66,178 research outputs found

    Effective surface and boundary conditions for heterogeneous surfaces with mixed boundary conditions.

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    To deal with multi-scale problems involving transport from a heterogeneous and rough surface characterized by a mixed boundary condition, an effective surface theory is developed, which replaces the original surface by a homogeneous and smooth surface with specific boundary conditions. A typical example corresponds to a laminar flow over a soluble salt medium which contains insoluble material. To develop the concept of effective surface, a multi-domain decomposition approach is applied. In this framework, velocity and concentration at micro-scale are estimated with an asymptotic expansion of deviation terms with respect to macro-scale velocity and concentration fields. Closure problems for the deviations are obtained and used to define the effective surface position and the related boundary conditions. The evolution of some effective properties and the impact of surface geometry, Péclet, Schmidt and Damköhler numbers are investigated. Finally, comparisons are made between the numerical results obtained with the effective models and those from direct numerical simulations with the original rough surface, for two kinds of configurations

    Effective slip boundary conditions for flows over nanoscale chemical heterogeneities

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    We study slip boundary conditions for simple fluids at surfaces with nanoscale chemical heterogeneities. Using a perturbative approach, we examine the flow of a Newtonian fluid far from a surface described by a heterogeneous Navier slip boundary condition. In the far-field, we obtain expressions for an effective slip boundary condition in certain limiting cases. These expressions are compared to numerical solutions which show they work well when applied in the appropriate limits. The implications for experimental measurements and for the design of surfaces that exhibit large slip lengths are discussed.Comment: 14 pages, 3 figure

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

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    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

    Boundary induced non linearities at small Reynolds Numbers

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    We investigate the influence of boundary slip velocity in Newtonian fluids at finite Reynolds numbers. Numerical simulations with Lattice Boltzmann method (LBM) and Finite Differences method (FDM) are performed to quantify the effect of heterogeneous boundary conditions on the integral and local properties of the flow. Non linear effects are induced by the non homogeneity of the boundary condition and change the symmetry properties of the flow inducing an overall mean flow reduction. To explain the observed drag modification, reciprocal relations for stationary ensembles are used, predicting a reduction of the mean flow rate from the creeping flow to be proportional to the fourth power of the friction Reynolds number. Both numerical schemes are then validated within the theoretical predictions and reveal a pronounced numerical efficiency of the LBM with respect to FDM.Comment: 29 pages, 10 figure

    Mesoscopic modeling of heterogeneous boundary conditions for microchannel flows

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    We present a mesoscopic model of the fluid-wall interactions for flows in microchannel geometries. We define a suitable implementation of the boundary conditions for a discrete version of the Boltzmann equations describing a wall-bounded single phase fluid. We distinguish different slippage properties on the surface by introducing a slip function, defining the local degree of slip for mesoscopic molecules at the boundaries. The slip function plays the role of a renormalizing factor which incorporates, with some degree of arbitrariness, the microscopic effects on the mesoscopic description. We discuss the mesoscopic slip properties in terms of slip length, slip velocity, pressure drop reduction (drag reduction), and mass flow rate in microchannels as a function of the degree of slippage and of its spatial distribution and localization, the latter parameter mimicking the degree of roughness of the ultra-hydrophobic material in real experiments. We also discuss the increment of the slip length in the transition regime, i.e. at O(1) Knudsen numbers. Finally, we compare our results with Molecular Dynamics investigations of the dependency of the slip length on the mean channel pressure and local slip properties (Cottin-Bizonne et al. 2004) and with the experimental dependency of the pressure drop reduction on the percentage of hydrophobic material deposited on the surface -- Ou et al. (2004).Comment: 21 pages, 10 figure

    Effective Surface and Boundary Condition for Heterogeneous Salt Media with Insoluble Material

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    Effective Surface and Boundary Condition for Heterogeneous Salt Media with Insoluble Materia

    Analysis of the land surface heterogeneity and its impact on atmospheric variables and the aerodynamic and thermodynamic roughness lengths

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    The land surface heterogeneity has a very significant impact on atmospheric variables (air temperature T-a, wind speed u, and humidity q), the aerodynamic roughness length z(0m), thermodynamic roughness length z(0h), and the excess resistance to heat transfer kB(-1). First, in this study the land surface heterogeneity has been documented through the comparison of surface reflectance r(0), surface temperature T-0, net radiation flux R-n, and sensible heat flux H partitioning over the different land cover types in the experimental areas of the Global Energy and Water Cycle Experiment (GEWEX) Asian Monsoon Experiment on the Tibetan Plateau (GAME/Tibet), the Coordinated Enhanced Observing Period (CEOP) Asia-Australia Monsoon Project on the Tibetan Plateau (CAMP/Tibet), the Heihe Basin Field Experiment (HEIFE), the Arid Environment Comprehensive Monitoring Plan, 95 (AECMP' 95), and the Dun Huang Experiment (DHEX). The results show that the surface heterogeneity was very significant in the areas of the HEIFE, the AECMP' 95, and the DHEX and that it was less significant in the areas of CAMP/Tibet and GAME/Tibet. Second, the vertical profiles of T-a, u, and q in the near-surface layer and above the blending height z(b) have been analyzed using the atmospheric boundary layer (ABL) tower data, radiosonde data, and tethered balloon data observed during the HEIFE, the DHEX, and the CAMP/Tibet. The results show that the land surface heterogeneity leads in the near-surface layer to different vertical profiles of u, T-a, and q overlying the surfaces of the Gobi and the oasis in the areas of the HEIFE and DHEX. The values of u, T-a, and q become well mixed above a height of about 300 m at the HEIFE and 150 m at the DHEX. z(0m), z(0h), and kB(-1) over the different land surfaces have also been determined in this study. The results show that the land surface heterogeneity leads to different aerodynamic and thermodynamic parameters over the areas of the HEIFE, the AECMP' 95, and the GAME/Tibe

    Mesoscopic modeling of a two-phase flow in the presence of boundaries: the Contact Angle

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    We present a mesoscopic model, based on the Boltzmann Equation, for the interaction between a solid wall and a non-ideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas, the liquid-solid and the gas-solid phases. We study the dependency of the contact angle on the two free parameters of the model, which determine the interaction between the fluid and the boundaries, i.e. the equivalent of the wall density and of the wall-fluid potential in Molecular Dynamics studies. We compare the analytical results obtained in the hydrodynamical limit for the density profile and for the surface tension expression with the numerical simulations. We compare also our two-phase approach with some exact results for a pure hydrodynamical incompressible fluid based on Navier-Stokes equations with boundary conditions made up of alternating slip and no-slip strips. Finally, we show how to overcome some theoretical limitations connected with a discretized Boltzmann scheme and we discuss the equivalence between the surface tension defined in terms of the mechanical equilibrium and in terms of the Maxwell construction.Comment: 29 pages, 12 figure

    A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces

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    A type of super-hydrophobic surface consists of a solid plane boundary with an array of grooves which, due to the effect of surface tension, prevent a complete wetting of the wall. The effect is greatest when the grooves are aligned with the flow. The pressure difference between the liquid and the gas in the grooves causes a curvature of the liquid surface resisted by surface tension. The effects of this surface deformation are studied in this paper. The corrections to the effective slip length produced by the curvature are analyzed theoretically and a comparison with available data and related mathematical models is presented.Comment: 19 pages, 5 figure
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