqueous drops on hydrocarbon liquids occurs only when particular surfactants are added to the droplets above a critical concentration. For surfactant solutions of didodecyl ammonium bromide (DDAB) in water spreading over mineral oil, rates of droplet expansion are much slower than those corresponding to pure liquids spreading over immiscible liquid substrates with the same initial spreading coefficients. We present a sorption-kinetic model to explain quantitatively the spreading histories for aqueous DDAB droplets on mineral oil. Due to surfactant transport limitations, spreading occurs only when enough surfactant arrives at the dilating lens surfaces to establish a slightly positive, but near-zero spreading coefficient. We solve the convective diffusion equation for a cylindrical disk-like lens under the integral constraint of a constant surfactant adsorption density corresponding to a near-zero spreading coefficient. All observed spreading behavior is correctly portrayed by the proposed sorption-kinetic model including final equilibrium lens formation and spreading rates that are sensibly independent of drop volume, but are strongly dependent on drop surfactant concentration. Quantitative agreement is found with the experimental spreading data for a surfactant diffusion coefficient of 6x10(-12) m(2)/s and an effective adsorption rate constant of 6.5x10(-7) m/s. Both values prove physically reasonable. The sorption-kinetic model provides a new mechanism for understanding slow surfactant-driven spreading. Copyright 2000 Academic Press.
ABSTRACT
The exposed part of the eyeball is covered by a tear film, which is vital for the proper function of the eye. The film thickness has been measured to be roughly 10 μm; however, how a tear film of this thickness is generated has not been clearly explained. It is proposed that the tear film is deposited analogous to a coating process by the rising meniscus of the upper lid during a blink. A coating model is formulated that not only predicts correctly the film thickness, but also captures the postblink lipid spreading commonly observed in experiments. A deposited tear film thins rapidly near the tear meniscus surrounding the film. Numerical simulation of this thinning reveals that the minimum film height obeys a power law. When the minimum height reaches the effective range of dewetting intermolecular forces, the film ruptures. The thinning time therefore defines a breakup time, and the thinning law shows explicitly how this breakup time is related to tear viscosity, surface tension, meniscus radius, and initial and final film thicknesses. The calculated breakup time agrees with those observed experimentally.
