DBS&H CEME, National University of Sciences and Technology, Islamabad, Pakistan.
Department of Mechanical Engineering, Manipal University Jaipur 303007, India.
Math Biosci. 2018 Jul;301:121-128. doi: 10.1016/j.mbs.2018.04.001. Epub 2018 Apr 6.
In this paper, we present an analytical study of pressure-driven flow of micropolar non-Newtonian physiological fluids through a channel comprising two parallel oscillating walls. The cilia are arranged at equal intervals and protrude normally from both walls of the infinitely long channel. A metachronal wave is generated due to natural beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. Appropriate expressions are presented for deformation via longitudinal and transverse velocity components induced by the ciliary beating phenomenon with cilia assumed to follow elliptic trajectories. The conservation equations for mass, longitudinal and transverse (linear) momentum and angular momentum are reduced in accordance with the long wavelength and creeping Stokesian flow approximations and then normalized with appropriate transformations. The resulting non-linear moving boundary value problem is solved analytically for constant micro-inertia density, subject to physically realistic boundary conditions. Closed-form expressions are derived for axial velocity, angular velocity, volumetric flow rate and pressure rise. The transport phenomena are shown to be dictated by several non-Newtonian parameters, including micropolar material parameter and Eringen coupling parameter, and also several geometric parameters, viz eccentricity parameter, wave number and cilia length. The influence of these parameters on streamline profiles (with a view to addressing trapping features via bolus formation and evolution), pressure gradient and other characteristics are evaluated graphically. Both axial and angular velocities are observed to be substantially modified with both micropolar rheological parameters and furthermore are significantly altered with increasing volumetric flow rate. Free pumping is also examined. An inverse relationship between pressure rise and flow rate is computed which is similar to that observed in Newtonian fluids. The study is relevant to hemodynamics in narrow capillaries and also bio-inspired micro-fluidic devices.
本文针对由两个平行振荡壁组成的通道内通过的偶极粘性非牛顿生理流体的压力驱动流动进行了分析研究。纤毛以相等的间隔排列并从无限长通道的两个壁正常突出。由于纤毛的自然拍打而产生了蠕动波，并且波的传播方向与流体流动的方向平行。通过纤毛拍打现象引起的纵向和横向速度分量的变形给出了适当的表达式，假设纤毛沿椭圆轨迹运动。根据长波长和蠕动 Stokes 流近似，将质量、纵向和横向（线性）动量以及角动量守恒方程进行了简化，然后通过适当的变换进行了归一化。对于恒定的微惯性密度，针对物理现实的边界条件，对非线性运动边界值问题进行了分析求解。导出了轴向速度、角速度、体积流量和压力上升的封闭形式表达式。结果表明，传输现象由几个非牛顿参数决定，包括偶极材料参数和 Eringen 耦合参数，以及几个几何参数，即偏心率参数、波数和纤毛长度。这些参数对流线型轮廓（旨在通过形成和演化的团块来解决捕获特征）、压力梯度和其他特性的影响以图形方式进行了评估。轴向和角速度都明显受到偶极流变参数的影响，此外，随着体积流量的增加而发生显著变化。还研究了自由泵送。计算出压力上升和流量之间的反比关系，这与牛顿流体中的观察结果相似。该研究与狭窄毛细血管中的血液动力学以及仿生微流体装置有关。
