Development of anisotropic mobility during two-phase flow

This paper investigates the development of anisotropic frictional resistance and mobility as a function of an applied stress in a partially molten aggregate. Shapes of initially spherical melt pockets and cylindrical melt tubules are calculated as a function of the applied stress using a perturbation analysis. The applied stress excites a local flow within the melt units (tubules or pockets) rendering their initially circular average cross-section elliptical. Average aspect ratio of tubule cross-sections predicted by the perturbation analysis is compared with the results from laboratory experiments. The increase in the average aspect ratio is related to an increase in the volume fraction of melt films. A derivation for the effective resistance and mobility tensors as a function of the applied stress is presented. The anisotropy of resistance and mobility increases continuously with the applied stress in a non-linear fashion. In the upper limit, the anisotropy of the mobility tensor can increase by a factor of 10 under an applied stress of 14 MPa.