Theoretical analysis of the effect of insoluble surfactant on the dip coating of chemically micropatterned surfaces

摘要

Microfluidic flow on chemically heterogeneous surfaces is a useful technique with applications ranging from selective material deposition to the self-assembly of nanostructures. The recent theoretical analysis by Davis [Phys. Fluids 17, 038101 (2005)] of the dip coating of a pure fluid onto vertical, wetting stripes surrounded by nonwetting regions quantified the experimentally observed deviations from the classical Landau-Levich result due to lateral confinement of the fluid by chemical surface patterning. In this present work, the analysis of dip coating of these heterogeneous surfaces is extended to a liquid containing an insoluble surfactant. Using matched asymptotic expansions based on lubrication theory in the limit of a small capillary number, the thickness of the deposited liquid film and the surfactant concentration in the deposited monolayer are predicted for a wide range of fluid properties and process parameters. The increase in the deposited film thickness is shown analytically to be limited by a multiplicative factor of 4(1/3) times the result for a pure liquid. Numerical results demonstrate that the thickening due to Marangoni effects is nonmonotonic in the capillary number because of the competition between viscous stresses, Marangoni stresses, and surface diffusion. (c) 2006 American Institute of Physics.