Enhanced diffusion for oscillatory viscoelastic flow

This paper examines the enhanced axial solute dispersion of a linear viscoelastic fluid, subjected to a longitudinal pressure gradient sinusoidal oscillation, in a duct between parallel walls. The viscoelastic fluid follows the material law of the Jeffrey fluid. An extension of Watson’s theory, developed in 1983, is used to solve the problem analytically. The diffusivity enhancement results are shown in dimensionless form and are presented as functions of the dimensionless group β = h(2ω/ν)1/2 as defined by Watson, the dimensionless retardation time, and the Schmidt, elasticity, and Euler dimensionless numbers. This paper compares the dispersion enhancement of the Jeffrey fluid, in relation to the Newtonian one, for several intervals of the dimensionless parameters. The results indicate very high dispersion enhancement in several cases, especially for high realistic Schmidt number values, and peaks appear at certain dimensionless parameter β values.