离子释放胶体粒子的互易定理
Reciprocal theorem for ion-releasing colloidal particles
AI总结：
研究离子释放胶体粒子互易定理，通过考虑催化粒子周围二次云影响即过量电荷\(Q\)，推导相关方程，展示其在多种粒子运动中的应用，发现额外项对粒子迁移率有不同影响，还讨论了与微游动器相互作用的相关性。
AI中文摘要：
我们描述了悬浮在电解质溶液中且受电场作用（电场可以是外加的或自发产生的）的粒子的互易定理的推广。重点关注释放离子的催化胶体。该推广的作用在于捕捉催化粒子周围二次云形成的影响，这等同于考虑系统的过量电荷\(Q\)。结果表明催化粒子的推进速度有与\(Q\)和外场\(E_{\infty}\)成比例的额外贡献。推导的\(Q\)的方程表明其符号由离子扩散率的差异定义，大小由表面离子的平均通量控制。我们展示了广义定理在均匀释放离子的被动粒子的电泳和扩散泳以及非均匀活性粒子（微游动器）的自推进中的应用。结果表明，在某些情况下互易定理中的额外项消失或对粒子迁移率影响很小，但在许多其他情况下它可能显著改变其大小甚至符号。此外，还简要讨论了我们的结果与微游动器相互作用的相关性。
英文摘要：
We describe a generalization of the reciprocal theorem for particles suspended in electrolyte solutions and subjected to an electric field that could be either applied or emerged spontaneously. Attention is focused on catalytic colloids that release ions. The power of the generalization is to capture the effect of formation of a secondary cloud around a catalytic particle, which is equivalent to accounting for an excess charge $Q$ of a system. Our results show that the propulsion speed of catalytic particles has an extra contribution proportional to $Q$ and an external field $E_{\infty}$. The derived equation for $Q$ reveals that its sign is defined by the difference in the ion diffusivity and the magnitude is controlled by the average flux of ions from the surface. We demonstrate the application of the generalized theorem to electro- and diffusiophoresis of homogeneously releasing ions passive particles, as well as to a self-propulsion of inhomogeneous active particles (microswimmers). It is shown that whilst in some situations the extra term in the reciprocal theorem vanishes or has a little effect on the particle mobility, in many others it may dramatically change its magnitude, and even sign. In addition, the relevance of our results for microswimmer interactions is discussed briefly.
