Flow boundary condition

P. A. Thompson, M. O. Robbins. Shear flow near solids epitaxial order and flow boundary conditions. Phys Rev A 47 6830-6837, 1990. 

FlameMaster v3.3 A C+ + Computer Program for OD Combustion and ID Laminar Flame Calculations. FlameMaster was developed by H. Pitsch. The code includes homogeneous reactor or plug flow reactors, steady counter-flow diffusion flames with potential flow or plug flow boundary conditions, freely propagating premixed flames, and the steady and unsteady flamelet equations. More information can be obtained from http //www.stanford.edu/group/pitsch/Downloads.htm. 

Bhidayasiri, R., S. Sivasegaram, and J. H. Whitelaw. 1997. The effect of flow boundary conditions on the stability of quarl stabilized flames. Combustion Science Technology 123 185-205. 

The theoretical results are evaluated through comparison with results of numerical integrations for the counterflow configuration with potential-flow boundary conditions. 

At the bottom of the soil profile, a Neumann-type no-flow boundary condition is specified as... 

In this chapter we review molecular dynamics simulations of thin films confined between two surfaces under shear. Potential models, temperature regulation methods, and simulation techniques are presented. Three properties (friction, shear viscosity, and flow boundary condition) that relate the dynamic response of confined thin films to the imposed shear velocity are presented in detail. 

In this chapter we review the application of MD techniques to the study confined thin films under shear. Three properties of particular interest are friction, shear viscosity, and flow boundary condition. For nanometer-scale material properties such as indentation and adhesion, we refer the reader to a recent review by Harrison and Brenner [49],... 

One of the fundamental assumptions in fluid mechanical formulations of Newtonian flow past solids is the continuity of the tangential component of velocity across a boundary known as the "no-slip" boundary condition (BC) [6]. Continuum mechanics with the no-slip BC predicts a linear velocity profile. However, recent experiments which probe molecular scales [7] and MD simulations [8-10] indicate that the BC is different at the molecular level. The flow boundary condition near a surface can be determined from the velocity profile. In molecular simulations, the velocity profile is calculated in a simitar way to the calculation of the density profile. The region between the walls is divided into a sufficient number of thin slices. The time averaged density for each slice is calculated during a simulation. Similarly, the time averaged x component of the velocity for all particles in each slice is determined. The effect of wall-fluid interaction, shear rate, and wall separation on velocity profiles, and thus flow boimdary condition will be examined in the following. 

In the SFA experiments there is no way to determine whether shear occurs primarily within the film or is localized at the interface. The assumption, made by experimentalists, of a no-slip flow boundary condition is invalid when shear localizes at the interface. It has also not been possible to examine structural changes in shearing films directly. MD simulations offer a way to study these properties. Simulations allow one to study viscosity profiles of fluids across the slab [21], local effective viscosity inside the solid-fluid interface and in the middle part of the film [28], and actual viscosity of confined fluids [29]. Manias et al. [28] found that nearly all the shear thinning takes place inside the adsorbed layer, whereas the response of the whole film is the weighted average of the viscosity in the middle and inside the interface. Furthermore, MD simulations also allow one to examine the structures of thin films during a shear process, resulting in an atomic-scale explanation [12] of the stick-slip phenomena observed in SFA experiments of boundary lubrication [7]. 

Three properties of fluids under shear are discussed in detail flow boundary condition, friction, and shear viscosity. It has been shown that the no-slip boundary condition assumed in fluid mechanical formulations of Newtonian flow past solids can fail at the molecular level. The velocity profiles deviate most from the continuum linear form at small pore separations, low temperatures, high pressures, and high shear rates. Friction is controlled by two factors - interfacial strength and in-plane ordering. 

For flows in conventional channels, the flow dimensions are much larger than the molecular mean free path. Therefore, fluid properties are determined primarily by intermolecular colUsions. As the channel size is reduced, the molecular mean free path becomes comparable to channel size. Intermolecular colhsions lose their importance and the interactions between the fluid and the wall become significant. The derivations of the shp flow boundary conditions using the kinetic theory of gases will be shown based on the derivations of [2] and [3] and are explained in the following manuscript in this book [4]. Briefly, the first order velocity shp is given by ... 

Using the integral transform method, [25] solved for the Nusselt number for flow in a rectangular microchannel subject to the constant temperature and slip flow boundary conditions. 

Because the electroosmotic flow field reaches steady state in milli-seconds, much shorter than the characteristic time scales of the sample loading and sample dispensing. Therefore, the electroosmotic flow here is approximated as steady state. Furthermore, we consider thin electrical double layer, and use the slip flow boundary condition to represent the electroosmotic flow. The liquid flow field can thus be described by the following non-dimensional momentum equation and the continuity equation. 

P. A. Thompson and M. O. Robbins, Phys. Rev. A, 41, 6830 (1990). Shear Flow Near Solids—Epitaxial Order and and Flow Boundary Conditions. 

This equation can be integrated subject to the electrokinetic and flow boundary conditions... 

This example is to test the swelling effects under capillary pressures up to 10 Pa occurring in extremely low-permeable bentonite materials. For this purpose, a simple 1-D case is set up. A one meter long bentonite column is heated on the left hand side. Element discretization length is 0.01m. The initial conditions of the system are atmospheric gas pressure, full liquid saturation and a temperature of 12°C. The heater has a constant temperature of 1(X) C. Flow boundary conditions on the left side are gas pressure of 10 Pa and 15% liquid saturation. On the right side we have atmospheric pressure, full liquid saturation and no diffusive heat flux. As a consequence, a typical desaturation process of bentonite is triggered. The complete set of initial and boundary conditions and the material properties for this example was described in detail by Kolditz De Jonge (2003). 

Boundary condition (1). Water flow boundary condition the side parallel with x axis is a water stop boundary, the side parallel with y axis is the boundary with constant water head. 

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