Incorporating Darcy's law for pure solvent flow through porous tubes: Asymptotic solution and numerical simulations
Incorporating Darcy's law for pure solvent flow through porous tubes: Asymptotic solution and numerical simulations
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结合达西定律实现纯溶剂流经多孔管：渐近解和数值模拟
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Richard M. Lueptow
中科院分区：
文献类型：
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作者：
N. Tilton;D. Martinand;E. Serre;Richard M. Lueptow
由于跨膜压力和速度之间的耦合，多孔管状膜中压力驱动、不可压缩、牛顿流体的广义解具有挑战性。到目前为止，所有的解析解都需要简化，例如忽略跨膜压力和速度之间的耦合，假设速度场的形式，或者扩展涉及管道长度的参数的幂。此外，以前的解决方案尚未与直接数值模拟（DNS）进行比较验证。我们全面回顾了这个问题，提出了一个强有力的分析解决方案，其中包括达西定律在膜上。我们没有对管的长度和速度场的形式作任何假设。通过与dns的详细对比验证了解析解，包括轴流耗尽和交叉流逆转的情况。我们探讨了用于模拟多孔管流动的典型假设的有效性，并在支持信息中提出了多孔通道的解决方案。
A generalized solution for pressure-driven, incompressible, Newtonian flow in a porous tubular membrane is challenging due to the coupling between the transmembrane pressure and velocity. To date, all analytical solutions require simplifications such as neglecting the coupling between the transmembrane pressure and velocity, assuming the form of the velocity fields, or expanding in powers of parameters involving the tube length. Moreover, previous solutions have not been validated with comparison to direct numerical simulation (DNS). We comprehensively revisit the problem to present a robust analytical solution incorporating Darcy's law on the membrane. We make no assumptions about the tube length or form of the velocity fields. The analytic solution is validated with detailed comparison to DNSs, including cases of axial flow exhaustion and cross flow reversal. We explore the validity of typical assumptions used in modeling porous tube flow and present a solution for porous channels in Supporting Information.