Boundary layers in a dilute particle suspension

Abstract

The general problem of a boundary-layer flow carrying a dilute, mono-disperse suspension of small particles (together with gravitational effects) is considered. The problem is modelled using the ‘dusty-gas’ equations, which are a coupled equation set linking the fluid motion to that of the particle motion (both of which are modelled as continua). A number of qualitatively distinct potential scenarios are predicted. These include a variety of boundary-layer breakdowns, and the formation of shock transitions in the distribution of the particulate phase (together with the development of particle-free zones). Numerical results predicting these differing behaviours are confirmed through local asymptotic analyses of the governing equations. Although we consider a general class of boundary layer, our results are compared and contrasted with previous studies of specific cases, most notably the constant freestream fluid velocity case (akin to the ‘clean’ Blasius boundary layer). In the case of a boundary-layer flow driven by a linearly retarding free stream (the analogue of the classical ‘Howarth’ boundary-layer problem), the effects of the particle phase are surprisingly seen to (slightly) delay the separation of the boundary layer.