ABSTRACT
St. Petersburg State University, Department of Chemistry, 198504 St. Petersburg, Petrodvorets, University Avenue 2, Russia
Contents
A. Introduction 1 B. Adequate description of simplest interfacial rheology 3 in tensor terms 1. Purely elastic two-dimensional continuum 3 2. Purely viscous two-dimensional continuum 12 C. Rheological equations and mechanical models 15 of interfacial continua D. Rheological equations for ideal interfacial surfactant 30 layers E. References 37
A. INTRODUCTION
Three-dimensional (bulk) rheology is one of the branches in continuum mechanics (hydrodynamics). However, while the main topics studied by the hydrodynamics is the determination of the spatial and time dependencies of the fields of velocity and contact forces (in the simplest case – the pressure) at given boundary conditions, the rheology studies a preparatory and more special problem: how to express the dependence of forces which arise in the infinitesimal element of a continuum on the deformations and the rate of deformation of this element. The forces relevant to this case are those which are transferred via a contact, and, therefore, are proportional to the contact area. Therefore the inertia of an element (similarly to other field-induced forces) is irrelevant: the inertia is proportional to a unit volume and therefore its contribution in the limiting case considered should be neglected. Thus, the approaches similar to that adopted in [1], where the inertia is involved into the rheological schemes, are incorrect in principle.
