Influence of Rheological Behavior of Purely Viscous Fluids on Analytical Residence Time Distribution in Straight Tubes

Abstract

In an effort to better understand the homogeneity of heat treatment of foodstuffs in holding tubes, the cumulative residence time distribution function is derived for a Herschel-Bulkley fluid from fully developed laminar flow in a straight circular tube under isothermal conditions when diffusional effects are negligible. The proposed analytical solution can be reduced to solutions for Newtonian, shearthinning, dilatant, Bingham fluids by setting particular rheological parameters, and consequently, it is possible to successfully explain the dependence of residence time distribution on fluid properties for almost all of the rheological models used for time-independent purely viscous fluids.

Resistance properties of coal–water slurry flowing through local piping fittings

“…It is very obvious that the experimental measurements are in agreement with the generalized Hagen-Poiseuille law (f = 16/Re g ) for the different concentration slurries. Moreover, it is interesting found that the laminar transitional is delayed and it may be due to the increased effective viscosity which is induced by particles and fluids interaction [26][27][28].…”

General pure convection residence time distribution theory of fully developed laminar flows in straight planar and axisymmetric channels

“…The latter encompass Herschel-Bulkley fluids (Delaplace et al, 2008;Sawinsky and Deak, 1995;Wein and Ulbrecht, 1972), Bingham and Rabinowitsch fluids (Wein and Ulbrecht, 1972) and Cassonian fluids (Sawinsky and Balint, 1984). The RTD of a Bingham fluid in a planar falling film was derived by Zakharov (2006).…”

“…Closed analytical forms of the diffusion-free RTD in laminar flows are known only for very few channel shapes and certain Newtonian, non-Newtonian or generalized velocity profiles, see Table 1. Examples are axisymmetric flows in a circular pipe (Bosworth, 1948;Danckwerts, 1953;Delaplace et al, 2008;Hsu and Wei, 2005;Osborne, 1975;Pegoraro et al, 2012;Sawinsky and Balint, 1984;Sawinsky and Deak, 1995;Wein and Ulbrecht, 1972;Zakharov, 2006), in a planar channel (Asbjornsen, 1961;Levenspiel et al, 1970;Sawinsky and Simandi, 1983;Zakharov, 2006) and in a concentric annulus (Nigam and Vasudeva, 1976). In all these cases the velocity profile is one-dimensional as it depends on one coordinate only.…”