In this work, we theoretically investigate the motion of an arbitrarily shaped particle in a linear density stratified fluid with weak stratification and negligible inertia. We calculate the hydrodynamic force and torque experienced by the particle using the method of matched asymptotic expansions. We analyse our results for two classes of particles (non-skew and skew) depending on whether the particle possesses a centre of hydrodynamic stress. For both classes, we derive general expressions for the modified resistance tensors in the presence of stratification. We demonstrate the application of our results by considering some specific examples of particles settling in a direction parallel to the density gradient by considering both the limits of high ( $Pe\gg 1$ ) and low ( $Pe\ll 1$ ) Peclet numbers. We find that presence of stratification causes a slender body to rotate and settle along the broader side due to the contribution of the hydrostatic torque. Our work sheds light on the impact of stratification on the transport of arbitrarily shaped particles in density stratified environments in low-Reynolds-number regimes.

中文翻译：

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密度分层流体中任意形状粒子的运动

在这项工作中，我们从理论上研究了任意形状粒子在线性密度分层流体中的运动，该流体具有弱分层和可忽略的惯性。我们使用匹配渐近展开的方法计算粒子所经历的流体动力和扭矩。我们根据粒子是否具有流体动力应力中心来分析两类粒子（非偏斜和偏斜）的结果。对于这两类，我们推导出存在分层的修正阻力张量的一般表达式。我们通过考虑高 ( $Pe\gg 1$ ) 和低 ( $Pe\ll 1$ ) Peclet 数的限制，通过考虑一些粒子在平行于密度梯度的方向沉降的特定示例来证明我们的结果的应用. 我们发现，由于静水扭矩的贡献，分层的存在会导致细长的物体沿较宽的一侧旋转和沉降。我们的工作阐明了分层对低雷诺数制度下密度分层环境中任意形状颗粒传输的影响。