具有分裂前沿的非线性过滤模型

IF 2.8 3区 工程技术 Q2 MECHANICS
Liudmila I. Kuzmina , Yuri V. Osipov , Artem R. Pesterev
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引用次数: 0

摘要

我们考虑了均质多孔介质中悬浮液的过滤问题,该介质由宏观一维模型描述,包括质量交换方程和沉积物生长动力学方程。标准模型假定悬浮颗粒的运动速度与载流体相同。然而,在一些实验中,观察到悬浮颗粒的前边界与载流体的前边界之间存在滞后。本文建议对标准模型进行修改,以描述流体前沿与颗粒前沿之间的分离情况。为此,在沉积物生长方程中引入了一个与悬浮液浓度有关的非光滑非线性函数。在非平滑悬浮函数的情况下,前沿的悬浮颗粒浓度会在有限的时间内降至零。此时,联合前沿分裂为纯注入水前沿和悬浮颗粒及保留颗粒前沿。颗粒前沿的移动速度比纯水前沿慢。在线性过滤函数(朗缪尔系数)的情况下,可以用封闭形式构建精确解。对于悬浮函数为平方根形式的过滤问题,可以得到明确的解析公式。在过滤函数不光滑的情况下,过滤时间是有限的。曲线边界将浓度随时间增加的过滤域与悬浮颗粒和滞留颗粒浓度达到极限的稳定域分开。稳定边界和颗粒前沿的极限速度是重合的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Non-linear filtration model with splitting front

We consider filtration of a suspension in a homogeneous porous medium which is described by a macroscopic 1-D model including the mass exchange equation and the kinetic equation for deposit growth. The standard model assumes that suspended particles move at the same speed as the carrier fluid. However, in some experiments, a lag between the front boundary of suspended particles and the front of the carrier fluid was observed. This article proposes a modification of the standard model that provides a description of the separation between the fluid front and the particle front. For this purpose, a non-smooth non-linear function depending on the concentration of the suspension is introduced into the deposit growth equation. In case of a non-smooth suspension function, the concentration of suspended particles at the front decreases to zero in a finite time. At this moment the united front splits into the front of pure injected water and the front of suspended and retained particles. The particle front moves slower than the pure water front. In case of a linear filtration function (Langmuir coefficient), an exact solution is constructed in a closed form. For the filtration problem with a suspension function in the form of a square root, explicit analytical formulae are obtained. In case of a non-smooth filtration function, the filtration time is finite. The curvilinear boundary separates the filtration domain, where concentrations increase with time, from the stabilization domain, where the concentrations of suspended and retained particles have reached their limits. The limit speeds of the stabilization border and of the particle front coincide.

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来源期刊
CiteScore
5.50
自引率
9.40%
发文量
192
审稿时长
67 days
期刊介绍: The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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