Continuum Approaches for Describing Solid-Gas and Solid-Liquid Flow

Two-phase continuum models have been used to describe the multiphase flow properties of solid-gas and solid-liquid mixtures. The approach is limited in that it requires many fitting functions and parameters to be determined empirically, and it does not provide natural explanations for some of the qualitative behavior of solid-fluid flow. In this report, we explore a more recent single-phase continuum model proposed by Jenkins and Savage (1982) to describe granular flow. Jenkins and McTigue (1989) have proposed a modified model to describe the flow of dense suspensions, and, hence, many of our results can be straightforwardly extended to this flow regime as well. The solid-fluid mixture is treated as a homogeneous, compressible fluid in which the particle fluctuations about the mean flow are described in terms of an effective temperature. The particle collisions are treated as inelastic. After an introduction in which we briefly comment on the present status of the field, we describe the details of the singlephase continuum model and analyze the microscopic and macroscopic flow conditions required for the approach to be valid. We then derive numerous qualitative predictions which can be empirically verified in small-scale experiments: The flow profiles are computed for simple boundary conditions, plane Couette flow and channel flow. Segregation effects when there are two (or more) particle sizes are considered. The acoustic dispersion relation is derived and shown to predict that granular flow is supersonic. We point out that the analysis of flow instabilities is complicated by the finite compressibility of the solid-fluid mixture. For example, the large compressibility leads to interchange (Rayleigh-Taylor instabilities) in addition to the usual angular momentum interchange in standard (cylindrical) Couette flow. We conclude by describing some of the advantages and limitations of experimental techniques that might be used to test predictions for solid-fluid flow. Acoession For NTIS GRA&I DTIC TAB 0 UnalLnounced [ Ju Jt } Icntioa D Isltiibution/ Avallabillty Codes iii'' N vail, and/or Dist Spe0.& V