Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt.
Department of Mathematics, Faculty of Science, Aswan University, Aswan, Egypt.
Sci Rep. 2023 May 29;13(1):8686. doi: 10.1038/s41598-023-35410-2.
The purpose of this paper is to present a rigorous analysis of streamline patterns and their bifurcation to a viscoplastic Bingham fluid model that involves heat and mass transfer in an electroosmotic flow through a complex wavy microchannel. The Bingham fluid act as a solid medium in the core layer, which divides the channel into three distinct sections utilized to model the problem as a switched dynamical system between these zones. To track multiple steady states (stagnation points) and related trapping phenomena, we perform both analytical and numerical bifurcation analysis of each subsystem with respect to different physical effects such as electrical double layer thickness and Helmholtz-Smoluchowski velocity. The key feature of the technique presented here is its ability to reveal the peristaltic transport characteristics of the Bingham fluid model in the presence or absence of symmetric flow properties. The primary novelty here is the ability to regulate the location and stability of the equilibrium points in the domain of interest. This leads to the detection of global bifurcations that reflect important dynamic elements of the model. Our results highlighted a new category of complex behavior that controls transitions between qualitatively different transport mechanisms, as well as a class of non-classical trapping phenomena.
本文旨在对流线型模式及其分岔进行严格分析，涉及到热和质量传递的电流变塑性宾汉流体模型在复杂的波浪形微通道中的流动。宾汉流体在核心层充当固体介质，将通道分为三个不同的部分，用于将问题建模为这些区域之间的开关动力系统。为了跟踪多个稳态（停滞点）和相关的捕获现象，我们针对不同的物理效应（如双电层厚度和亥姆霍兹-斯莫卢霍夫斯基速度）对每个子系统进行了分析和数值分岔分析。这里提出的技术的关键特点是能够揭示宾汉流体模型在存在或不存在对称流动特性的情况下的蠕动传输特性。这里的主要新颖之处在于能够调节感兴趣域中平衡点的位置和稳定性。这导致了全局分岔的检测，反映了模型的重要动态元素。我们的结果强调了一种新的复杂行为类别，它控制了不同传输机制之间的转变，以及一类非经典的捕获现象。
