The yield stress of foamy sands

The yield stress of a mixture of foam and solids, or foamy sand, was investigated theoretically using a two-dimensional (2-D) periodic model. The range of solid fractions considered ranged from about 40 to 68%. The yield stress of a foamy sand increases with gas fraction at a given solid fraction and increases with solid fraction at a given gas fraction. At a fixed fraction of solid plus gas, yield stress is relatively insensitive to gas or solid fraction alone. There exists a maximum liquid fraction above which the yield stress disappears. These trends agree with those reported for foamy sands encountered in tunneling through soft sediments and proppant-laden fracturing fluids used in the petroleum industry.