In recent years a number of theoretical, experimental and computational research programs (Refs. [5], [8] and [3] for example) have substantially increased our fundamental understanding of the mechanics of flowing granular material. However most of these studies have concentrated on the simplest type of flow namely that of uniform size particles in the absence of any interstitial fluid effects or other complicating factors. The purpose of the present paper is to investigate the effects of interstitial fluid. In his classic study of granular flows Bagnold (1954) observed from his Couette flow studies that viscous effects of the interstitial fluid became significant when a number (which is now termed the Bagnold number, Ba) defined as [equation] becomes less than about 450. Here [delta] is the velocity gradient or shear rate. (We have chosen to omit from the definition of Ba a volume fraction parameter which is usually of order unity and is therefore not important qualitively). In the Couette flow experiments the appropriate shear rate, [delta], is clearly defined; in other flows (such as the very practical flow in a hopper) the corresponding condition (or shear rate) in not known. The purpose here is to investigate the effects of the interstitial fluid in the primarily extensional flows which occur in the flow of a granular material in a hopper
