Boundary conditions impermeable surface

A no-slip boundary condition is used on all impermeable solid surfaces, but the choice of boundary conditions for the inlet and outlet of the model is not so... 

The z boundary conditions specify both the extent of the region and the physical interaction of the material with the boundaries. It will be convenient in solving Eq. (5.14) to assume that an impermeable barrier to diffusion exists at a height z = H. Then the case of an unbounded region z 0 is obtained by letting //—> < . The surface (z = 0) boundary condition can be represented in general as... 

The boundary conditions (6.4.7), (6.4.8) stand for the non-slip of the fluid at the walls and impermeability of the walls for ions, respectively. The electrostatic (6.4.9), exact for a metal wall, is adopted here as the simplest physically meaningful condition corresponding to a given surface charge density of the wall (n in (6.4.9) stands for a unity outer normal). It will... 

At the impermeable wall boundaries of the solution domain, normally a no slip boundary condition is employed. This is achieved by setting the transverse fluid velocity equal to that of the surface and setting the normal velocity to zero. Since the normal velocity at the wall is known, the value of pressure at the wall boundary is not required to be known. For species concentrations or temperatures, any of the following conditions can be specified at the wall boundaries ... 

For single-phase turbulent reactor flows, the typical boundary conditions include impermeable solid walls, free surfaces, pressure boundaries, S3mimetry axis, inlet- and outlet conditions. 

Serious efforts have been made to explain the atypical lithium transport behavior using modified diffusion control models. In these models the boundary conditions -that is, "real potentiostatic constraint at the electrode/electrolyte interface and impermeable constraint at the back of the electrode - remain valid, while lithium transport is strongly influenced by, for example (i) the geometry of the electrode surface [53-55] (ii) growth of a new phase in the electrode [56-63] and (iii) the electric field through the electrode [48, 56]. 

If the surface = 0 is impermeable to the solute, then the boundary condition... 

If the surface is permeable to the flow as, for example, with a membrane, then there is also a finite flux normal to the surface. The extent to which the species permeates will depend on the rejection characteristics of the membrane, and we shall discuss this boundary condition later in connection with membrane filtration. Here, we suppose the surface to be impermeable so that u = 0, in which case at the reaction surface... 

The isothermal flow of incompressible liquid is described by equations (5.13) and (5.21), and the viscosity coefficient n = const. Hence, there are four equations for four unknowns - the pressure p and three velocity components u, v, and w. Thus, the system of equations is a closed one. For its solution it is necessary to formulate the initial and boundary conditions. Let us discuss now possible boundary conditions. Consider conditions at an interface between two mediums denoted as 1 and 2. The form and number of boundary conditions depends on whether the boundary surface is given or it should be found in the course of solution, and also from the accepted model of the continuum. Consider first the boundary between a non-viscous liquid and a solid body. Since the equations of motion of non-viscous liquid contain only first derivatives of the velocity, it is necessary to give one condition of the impermeability u i = u 2 at the boundary S, where u is the normal component of the velocity. The equations of motion of viscous liquid include the second-order derivatives, therefore at the boundary with a solid body it is necessary to assign two conditions following from the condition of sticking u i = u 2, Wii = u i where u is the tangential to S component of the velocity. If the boundary S is an interface between two different liquids or a liquid and a gas, then it is necessary to add the kinematic condition Ui = U2 =... 

Besides this confusion over v and F, it is further incoirect to confuse a thermodynamic quantity ifi) with a hydrodynamic one (F,). The quantity Fe was determined from the hydrodynamic theory of rigid, impermeable ellipsoids. However, the protein may not be ellipsoidal in shape, it may not be rigid in a hydrodynamic field, and it may not be impermeable to the flow of solvent. In addition, the hydrodynamic boundary condition of no slippage on the. surface of the particle may not be satisfied, and the... 

At all impermeable solid surfaces, a no-slip condition, that is, a zero velocity boundary condition, is assumed. Boundary conditions at the interface of the fluid flow channel and porous media are given on the basis of the assumption of continuity in the solutions of pressure and normal component velocity for the two adjacent regions. 

Hubbert (1967) described a trap for either oil or gas as an underground region of low potential for the respective fluid, which is either completely enclosed by equipotential surfaces and regions of higher potential, or else jointly enclosed by higher equipotential surfaces and an impermeable boundary. The potential of a unit mass of separate phase hydrocarbons in water-saturated rock under hydrodynamic conditions is given by... 

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