Yield and Solidification of Yield-Stress Materials in Rigid Networks and Porous Structures

Abstract

In this paper, we address the issue of threshold yield pressure of yield-stress materials in rigid networks of interconnected conduits and porous structures subject to a pressure gradient. We compare the results as obtained dynamically from solving the pressure field to those obtained statically from tracing the path of the minimum sum of threshold yield pressures of the individual conduits by using the threshold path algorithms. We refute criticisms directed recently to our previous findings that the pressure field solution generally produces a higher threshold yield pressure than the one obtained by the threshold path algorithms. Issues related to the solidification of yield stress materials in their transition from fluid phase to solid state have also been investigated and assessed as part of the investigation of the yield point. Keywords: fluid mechanics; yield-stress; threshold yield pressure; threshold solidification pressure; network of conduits; porous media; threshold path algorithms.Recently, Balhoff et al [12] (henceforth called BRKMP) conducted a study in which they investigated this issue, among other issues, in detail and challenged the previous findings of SB. They argued that the threshold yield pressure obtained from solving the balance equations must be the same as the one obtained from the threshold path algorithms. They supported their theoretical reasoning by flow simulations in which they used a robust solving scheme based on the Newton-Raphson method in conjunction with the mass conservation and characteristic flow models. They even produced a mathematical proof using a graph theory framework

The yield condition in the mobilization of yield-stress materials in distensible tubes

“…There are two possibilities for modeling the yield-stress materials before reaching their yield point: either they are solid-like materials or they are highly-viscous fluids. A detailed discussion about this issue, among other relevant issues, is given in [29]. Our proposal for identifying the yield point according to each one of these two possibilities is discussed in the following two subsections.…”

“…Our proposal in this case is that the material prior to yield should be modeled as a Newtonian fluid with a very high viscosity. The assumption of a Newtonian fluid is justified by the fact that at such regimes of very low rate of deformation the material is at its low Newtonian plateau since all non-Newtonian rheological effects are induced only by a measurable deformation [29]. We therefore use the one-dimensional Navier-Stokes flow model to identify the pressure field prior to yield and hence the yield condition.…”

“…We are not aware of a previous attempt to find the condition for the yield of yield-stress materials in distensible tubes. Past investigations are generally focused on the flow of yield-stress fluids in rigid conduits and structures such as ensembles of conduits and porous media [4,[21][22][23][24][25][26][27][28][29]. There are some other studies (e.g.…”