Vainshtein P, Shapiro M
Laboratory of Transport Processes in Porous Materials, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.
J Colloid Interface Sci. 2009 Feb 1;330(1):149-55. doi: 10.1016/j.jcis.2008.10.050. Epub 2008 Nov 1.
We investigate theoretically forces acting on a porous particle in an oscillating viscous incompressible flow. We use the unsteady equations describing the creeping flow, namely the Stokes equations exterior to the particle and the Darcy or Brinkman equations inside it. The effect of particle permeability and oscillation frequency on the flow and forces is expressed via the Brinkman parameter beta = a/square root(k) and the frequency parameter Y = square root(a(2)omega/2nu) = a/delta, respectively. Here a is particle radius, k is its permeability, omega is the angular frequency, delta is the thickness of Stokes layer (penetration depth) and nu is the fluid kinematic viscosity. It is shown that the oscillations interact with permeable structure of the particle and affect both the Stokes-like viscous drag and the added mass force components.
我们从理论上研究了在振荡粘性不可压缩流中作用于多孔颗粒的力。我们使用描述蠕动流的非定常方程，即在颗粒外部的斯托克斯方程以及颗粒内部的达西方程或布林克曼方程。颗粒渗透率和振荡频率对流动和力的影响分别通过布林克曼参数β = a/√k 和频率参数Y = √(a²ω/2ν) = a/δ 来表示。这里a是颗粒半径，k是其渗透率，ω是角频率，δ是斯托克斯层（穿透深度）的厚度，ν是流体运动粘度。结果表明，振荡与颗粒的可渗透结构相互作用，并影响类斯托克斯粘性阻力和附加质量力分量。
