Aspects of the thermodynamic stability of fibre suspension flows

Abstract

We examine the circumstances under which the constitutive equations for fibre suspension flows are consistent with the second law of thermodynamics, and the conditions under which fibre suspension flows are stable, in the energetic sense. The constitutive model investigated is that based on the use of orientation tensors, and these issues are examined in the context of a selection of closure approximations: the linear and quadratic closures, a rule due to Hinch and Leal, the smooth orthotropic closure rule of Cintra and Tucker, and the natural closure of Verleye and Dupret. It is shown that, with the use of the linear closure approximation, the constitutive equations are consistent with the second law, and the flows are monotonically stable, if the particle number does not exceed 35/2. The quadratic closure is consistent and stable, as is the natural closure, at least in the two-dimensional case. It is not possible to determine the stability or otherwise of the Hinch–Leal closure for arbitrary flows, though for biaxial elongation, a case which is known to lead to non-physical results, the closure rule is consistent with the second law of thermodynamics. The smooth orthotropic rule of Cintra and Tucker is shown not to be consistent with the second law for arbitrary flows.