Dynamic stability of non-dilute fiber shear suspensions

Abstract

Temporal stability analysis of fiber suspended shear flow is performed. After introducing the second order structure tensor to determine the Folgar-Tucker inter-fiber interactions based on the Langevin’s equation, a system governing the flow stability is derived in conjunction with the fiber orientation closure. Effect of the inter-fiber interactions on the dynamic stability is studied by solving the general eigenvalue problem. Results show that fiber interaction has significant stabilizing effects on the flow. The most unstable wave number changes with the interaction coefficient. For given interaction coefficient, wave number and other relevant parameters, there is a Re number which corresponds to the critical flow. This Re number is related to the wave number.