Xu Jin, Louge Michel Y
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062405. doi: 10.1103/PhysRevE.92.062405. Epub 2015 Dec 10.
We explore a mean-field theory of fluid imbibition and drainage through permeable porous solids. In the limit of vanishing inertial and viscous forces, the theory predicts the hysteretic "retention curves" relating the capillary pressure applied across a connected domain to its degree of saturation in wetting fluid in terms of known surface energies and void space geometry. To avoid complicated calculations, we adopt the simplest statistical mechanics, in which a pore interacts with its neighbors through narrow openings called "necks," while being either full or empty of wetting fluid. We show how the main retention curves can be calculated from the statistical distribution of two dimensionless parameters λ and α measuring the specific areas of, respectively, neck cross section and wettable pore surface relative to pore volume. The theory attributes hysteresis of these curves to collective first-order phase transitions. We illustrate predictions with a porous domain consisting of a random packing of spheres, show that hysteresis strength grows with λ and weakens as the distribution of α broadens, and reproduce the behavior of Haines jumps observed in recent experiments on an ordered pore network.
我们探索了流体通过可渗透多孔固体的吸渗和排渗的平均场理论。在惯性力和粘性力消失的极限情况下，该理论根据已知的表面能和孔隙空间几何形状，预测了将施加在连通区域上的毛细管压力与其在湿润流体中的饱和度相关联的滞后“保留曲线”。为避免复杂的计算，我们采用最简单的统计力学，其中一个孔隙通过称为“颈部”的狭窄开口与其相邻孔隙相互作用，且孔隙要么充满湿润流体，要么为空。我们展示了如何根据两个无量纲参数λ和α的统计分布来计算主要保留曲线，这两个参数分别测量颈部横截面和可湿润孔隙表面相对于孔隙体积的比表面积。该理论将这些曲线的滞后现象归因于集体一级相变。我们用由球体随机堆积组成的多孔区域说明了预测结果，表明滞后强度随λ增大而增大，随α分布变宽而减弱，并重现了最近在有序孔隙网络实验中观察到的海恩斯跳跃行为。
