Molecular diffusion and slip boundary conditions at smooth surfaces with periodic and random nanoscale textures

The influence of periodic and random surface textures on the flow structure and effective slip length in Newtonian fluids is investigated by molecular dynamics (MD) simulations. We consider a situation where the typical pattern size is smaller than the channel height and the local boundary conditions at wetting and nonwetting regions are characterized by finite slip lengths. In case of anisotropic patterns, transverse flow profiles are reported for flows over alternating stripes of different wettability when the shear flow direction is misaligned with respect to the stripe orientation. The angular dependence of the effective slip length obtained from MD simulations is in good agreement with hydrodynamic predictions provided that the stripe width is larger than several molecular diameters. We found that the longitudinal component of the slip velocity along the shear flow direction is proportional to the interfacial diffusion coefficient of fluid monomers in that direction at equilibrium. In case of random textures, the effective slip length and the diffusion coefficient of fluid monomers in the first layer near the heterogeneous surface depend sensitively on the total area of wetting regions.Comment: 30 pages, 11 figure

Influence of periodic wall roughness on the slip behaviour at liquid/solid interfaces: molecular-scale simulations versus continuum predictions

The influence of surface roughness on the slip behaviour of a Newtonian liquid in steady planar shear is investigated using three different approaches, namely Stokes flow calculations, molecular dynamics (MD) simulations and a statistical mechanical model for the friction coefficient between a corrugated wall and the first liquid layer. These approaches are used to probe the behaviour of the slip length as a function of the slope parameter ka = 2πa/λ, where a and λ represent the amplitude and wavelength characterizing the periodic corrugation of the bounding surface. The molecular and continuum approaches both confirm a monotonic decay in the slip length with increasing ka but the rate of decay as well as the magnitude of the slip length obtained from the Stokes flow solutions exceed the MD predictions as the wall feature sizes approach the liquid molecular dimensions. In the limit of molecular-scale wall corrugation, a Green–Kubo analysis based on the fluctuation–dissipation theorem accurately reproduces the MD results for the behaviour of the slip length as a function of a. In combination, these three approaches provide a detailed picture of the influence of periodic roughness on the slip length which spans multiple length scales ranging from molecular to macroscopic dimensions

Molecular Origin and Dynamic Behavior of Slip in Sheared Polymer Films

The behavior of the slip length in thin polymer films subject to planar shear is investigated using molecular dynamics simulations. At low shear rates, the slip length extracted from the velocity profiles correlates well with that computed from a Green-Kubo analysis. Beyond chain lengths of about N = 10, the molecular weight dependence of the slip length is dominated strongly by the bulk viscosity. The dynamical response of the slip length with increasing shear rate is well captured by a power law up to a critical value where the momentum transfer between wall and fluid reaches its maximum

Approaching the losses caused by imperfect short-term financing at the Russian farms

This study investigates whether an insufficient short-term financing causes losses for Russian agricultural farm and what is their upper boundary. The modified Bayesian formalism provides a workaround for scarce and in-complete data in our data set. This formalism is incorporated into the objective function of an optimisation model so that this function expresses the empirical dependence of profit on cash flow and debts. The model seeks for the optimal quarterly cash flow distribution within a year. Empirical application employs the data from 60 quarterly reports of six agricultural enterprises in the Moscow Region in 1995-1998. The losses per total farm expenses vary from 2.2 to 42.6% depending on a farm and a year. In more than a half of cases they are greater than 10%. The opportunities to improve farm financial performance can be revealed from individual changes in the quarterly cash flow distribution.imperfect short-term financing losses Russian agriculture Bayesian scarce missed data