AI 中文总结
本研究利用洛伦兹互易定理推导了斯托克斯流中局域力驱动的球形粘性液滴平移速度积分表达式，区分了内外力的不同响应，为构建可控远场的类squirmer液滴解奠定基础。
AI 中文摘要
粘性液滴内部或外部流体中的局域力可驱动液滴平移。利用洛伦兹互易定理，我们推导了球形牛顿液滴的平移速度积分表达式，该液滴受限于任意一种流体中的局域力与源分布，以及界面牵引力。对于清洁液滴，我们得到了其对斯托克斯子（Stokeslets）、力偶极子、旋转子（rotlets）、一般二阶力矩和源偶极子的显式响应，这些响应是位置、方向和粘度比的函数。内部力遵循有限选择规则：仅二阶及以下的力矩和一阶源矩直接对平移有贡献。外部力可与各阶多极子耦合，产生与距离相关的响应。尽管不同的 enclosed 奇点可产生相同的液滴速度，但通过以液滴为中心的球谐斯托克斯模式解析其外部流，可为潜在的力提供额外约束。我们还区分了由指定核矩控制的正则化力分布，以及由低阶表面牵引力矩和指定滑移控制的解析刚性颗粒。该框架统一了这些表示，并展示了外部流测量如何提供超出液滴平移的信息，为构建具有可控远场行为的类似 squirmer 的粘性液滴解奠定了基础。
英文摘要
Localized forcing in the fluid inside or outside a viscous drop can drive drop translation. Using the Lorentz reciprocal theorem, we derive an integral expression for the translational velocity of a spherical Newtonian drop subject to localized force and source distributions in either fluid and to interfacial traction. For a clean drop, we obtain explicit responses to Stokeslets, force dipoles, rotlets, general second force moments, and source dipoles as functions of position, orientation, and viscosity ratio. Interior forcing obeys a finite selection rule: only force moments through second order and the first source moment contribute directly to translation. Exterior forcing can couple to multipoles of all orders and produces distance-dependent responses. Although different enclosed singularities can produce the same drop velocity, resolving their exterior flows in drop-centered spherical Stokes modes provides additional constraints on the underlying forcing. We also distinguish regularized force distributions, governed by prescribed kernel moments, from resolved rigid particles, governed by low-order surface-traction moments and prescribed slip. The framework unifies these representations and shows how exterior-flow measurements provide information beyond drop translation, laying the foundation for constructing squirmer-like viscous drop solutions with controllable far-field behaviors.
Comments21 pages (15 pages of main text, and 6 pages of appendix), 2 figures, 2 tables
