Determination of Bulk and Surface Diffusion Coefficients from Experimental Data for Thin Liquid Film Drainage

Drag of a Solid Particle Trapped in a Thin Film or at an Interface: Influence of Surface Viscosity and Elasticity

“…B is a constant to be determined from the boundary conditions (Eq. [9]). The geometry of the problem (see Eq.…”

“…The geometry of the problem (see Eq. [8] and the linearized boundary conditions [9] and [10]) allows us to decouple the z and φ components in the velocity field according tõ…”

“…As for the diffusion process, we will consider only surface diffusion, not the bulk diffusion (9). Strictly speaking, this restriction makes our model applicable only to films of insoluble surfactants.…”

Influence of Ionic Surfactants on the Drainage Velocity of Thin Liquid Films

“…23). Hence, from the general definitions of the surface diffusion flux (28,29) and the electrochemical potential (23,24), and from the leading-order concentration distribution [6] the following simple relationship is obtained:…”

Flow-induced melting of condensed domains within a dispersed Langmuir film

“…Now, if we consider that the growth process of the LC domains is controlled by the surface diffusive equation, ‫⌫ץ‬ / ‫ץ‬t ϳ D s ͑1 / r͒͑d / dr͓͒r͑d⌫ / dr͔͒, a second timescale can be estimated, T diff ϳ͑r o − r i ͒ 2 / D s ϳ 40 h, with a surface diffusion coefficient of PDA molecules, D s ϳ 10 −8 m 2 / s, typical of organic surfactants in LM. 15 Since T diff is close to the experimental time delay observed to get a steady distribution of the LC domains ͑15 h͒, surface diffusion can be again considered as the limited kinetics in our experiments despite the flow imposed.…”