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Is there any precise model (More precise than the random walk model) that describes a particle's movement in water ?

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Can you expand on your question a bit? Are you just considering Brownian motion, or do you mean motion in some arbitrary velocity field? If you're only interested in Brownian motion then the Wikipedia article describes several mathematical models of various complexities. –  John Rennie Jul 19 '12 at 9:43
    
Thank you for your answer. In fact, Brownian motion is not a precise model to study the advection diffusion problem for a particle. There are a lot of anomalies that rises when using such a model. I'm looking for more advanced or complex models that I can use to develop my own model for simulation purposes. –  Samatix Jul 19 '12 at 10:45
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