受限剪切流中持续释放活性粒子的稳态输运
Steady transport of active particles under continuous release in confined shear flow
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中文总结 AI 辅助
本研究建立受限剪切流中持续释放活性粒子稳态输运的空间理论，经模拟验证，揭示了不同条件下活性粒子的浓度分布与迁移规律。
中文摘要 AI 辅助
持续释放是输运过程中的基本源条件，但现有理论研究多聚焦于被动溶质的下游浓度发展，或活性粒子的充分发展截面分布。我们针对受限剪切流中持续释放活性粒子的稳态输运问题，建立空间理论，求解从入口到远场的浓度场。基于Smoluchowski方程，我们构建含点源入口通量与边界条件的边值问题，将流向坐标与截面变量分离，得到非自伴广义特征值问题，叠加其空间模态以构造解。在Galerkin谱框架内求解该特征问题，保留下游可容许模态，通过加权双正交展开由入口通量确定模态系数。与基于个体的模拟结果吻合良好，验证了该理论。对于对流主导条件下的平面泊肃叶流，我们发现球形粒子在早期发展区存在显著的位置-取向相干性：游动与剪切取向使种群经历连续角阶段，在下游产生交替的偏中心与中心线富集区，而扩散逐渐削弱该相干性。粒子伸长增强取向对齐，产生早期三峰垂直分布，下游形成更强、更持久的侧向富集，同时降低向心迁移的相干性，从而抑制次级中心线富集。流向边际浓度呈非单调变化，反映平均流向速度的变化，其远场极限为渐近漂移速度的倒数。
英文摘要
Continuous release is a fundamental source condition in transport, yet theoretical treatments have focused on downstream concentration development for passive solutes or fully developed cross-sectional distributions of active particles. We develop a spatial theory for the steady transport of active particles under continuous release in confined shear flows, resolving the concentration field from the inlet to the far field. Based on the Smoluchowski equation, we formulate a boundary-value problem with point-source inlet flux and boundary conditions. Separation of the streamwise coordinate from the cross-sectional variables yields a non-self-adjoint generalized eigenvalue problem, whose spatial modes are superposed to construct the solution. The eigenproblem is solved within a Galerkin spectral framework; downstream-admissible modes are retained and their coefficients determined from the inlet flux through a weighted biorthogonal expansion. Excellent agreement with individual-based simulations validates the theory. For plane Poiseuille flow under convection-dominated conditions, we find pronounced position--orientation coherence for spherical particles in the early developing region: swimming and shear reorientation drive the population through successive angular stages, generating alternating off-centre and centreline accumulation regions downstream, while dispersion progressively weakens this coherence. Particle elongation enhances orientational alignment, producing an early three-peaked vertical profile and stronger, more persistent lateral accumulation downstream, while reducing the coherence of centreward migration and thereby suppressing secondary centreline accumulation. The streamwise marginal concentration varies non-monotonically, reflecting changes in the mean streamwise velocity, with its far-field limit given by the reciprocal of the asymptotic drift velocity.
