A toy model for gas viscosity

Abstract

We present a greatly simplified model (a ‘toy model’) for the rheological behavior of gases in laminar motion, whose viscosity arises mainly from thermal diffusion of momentum among layers. The model is based on the usual mesoscopic representation of a fluid in laminar motion (i.e. many layers reciprocally sliding on each other), where the mechanical coupling among layers is modeled by means of mass exchange, that in turns results in momentum diffusion transversally to the fluid flow. In particular, the model is based on the conceptual analogy between: a laminarly flowing fluid, on one side, and, on the other side, an arbitrary number of identical trains sliding on parallel rails, reciprocally interacting through mass exchange between nearest neighbors. Before presenting the complete model, a simplest case is considered, in order to familiarize learners with the idea that mass exchange between two mechanical systems can give rise to an emerging interaction force between them. The proposed model, appropriate for university students (and, limited to the simplest case, for upper high school students, too), helps them to understand the basic idea of viscosity as a transport phenomenon, giving the opportunity to better understand—in a unitary way—the physics underlying various transport phenomena, such as: electric conduction, heat conduction, diffusion. Moreover, the computational implementation of the model is done by using a mathematical formalism, which in turns permits students to familiarize (in a classical physics context) with the matrix notation and the physical meaning of matrix elements, to the benefit of their subsequent quantum mechanics studies.