| Abstract: | A discrete Galerkin boundary element technique with a quadratic approximatión of the variables was developed to simulate the three-dimensional (3D) viscous flow established in periodic assemblages of particles in suspensions and within a periodic porous medium. The Batchelor's unit-cell approach is used. The Galerkin formulation effectively handles the discontinuity in the traction arising in flow boundaries with edges or corners, such as the unit cell in this case. For an ellipsoidal dilute suspension over the range of aspect ratio studied (1 to 54), the numerical solutions of the rotational velocity of the particles and the viscosity correction were found to agree with the analytic values within 0.2% and 2% respectively, even with coarse meshes. In a suspension of cylindrical particles the calculated period of rotation agreed with the experimental data. However, Burgers' predictions for the correction to the suspension viscosity were found to be 30% too low and therefore the concept of the equivalent ellipsoidal ratio is judged to be inadequate. For pressure-driven flow through a fixed bed of fibres, the prediction on the permeability was shown to deviate by as much as 10% from the value calculated based on approximate permeability additivity rules using the corresponding values for planar flow past a periodic array of parallel cylinders. These applications show the versatility of the technique for studying viscous flows in complicated 3D geometries. |
