BOUNDARY-VALUE-PROBLEMS INVOLVING HERSCHEL-BULKLEY MATERIAL

The behaviour of a Herschel-Bulkley material near the apex of a semi-i nfinite plate is studied. The plate is immersed in the centre of a lon gitudinal strip the sides of which are subjected to equal and opposite velocities. The problem is considered in the hodograph plane, where i t is possible to obtain a solution. Transforming this solution back to the real plane yields an exact expansion of the velocity field near t he apex of the plate. The leading term of the velocity field is checke d by using an invariant integral which involves the energy-momentum te nsor of the system. A reciprocal theorem is also derived, whereby the coefficient of the singular strain rate field at the plate edge is rel ated to finite integrals in the hodograph plane. A check of this metho d is effected by comparison with the solution of the above problem.