The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Liquid-phase combinatorial synthesis.

A concept termed liquid-phase combinatorial synthesis (LPCS) is described. The central feature of this methodology is that it combines the advantages that classic organic synthesis in solution offers with those that solid-phase synthesis can provide, through the application of a linear homogeneous polymer. To validate this concept two libraries were prepared, one of peptide and the second of nonpeptide origin. The peptide-based library was synthesized by a recursive deconvolution strategy [Erb, E., Janda, K. D. & Brenner, S. (1994) Proc. Natl. Acad. Sci. USA 91, 11422-11426] and several ligands were found within this library to bind a monoclonal antibody elicited against beta-endorphin. The non-peptide molecules synthesized were arylsulfonamides, a class of compounds of known clinical bactericidal efficacy. The results indicate that the reaction scope of LPCS should be general, and its value to multiple, high-throughput screening assays could be of particular merit, since multimilligram quantities of each library member can readily be attained.