Stratification local density

Stratification, as illustrated by the plots in Figs. 5.4-5.G, is due to constraints on the packing of molecules next to the substrate surface and is therefore largely determined by the repulsive part of the intermolecular potential [38). Stratification is observed even in the complete absence of intermolecular attractions, such as in the case of a hard-sphere fluid confined between planar hard walls [165-167]. For this system Evans et al. [168] demonstrated that, as a consequence of the damped oscillatory character of the local density in the vicinity of the walls, is itself a damped oscillatory function of s, if s is of the order of a few molecular diameters, which is confirmed by the plot in Fig. 5.3. 

This argiimcntation is further supported by the predictions of a simple mean-field theory of the ferroelectric transition, which was originally presented in Ref. 257. Within this theory, we neglect any stratification (i.e., inhomogeneities of the local density) as well as any oscillations in the order parameter (which are indeed observed in the computer simulations). We also neglect nontrivial interparticle correlations. Our system can then be viewed as a system composed of N uncorrelated dipolar particles individually interacting with the mean field... 

Appropriate initial and boundary conditions should also be added to complete the mathematical formulation. In Equation (1) C(r,t) is the local concentration vector, F(C 5) a vector function representing the reaction kinetics, B stands for a set of control parameters and D is the matrix of transport coefficients. In most chemical systems involving small molecules in aqueous solutions, the diffusion processes are well described by a diagonal matrix with constant positive diffusion coefficients. However, in some systems it is the coupling between the transport processes that provides the engine of the instability. For instance, stratification occurs in electron-hole plasmas in semiconductors subjected to electromagnetic radiations because of the effect of the temperature field on the carrier density distribution (thermodiffusion)... 

Since the temperature difference across the Uquid-liquid interface between the two layers is small, of the order of 0.1-1.0 K, the ntixing effect of thermally driven molecular diffusion in the absence of any convective motion is relatively small. The associated density difference across the Uquid-liquid interface acts so as to suppress local convective mixing and the stratification is therefore extremely stable. 

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