Transport Phenomena and Fluid Dynamics

Most systems in nature are dynamic, that is, change in time. In non-equilibrium processes there are flows ( transports ) of mass, momentum and energy, from one place to the other. If a system is near equilibrium the transports occur in such ways that the distributions of the mass, momentum, and energy, which are non-uniform and time dependent, are relaxed to the equilibrium, where there are no flows. One example is the diffusion of particles from a crowded region to a less one. The equilibrium state represents a stationary state. The other stationary state is the non-equilibrium, steady state where there are constant flows driven by external means. For example, a rod whose ends are maintained at two different temperatures is in a steady state with a constant heat flow from a high temperature end to a lower one. The temperature gradient in the rod is the driving force for the heat flow. Biological complexes are bathed in aqueous environments. Over the scales much longer than the mean free length between collisions of the solvent molecules, the solvents can be treated as continuous fluids. The complex fluids such as solutions of biopolymers and cells probed over a certain long length scale can also be treated as continua. For these cases the hydrodynamic description of transport in terms of densities of fluids’ conserved quantities —the mass, momentum, and energy— is very useful. The governing dynamics for these hydrodynamic variables, which is also called hydrodynamics or fluid mechanics, is widely applicable to the problems, not only in basic sciences but also in engineering disciplines. For biological organisms in particular, fluid motion is something with which they must contend: a factor to which their design reflects adaptation (Vogel 1984). In this chapter we study basic principles and apply them to some important fluid flows which allow analytical treatments.