Conservation and constitutive equations for adsorbed species undergoing surface diffusion and convection at a fluid-fluid interface

摘要: Abstract A rigorous mathematical theory is presented for mass transfer of a solute by diffusion and convection at near an interface between two immiscible solvent liquids. The objective this study to determine, simple model system, the conditions under which detailed resolution concentration flux profiles can be replaced (insofar as macroscopically observable are concerned) with jump that relate bulk or macroscopic values on sides interface. “statistical—mechanical” underlying theoretical development consists spherical Brownian particles, either wholly immersed in one contiguous fluids, else straddling Adsorption forces tending cause accumulation “surfactant” particles regarded deriving from position-dependent potential energy function. This system characterized three independent length scales: macroscale L , relevant gradients fluids away interface; smaller I characteristic normal interface, 1 provides proper scale hydrodynamic “wall effects” fluid upon particle motion. It continuum description transfer. Relative microscales l vanishingly small. Singular perturbation techniques employed provide complete spatial profiles, right down scales and/or δ = l/L δϵ /L small parameters. Three distinct situations emerge ⪡ 1, depending value ϵ rate decrease any wall effects increasing distance undeformed First, when fall off faster than linearly distance, set local derived includes both attraction/repulsion effects, while transport bulk-phase occurs consistent advection velocity diffusivity infinite, unbounded fluid. Second, but ϵδ O(1), again linearly, still derived, these must supplemented “hindered” corrections fluids. Finally, other circumstances, we show not possible; here, cannot ignore features In those cases where rigorously, qualitative interfacial discussed order obtain physical understanding processes our system. shown rigorously resemble normally assumed We consider particularly significant.