rupture, shock waves, oscillations, etc.) will depend on the The detailed description of the influence of a chemical reaction geometry of the film. Another important factor influencing on the dynamic behavior of a thin liquid film is of significant the dynamics of the liquid film is the presence of gradients importance in many engineering and biological applications. In of additives (solutal Marangoni effect) or gradients of temthis paper, the dynamics of a thin liquid film on a solid substrate perature (thermal Marangoni effect). If we consider only is followed until film rupture or formation of local contacts. A surface concentration gradients, two situations are possible: surface chemical reaction between insoluble surfactant molecules gradients induced by adsorption/desorption of soluble sur-(receptors) on the free surface of the film and binding sites on the factants and gradients induced by surface chemical reactions solid substrate is considered. Asymptotic expansion of the equations for fluid motion with van der Waals, capillary, and Maran-affecting insoluble surfactants. goni forces leads to a model with three nonlinear evolution equa-The crudeness of the earliest linear models for interfacial tions describing the dynamics of the surface deformation and the stability has been overcome in recent years by numerous kinetics of free and bound receptors. Chemical and hydrodynamic nonlinear approaches. Nonlinear methods based on the long modes are predicted and simulated numerically with different stawavelength nature of the response have provided sets of bility regimes: for a simple linear surface reaction, the concentranonlinear evolution equations in several cases: a thin film tion of receptors follows the deformation of the surface; for a on a solid substrate (1), a free film with tangential immobile nonlinear surface reaction with affinity enhanced at small dissurfaces (2, 3), or a free film without surfactants (4). Nontances, a clustering of receptors is observed at the local points of linear preliminary studies taking into account the presence of contact. A completely new regime is also obtained where the rupinsoluble surfactants were treated in Refs. (5, 6). Marangoni ture (or contact) time is delayed by several orders of magnitude,
and the concentrations and film thickness may oscillate. This study waves induced by a multistable chemical reaction are decould be relevant to biological applications where adhesion bescribed in Ref. (7). Several cases of droplet spreading on a tween cells and substrates can be modeled by considering the dythin viscous film were extensively examined in an attempt namics of the thin film between them. The results are first comto understand and control the pulmonary flow ( 8). An analypared with experiments on biological cells adhering to glass or sis of the bifurcating solutions was performed for the case other solid substrates where periodic patterns (wavelike morpholoof nonlinear solutal convection in thin liquid layers (9). The gies) are observed with a clustering of adhesion receptors at the development of singularities in a thin neck was also dislocal contact points. A second possible application is the activation cussed recently in Ref. (10).
of T lymphocytes, a major immunological cell type, which requires In a preceding paper (11), we compared the stability and the clustering of cell surface receptors by interaction of T-cell receptors with surface-bound ligands.