Motion Law of a Sphere in Bingham Fluid with Thixotropy

The thixotropy properties and the motion law of a sphere in the Bingham fluid have been studied. Through observation of the settling motion of a single sphere in the Bingham fluid on the X- ray screen, it has been discovered that the mud in estuaries and along sea bay. and the hyperconcentrated flow all behave as the Bingham fluid with thixotropy properties as the large sediment concentration. Through derivation, the theoretical relationship between the yield stress and non-settling maximum sphere supported by the stress for the Bingham fluid has been developed, the equations for calculating the increasing yield stress and the non-settling maximum sphere diameter with the duration at rest of the slurry have been obtained. In consideration of the effect of thixotropy on fluid motion, the Navier-Stokes equation group for the Bingham thixotropy fluid has been developed. Through further study of the flow boundary condition of settling motion of a single sphere in the Bingham thixotropy fluid, and the solving of the Navier-Stokes equation group under the small Reynolds number, the theoretical equation of the drag force of the Bingham thixotropy fluid flowing around a sphere has been deduced. The theoretical relationship between drag coefficient and Reynolds number has been derived. By use of the experimental data of Theological test of various slurries measured with viscometer and those of single sphere motion observed on the X-ray screeen, the above equations have been verified. The equations are in good agreement with the experimental data for various slurries.