胶体中的耗尽效应：相关的布朗运动
On the Depletion Effect in Colloids: Correlated Brownian Motions
摘要：
我们的目标是制定和分析一个物理上合理的和数学上合理的模型，以更好地理解在胶体分散体的结块现象。我们的模型是随机的，但严格来自一个确定性的设置在牛顿设置。一个严格的过渡，从确定性的平均场动力学的几个大粒子和无限多的小粒子的随机运动的大粒子被调用。然后用关联布朗运动系统描述大颗粒的随机运动。转换中的缩放保持特征相关长度。从极限随机方程，我们计算两个大粒子之间的分离的概率通量。我们表明，在短时间内，两个粒子足够接近，往往会相互吸引。这与胶体中观察到的耗尽现象相一致。为了进行这种计算，我们以适当的方式扩展了Van Kampen的一维通量率的概念，以考虑高维效应。
英文摘要：
Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clumping in colloid dispersions. Our model is stochastic but rigorously derived from a deterministic setup in a Newtonian setting. A rigorous transition from deterministic mean-field dynamics of several large particles and infinitely many small particles to the stochastic motion of the large particles is invoked. Then the stochastic motion of the large particles is described by a system of correlated Brownian motions. The scaling in the transition preserves a characteristic correlation length. From the limiting stochastic equations we compute the probability fluxes for the separation between two large particles. We show that, for short times, two particles sufficiently close together tend to be attracted to each other. This agrees with the observed depletion phenomena in colloids. To do this computation, we extend the notion of Van Kampen's one-dimensional flux rate in an appropriate way to account for higher dimensional effect.
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