Fluid dynamics, mass transport and friction

Transfer properties, the heat and mass transfer coefficient and friction factor, depend not only on transport and thermodynamic properties but also on the hydro-dynamic behavior of a fluid. The geometry of the system will influence the hydro-dynamic behavior. By reducing the parameters by arranging them into dimensionless groups, we can reduce the number of parameters that have to be varied to correlate any of the transfer properties. For example, the ffiction factor equation. 

The dynamics is obtained hy numerical solving a set of the coupled Boltzmann-BGK transport equations (d. eqn [35]) on a spatial lattice in discrete time steps with a discrete set of microscopic vdodties. At each time step, the prohahility density evolved hy each LB equation is adverted to nearest neighhoting lattice sites and modified by molecular collisions, which are local and conserve mass and momentum. As a result, a LB fluid is shown to obey the Navier-Stokes equation (in the limit of a small lattice spacing and small time step). For dilute polymer solutions, the method typically involves phenomenological coupling between the polymer chain and the flowing fluid in the form of a linear friction term based on an effective viscosity. 

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