Significance of the microfluidic concepts for the improvement of macroscopic models of transport phenomena

Abstract

Complexity of transport phenomena - ranging from macroscopic motion of matter, heat transfer, over to the molecular motions determining the overall flow properties of fluids, or generally aggregation states of matter – inhibited development of a single mathematical model describing simultaneously transport processes at all relevant scales. In classical engineering sciences at each scale level we have different equations, different fundamental variables and different methods of solution [4]. The established basis of the classical fluid dynamics - the Navier-Stokes equations [1, 3] - have apparently nothing in common with molecular physics. At the macroscopic scale of motion the molecular structure of matter and the microscopic molecular motions are ignored (even though they determine the local macroscopic behaviour) [1, 3, 4]. To describe multiphase flows, still other methods must be used – increasing further the number of equations, methods of solution etc. The serious disadvantage of this approach is, that equations describing macroscopic models (Navier-Stokes and there from derived equations), introduce multiple theoretical problems: - higher order continuity requirements [3]; - numerous paradoxes in simple macroscopic flows (Bernoulli eq.); - different equations with different fundamental variables and different methods of solution, build a set of disciplines devoted in principle to a single problem – dynamics of disperse systems.