Flow boundary slip

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. 

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. 

Assuming the flow to be in the positive x-direction, we have set y- -duldr since y must be positive. The boundary conditions with no slip at the wall and with the shear continuous at the plug flow boundary r = r are... 

Continuum flow with slip boundary conditions (10- [Pg.27]

The term mass flow was coined to describe converging flow with slip taking place on the boundary surfaces of the confining container. The meaning of the term has been extended in use, to describe the situation of total movement of bin contents. This essentially requires the material to slip on all contact surfaces of the container, whether converging or not. In all situations the outlet of a bin must be active over the whole cross-section to enable mass flow. 

The flow rate can be obtained using the above slip flow boundary condition, and assuming LJR [Pg.196]

The sedimentation velocity of particles under gravity can be measured and compared with the predicted values based on no-slip and slip flow boundary conditions. The ratio of the sedimentation velocity as a function of slip length can be derived as... 

Boundary Slip of Liquids, Fig. 6 Slip length versus shear rate for flow of n-hexadecane in microchannel of different channel depths (//) and surface roughness... 

Boundary Slip of Liquids, Fig. 7 Velocity profile for (a) Couette and (b) Poiseuille flow comparison between molecular dynamics simulation, no-slip boimdary condition, and partial slip boundary condition... 

Choi et al. [1] examined the apparent slip effects of water in hydrophobic and hydrophilic microchannels experimentally using precision measurements of flow rate versus pressure drop. They correlated their experimental results to that from analytical solution of flow through a channel with slip velocity at the wall. There was clear difference between the flows of water on a hydrophilic and hydrophobic surface indicating the effect of slip flow (Fig. 2). Neto et al. [3] have reported clear evidence of boundary slip for a sphere-flat geometry from force measurements using atomic force microscopy. The degree of slip is observed to be the function of both liquid viscosity and shear rate (Fig. 4). 

Goldstein D, Handler R, Sirovich L (1993) Modeling a no-slip flow boundary with an external force field. J Comput Phys 105 354—366... 

Slipping flow boundary condition is valid based on thin... 

The steady-state heat convection between two parallel plates and in circular, rectangular, and annular channels with viscous heat generation for both thermally developing and fully developed conditions is solved. Both constant wall temperature and constant heat flux boundary conditions are crmsidered. The velocity and the temperature distributions are derived from the momentum and energy equations, and the proper slip-flow boundary conditions are considered. 

In microreactors, the friction factor is not independent of wall surface roughness. Moreover, molecular interaction with the walls increases relative to intermolecular interactions when compared to macro-scale flows. In macro-scale systems, two boundary conditions will be applied, that is, a no-slip-flow in which the fluid next to the wall exhibits the velocity of the fluid normally being zero in the most common conditions, and a slip flow in which the velocity of the fluid next to the wall is not zero, and is affected by the wall friction effects and shear stress at the wall. In the case of the slip-flow conditions, a significant reduction in the friction pressure drop and thus reducing the power consumption required to feed the fluid into the microchannel reactor. For most cases in microreactors, the = 0.1 continuum flow with slip boundary conditions is applied. In addition, the pressure drop inside the microreactor is minimal in comparison to that of macro-scale systems (Hessel et ai, 2005b). 

With regards to the boundary condition, the principle of mirror reflection was used in the symmetry axis and the body surface to model the conditions of zero normal component flow and slip (or no-slip) flow on the surface body. In the upstream of the external boundary, parameters of unperturbed... 

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