A theoretical study is conducted for magnetohydrodynamic pumping of electro-conductive couple stress physiological liquids (e.g. blood) through a two-dimensional ciliated channel. A geometric model is employed for the cilia which are distributed at equal intervals and produce a whip-like motion under fluid interaction which obeys an elliptic trajectory. A metachronal wave is mobilized by the synchronous beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. A transverse static magnetic field is imposed transverse to the channel length. The Stokes’ couple stress (polar) rheological model is utilized to characterize the liquid. The normalized two-dimensional conservation equations for mass, longitudinal and transverse momentum are reduced with lubrication approximations (long wavelength and low Reynolds number assumptions) and feature a fourth order linear derivative in axial velocity representing couple stress contribution. A coordinate transformation is employed to map the unsteady problem from the wave laboratory frame to a steady problem in the wave frame. No slip conditions are imposed at the channel walls. The emerging linearized boundary value problem is solved analytically and expressions presented for axial (longitudinal) velocity, volumetric flow rate, shear stress function and pressure rise. The flow is effectively controlled by three geometric parameters, viz cilia eccentricity parameter, wave number and cilia length and two physical parameters, namely magnetohydrodynamic (MHD) body force parameter and couple stress non-Newtonian parameter. Analytical solutions are numerically evaluated with MATLAB software. Axial velocity is observed to be enhanced in the core region with greater wave number whereas it is suppressed markedly with increasing cilia length, couple stress and magnetic parameters, with significant flattening of profiles with the latter two parameters. Axial pressure gradient is decreased with eccentricity parameter whereas it is elevated with cilia length, in the channel core region. Increasing couple stress and magnetic field parameter respectively enhance and suppress pressure gradient across the entire channel width. The pressure-flow rate relationship is confirmed to be inversely linear and pumping, free pumping and augmented pumping zones are all examined. Bolus trapping is also analyzed. The study is relevant to MHD biomimetic blood pumps.

进行了理论研究，以通过二维纤毛通道对电磁耦合应力生理液体（例如血液）进行磁流体动力泵送。对于纤毛采用几何模型，该几何模型以相等的间隔分布，并在服从椭圆形轨迹的流体相互作用下产生鞭状运动。纤毛的同步跳动动了一个准时波，波的传播方向与流体的流动方向平行。横向于通道长度施加横向静磁场。斯托克斯的耦合应力（极性）流变模型用于表征液体。质量的归一化二维守恒方程，纵向和横向动量可通过润滑近似值（长波长和低雷诺数假设）降低，并且在轴向速度上具有四阶线性导数，表示偶数应力的贡献。采用坐标变换将非稳定问题从波浪实验室框架映射到波浪框架中的稳定问题。在通道壁上不施加任何滑移条件。通过解析解决了新兴的线性化边值问题，并给出了轴向（纵向）速度，体积流量，切应力函数和压力升高的表达式。通过三个几何参数有效地控制流量，即纤毛偏心率参数，波数和纤毛长度以及两个物理参数，即磁流体动力学（MHD）体力参数和耦合应力非牛顿参数。使用MATLAB软件对分析解决方案进行数值评估。观察到轴心速度在核心区域随波数增加而增强，而随着纤毛长度，耦合应力和磁参数的增加而明显受到抑制，而后两个参数使轮廓显着展平。在通道中心区域，轴向压力梯度随偏心率参数而降低，而随纤毛长度而升高。耦合应力和磁场参数的增加分别增强和抑制了整个通道宽度上的压力梯度。确认压力-流量关系呈反线性关系，并且检查了泵送，自由泵送和扩大的泵送区域。还分析了团块捕获。这项研究与MHD仿生血泵有关。