Zamankhan Parsa, Takayama Shuichi, Grotberg James B
Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.
ANSYS, Inc., 900 Victors way, Ann Arbor, MI 48108, USA.
Phys Rev Fluids. 2018 Jan;3(1). doi: 10.1103/PhysRevFluids.3.013302. Epub 2018 Jan 25.
Bingham fluids behave like solids below a von Mises stress threshold, the yield stress, while above it they behave like Newtonian fluids. They are characterized by a dimensionless parameter, Bingham number (Bn), which is the ratio of the yield stress to a characteristic viscous stress. In this study, the non-inertial steady motion of a finite size gas bubble in both a plane 2D channel and an axi-symmetric tube filled by a Bingham fluid has been studied numerically. The Bingham number, Bn, is in the range 0 ≤ Bn ≤ 3, where Bn=0 is the Newtonian case, while the Capillary number which is the ratio of a characteristic viscous force to the surface tension has values Ca=0.05, 0.10, and 0.25. The volume of all axi-symmetric and 2D bubbles has been chosen to be identical for all parameter choices and large enough for the bubbles to be long compared to the channel/tube width/diameter. The Bingham fluid constitutive equation is approximated by a regularized equation. During the motion, the bubble interface is separated from the wall by a static liquid film. The film thickness scaled by the tube radius (axi-symmetric)/half of the channel height (2D) is the dimensionless film thickness, . The results show that increasing Bn initially leads to an increase in , however, the profile versus Bn can be monotonic or non-monotonic depending on Ca values and 2D/axi-symmetric configurations. The yield stress also alters the shape of the front and rear of the bubble and suppresses the capillary waves at the rear of the bubble. The yield stress increases the magnitude of the wall shear stress and its gradient and therefore increases the potential for epithelial cell injuries in applications to lung airway mucus plugs. The topology of the yield surfaces as well the flow pattern in the bubble frame of reference varies significantly by Ca and Bn.
宾汉流体在低于冯·米塞斯应力阈值（即屈服应力）时表现得像固体，而在高于该阈值时则表现得像牛顿流体。它们由一个无量纲参数——宾汉数（Bn）来表征，宾汉数是屈服应力与特征粘性应力的比值。在本研究中，对有限尺寸气泡在二维平面通道和由宾汉流体填充的轴对称管中的非惯性稳态运动进行了数值研究。宾汉数Bn的取值范围为0≤Bn≤3，其中Bn = 0为牛顿流体情况，而毛细管数（特征粘性力与表面张力的比值）取值为Ca = 0.05、0.10和0.25。对于所有参数选择，所有轴对称和二维气泡的体积都被选为相同，并且足够大，使得气泡的长度相对于通道/管的宽度/直径较长。宾汉流体本构方程由一个正则化方程近似。在运动过程中，气泡界面通过一层静态液膜与壁面分离。用管半径（轴对称情况）/通道高度的一半（二维情况）缩放后的膜厚度即为无量纲膜厚度。结果表明，增加Bn最初会导致增加，然而， 与Bn的关系曲线可能是单调的，也可能是非单调的，这取决于Ca值和二维/轴对称构型。屈服应力还会改变气泡前后的形状，并抑制气泡后部的毛细波。屈服应力会增加壁面剪应力的大小及其梯度，因此在应用于肺气道粘液栓时会增加上皮细胞损伤的可能性。屈服面的拓扑结构以及气泡参考系中的流动模式会因Ca和Bn而有显著变化。
