Two Mechanisms For Segregating Mixtures Of Brownian Particles

We present two mechanisms for segregating mixtures of Brownian particles. In the firstrnmodel, we used a W-potential, which is piece-wise linear, with non-homogeneous temperaturernbackground to separate mixtures of two types of Brownian particles that differ in theirrndiffusion constants. We found closed form expression for the dynamics of the separation asrna function of the parameters characterizing the model. For a given set of model parameter,rnwe explored how the separation evolves with time and found it to take a maximum value at arnfinite time. We are specifically interested in how the barrier height affects the process of segregationrnand found that the best separation between the particles occurs at infinite potentialsrnwhich corresponds to waiting for infinite times. As such we optimized the segregation andrnfound the barrier height that gives us the optimized separation. In the second model, we usedrna periodic sawtooth potential, created by a uniform gravitational field, to separate mixtures ofrntwo types of Brownian particles. With the application of a small load and a non-homogeneousrntemperature background, we have shown that it is possible to separate two types of Brownianrnparticles that have different masses by making them move in opposite directions

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