We present a comprehensive 3D numerical study of particles with imposed velocities relative to the local bulk flow (termed “slip velocities”) in a viscoelastic shear flow. We consider the force on a spherical particle sedimenting, a spherical bubble rising, and a spherical neutral squirmer swimming in an imposed viscoelastic shear flow. We demonstrate that any particle moving with a slip velocity in the flow or gradient direction of the shear flow experience a lateral lift force. We calculate and compare the magnitude and direction of the lift force in all situations. At small Deborah (De) and Weissenberg (Wi) numbers, our results show good agreement with an existing perturbation theory for rigid particles (Einarsson and Mehlig, 2017 [1]) and new perturbation theories for drops and for squirmers respectively. Our simulations extend these results to higher De and Wi regimes. Through our simulations, we uncover the physical mechanism of the lateral force on all particles. For rigid particles, we find the lift force arises from an imbalance in polymer stress on either side of the particle, which in turn is due to the imbalance of polymer stretch surrounding the particle. If this lift force is not balanced by an external force, a lateral drift velocity arises. We further consider the implication of this lateral drift for rigid particles hydrodynamically forced in a viscoelastic Poiseuille flow, where particles can migrate either toward the channel center plane or toward the wall, depending on whether the direction of the applied force is in the direction aligned or opposite to the direction of the Poiseuille flow, respectively. We study both the migration of a single particle as well as a suspension of particles in channel flow. Even with the addition of hydrodynamic interactions, we show that particles forced in the direction of the Poiseuille flow migrate towards the channel center.

我们对粘弹性剪切流中具有与局部体积流（称为“滑移速度”）有关的施加速度的粒子进行了全面的3D数值研究。我们考虑在施加的粘弹性剪切流中作用于球形颗粒沉降，球形气泡上升和球形中性发球体的力。我们证明，任何在剪切流的流动或梯度方向上以滑移速度运动的颗粒都会受到横向升力。我们计算并比较所有情况下的提升力的大小和方向。在较小的Deborah（De）和Weissenberg（Wi）数下，我们的结果表明与现有的刚性粒子扰动理论（Einarsson和Mehlig，2017 [1]）以及新的液滴和蠕动扰动理论具有良好的一致性。我们的模拟将这些结果扩展到更高的De和Wi体制。通过我们的模拟，我们发现了所有粒子上的横向力的物理机制。对于刚性颗粒，我们发现提升力是由颗粒两侧的聚合物应力不平衡引起的，这又是由于围绕颗粒的聚合物拉伸不平衡所致。如果该升力不能被外力平衡，则会产生横向漂移速度。我们进一步考虑了这种横向漂移对在粘弹性Poiseuille流中受流体动力作用的刚性粒子的影响，其中，粒子可以朝着通道中心平面或朝壁移动，具体取决于施加力的方向是对齐的方向还是方向。与Poiseuille流的方向相反。我们研究了单个颗粒的迁移以及通道流中颗粒的悬浮。即使增加了流体动力学相互作用，我们也显示了在泊瓦伊流中被迫的粒子向通道中心迁移。