Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia.
Department of Mathematics, University of Chakwal, Chakwal, Pakistan.
Sci Rep. 2022 Nov 8;12(1):18992. doi: 10.1038/s41598-022-23402-7.
Stokes's equation in the fluid domain and Brinkman's equation in the porous media are combined in the current study which is designated by the Stokes-Brinkman coupling. The current paper gives a theoretical analysis of the Stokes-Brinkman coupling. It has been shown that such a model is a good match for the knee joint. A flow model has been investigated in order to get a better understanding of the convective diffusion of the viscous flow along the articular surfaces between the joints. The Beavers and Joseph slip conditions which are a specific boundary condition for the synovial fluid are used to solve the governing system of partial differential equations for the synovial fluid and the results are provided here. We develop formulas for the interfacial velocity for both flow through special slip condition and analyse the link between the slip parameters [Formula: see text] and [Formula: see text]. Thus, the damping force due to the porous medium naturally when we non-dimensionalize, some parameter which are controlling the structure like, [Formula: see text] and [Formula: see text]. Through the development of an analytical solution and numerical simulation (using the finite volume approach) it is hoped that the mechanisms of nutritional transport into the synovial joint will be better understood. According to the data the average concentration has a negative connection with both the axial distance and the duration spent in the experiment. Many graphs have been utilized to gain understanding into the problem's various characteristics including velocity and concentration, among others. Hyaluronate (HA) is considered to be present in porous cartilage surfaces and the viscosity of synovial fluid fluctuates in response to the amount of HA present.
当前的研究将流域中的 Stokes 方程和多孔介质中的 Brinkman 方程结合起来，称为 Stokes-Brinkman 耦合。本文对 Stokes-Brinkman 耦合进行了理论分析。结果表明，该模型非常适合膝关节。为了更好地了解关节表面粘性流的对流扩散，研究了一种流动模型。Beavers 和 Joseph 滑移条件是滑液的特定边界条件，用于求解滑液的控制微分方程组，并在此提供结果。我们为特殊滑移条件下的流动开发了界面速度公式，并分析了滑移参数[Formula: see text]和[Formula: see text]之间的联系。因此，当我们进行无量纲化时，由于多孔介质会产生阻尼力，某些控制结构的参数，如[Formula: see text]和[Formula: see text]。通过开发解析解和数值模拟（使用有限体积法），希望更好地理解营养物质进入滑膜关节的机制。根据数据，平均浓度与轴向距离和实验持续时间都呈负相关。利用许多图表来了解问题的各种特性，包括速度和浓度等。透明质酸（HA）被认为存在于多孔软骨表面，滑液的粘度会根据 HA 的含量而波动。
