Modification of Darcy's law to model mould interface effects in composites processing

Abstract

Darcy's law for the flow of fluids in porous media is frequently used to describe the flow of resins in beds of reinforcement. An extension is proposed, to permit the modelling of the longer range viscous forces which result from externally applied shear flows and other surface boundary conditions. This allows the decay of velocity perturbations due to tooling surface effects to be modelled. In profiles of thick section, decay of the velocity perturbation takes place exponentially over a characteristic distance equal to the square root of the Darcy permeability. The new model enables solutions to be obtained for the resin velocity profiles across the finite sections encountered in processes such as pultrusion and resin transfer moulding. However, the range of bed permeabilities and flow dimensions likely to be encountered in most real composite systems is such that the solutions obtained will, in nearly all cases, reduce to the simpler exponential decay solution. The model allows the equivalent resin film thickness at the mould interface to be calculated and could, in addition, form the basis of a new method for measuring permeability under processing conditions.