Particle—fluid interactions slip velocities

Detailed consideration of the interaction between particles and fluids is given in Volume 2 to which reference should be made. Briefly, however, if a particle is introduced into a fluid stream flowing vertically upwards it will be transported by the fluid provided that the fluid velocity exceeds the terminal falling velocity m0 of the particle the relative or slip velocity will be approximately o- As the concentration of particles increases this slip velocity will become progressively less and, for a slug of fairly close packed particles, will approximate to the minimum fluidising velocity of the particles. (See Volume 2, Chapter 6.)... 

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. 

From this, the velocities of particles flowing near the wall can be characterized. However, the absorption parameter a must be determined empirically. Sokhan et al. [48, 63] used this model in nonequilibrium molecular dynamics simulations to describe boundary conditions for fluid flow in carbon nanopores and nanotubes under Poiseuille flow. The authors found slip length of 3nm for the nanopores [48] and 4-8 nm for the nanotubes [63]. However, in the first case, a single factor [4] was used to model fluid-solid interactions, whereas in the second, a many-body potential was used, which, while it may be more accurate, is significantly more computationally intensive. 

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