# Numerical simulation of wetting hydrodynamics for pure liquids and surfactant solutions

#### Abstract

Newtonian fluids generate infinite shear stress values at dynamic contact lines when the customary no-slip boundary conditions of continuum mechanics are applied. The resulting, unbounded interface curvature precludes the specification of a true dynamic contact angle.^ Application of slippage at the solid-liquid interface, over an inner dimension of characteristic length, L$\rm\sb{S},$ removes the stress divergence problem, allowing solution by singular perturbation techniques. A three region expansion indicates the existence of a geometry-independent meniscus slope in the intermediate region. The slope of the free surface in this region could be substituted for the dynamic contact angle as a boundary condition in the determination of the overall meniscus shape.^ Numerical simulations of a plate vertically immersing into an infinitely deep bath have been utilized to demonstrate the geometry-independent slope of the free surface in the approximate vicinity of the dynamic contact line. Our results demonstrate that the slope of the meniscus, at a distance of 10 slip lengths from the dynamic contact line, is geometry-independent for capillary numbers $\le$0.01.^ The effects upon the interface shape of surfactants, both insoluble and soluble, was also modeled. Higher surface elasticity resulted in a lower curvature of the interface, and generated a greater degree of tilting in the direction of motion of the plate. Higher surface Peclet numbers, equivalent to reduced surface diffusivities, enhanced the surface elasticity effects through the establishment of larger surfactant concentration gradients. The insoluble surfactant effects were attenuated in the soluble surfactant case. For the soluble surfactant case, increased values of the Gibbs adsorption length, which effectively allows a higher level of surfactant adsorption on the free surface, reduced the interface curvature and gave a more pronounced tilt. ^

#### Subject Area

Engineering, Chemical|Engineering, Mechanical

#### Recommended Citation

David Edward Finlow, "Numerical simulation of wetting hydrodynamics for pure liquids and surfactant solutions" (1996). Dissertations and Master's Theses (Campus Access). Paper AAI9702097.
http://digitalcommons.uri.edu/dissertations/AAI9702097

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