Stress in Dilute Suspensions
Generally, two types of theory are used to describe the field equations for suspensions. The so-called “postulated” equations are based on the kinetic theory of mixtures, which logically ought to give reasonable equations for solutions. The basis for the use of such theory for suspensions is tenuous, though it at least gives a logical path for mathematical arguments. It has the disadvantage that it leads to a system of equations which is underdetermined, in a sense that can be made precise. On the other hand, the so-called “averaging” theory starts with a determined system, but the very process of averaging renders the resulting system underdetermined. I suggest yet a third type of theory. Here, the kinetic theory of gases is used to motivate continuum equations for the suspended particles. This entails an interpretation of the stress in the particles that is different from the usual one. Classical theory is used to describe the motion of the suspending medium. The result is a determined system for a dilute suspension. Extension of the theory to more concentrated systems is discussed.
KeywordsKinetic Theory Multiphase Flow Continuum Theory Average Theory Determined System
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