双介质楔形几何中的泳动相互作用
Phoretic interactions in two-medium wedge geometries
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中文总结 AI 辅助
本文针对双介质楔形几何中极限佩克莱数与雷诺数下的活性胶体扩散泳动，采用傅里叶-孔托罗维奇-列别杰夫变换得到精确解，揭示几何与界面性质对泳动的调控作用，为受限多相环境的泳动输运控制提供了框架。
中文摘要 AI 辅助
我们研究了三维楔形几何中化学各向同性活性胶体的扩散泳动，该楔形由两种不同流体介质形成，且处于佩克莱数（Péclet）和雷诺数（Reynolds）均趋近于零的极限情况。通过傅里叶-孔托罗维奇-列别杰夫变换（Fourier-Kontorovich-Lebedev transform）获得浓度场，得到了适用于任意楔形开口角和界面对比度的精确表达式。我们引入界面参数Γ=(1−λℓ)/(1+λℓ)，其中λ表示扩散率对比度，ℓ表示溶质分配系数。当Γ=±1且楔形角可公度时，解简化为有限镜像构造，偶可公度与奇可公度对应不同结构。该通解还可还原出平面界面和半无限界面的极限情况。从浓度场推导得到主导阶平移泳动速度，揭示了楔形几何与界面性质之间的强相互作用，这种相互作用决定了粒子运动的大小和方向。本研究为理解和控制受限多相环境中的泳动输运提供了框架，并为扩展到有限尺寸几何以及混合流体-流体和固体边界条件奠定了基础，研究结果可应用于控制受限多相环境中活性粒子的输运，在此环境中可利用界面性质和几何来调节泳动运动。
英文摘要
We investigate the diffusiophoretic motion of a chemically isotropic active colloid in a three-dimensional wedge formed by two distinct fluid media, in the limit of vanishing Péclet and Reynolds numbers. The concentration field is obtained using the Fourier-Kontorovich-Lebedev transform, yielding an exact representation for arbitrary wedge opening angles and interfacial contrasts. We introduce the interfacial parameter $Γ=(1-λ\ell)/(1+λ\ell)$, where $λ$ denotes the diffusivity contrast and $\ell$ the solute partition coefficient. For $Γ=\pm1$ and commensurate wedge angles, the solution reduces to finite image constructions, with distinct structures for even and odd commensurability. The general solution also recovers the planar-interface and semi-infinite-interface limits. The leading-order translational phoretic velocity is derived from the concentration field, revealing a strong interplay between wedge geometry and interfacial properties that governs both the magnitude and direction of particle motion. This work provides a framework for understanding and controlling phoretic transport in confined multiphase environments and offer a basis for extensions to finite-size geometries and mixed fluid--fluid and solid boundary conditions. Our results may find applications in the control of active-particle transport in confined multiphase environments, where interfacial properties and geometry can be exploited to tune phoretic motion.
发表机构
- School of Mathematics and Statistics, The Open University（开放大学数学与统计学院）
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