Boundary conditions stochastic coupling

We begin in Section II with a review of the fundamental concepts of hydrodynamics and boundary conditions. In Section III, we present some common descriptions of coupling, followed in Section IV by a discussion of viscoelastic adsorbate films and the so-called inner slip. In Section V, we consider with the concept of stochastic boundary conditions, which we believe will be an important topic in situations where random fluctuations are strong. Finally, in Section VI, we present our concluding ideas and discuss some areas for future study. 

Inner slip, between the solid wall and an adsorbed film, will also influence the surface-liquid boundary conditions and have important effects on stress propagation from the liquid to the solid substrate. Linked to this concept, especially on a biomolecular level, is the concept of stochastic coupling. At the molecular level, small fluctuations about the ensemble average could affect the interfacial dynamics and lead to large shifts in the detectable boundary condition. One of our main interests in this area is to study the relaxation time of interfacial bonds using slip models. Stochastic boundary conditions could also prove to be all but necessary in modeling the behavior and interactions of biomolecules at surfaces, especially with the proliferation of microfluidic chemical devices and the importance of studying small scales. 

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