Dynamics of a Thin Liquid Film with a Surface Chemical Reaction

Abstract

The detailed description of the influence of a chemical reaction on the dynamic behavior of a thin liquid film is of significant importance in many engineering and biological applications. In this paper, the dynamics of a thin liquid film on a solid substrate is followed until film rupture or formation of local contacts. A surface chemical reaction between insoluble surfactant molecules (receptors) on the free surface of the film and binding sites on the solid substrate is considered. Asymptotic expansion of the equations for fluid motion with van der Waals, capillary, and Marangoni forces leads to a model with three nonlinear evolution equations describing the dynamics of the surface deformation and the kinetics of free and bound receptors. Chemical and hydrodynamic modes are predicted and simulated numerically with different stability regimes: for a simple linear surface reaction, the concentration of receptors follows the deformation of the surface; for a nonlinear surface reaction with affinity enhanced at small distances, a clustering of receptors is observed at the local points of contact. A completely new regime is also obtained where the rupture (or contact) time is delayed by several orders of magnitude, and the concentrations and film thickness may oscillate. This study could be relevant to biological applications where adhesion between cells and substrates can be modeled by considering the dynamics of the thin film between them. The results are first compared with experiments on biological cells adhering to glass or other solid substrates where periodic patterns (wavelike morphologies) are observed with a clustering of adhesion receptors at the local contact points. A second possible application is the activation of T lymphocytes, a major immunological cell type, which requires the clustering of cell surface receptors by interaction of T-cell receptors with surface-bound ligands.