Crossflow of elastic liquids through arrays of cylinders

Flow of wormlike micelle solutions through a periodic array of cylinders

“…These trends also match very well with recent observations by Talwar et al [19] who studied the flow of polymer solutions through periodic arrays of cylinders as well as others [17,19,24,26,27,46,[61][62][63]. They reported a dimensionless drag in terms of the product of the friction factor and the Reynolds number fRe.…”

Flows of inelastic non-Newtonian fluids through arrays of aligned cylinders. Part 1. Creeping flows

“…We have used here simply the averaged fluid velocity and the cylinder radius in the viscosity scale, i.e., η = η a ≡ K(U/a) n−1 . The shear rate (in , see (5)) in the gap between the cylinders scales with the ratio of a velocity scale U L ≡ U c/L (with c half the height of the unit cell, see Figure 1) and a length scale L. The latter are approximately the averaged velocity in the gaps between the cylinders and half the minimum gap size, respectively. Hence, scaling the shear rate with the velocity averaged over the unit cell and the cylinder radius introduces a dependence of C d on n.…”

“…Although the equations of motion for creeping flows of power-law fluids are not linear, and a superposition principle does not hold, the resulting velocity field exhibits the same fore/aft symmetry in that case as well. This is the result of the underlying linearity in (2), and in (5) not changing sign when the sign of the velocity vector is changed. We have however not made use of this symmetry in our calculations.…”

“…Prior work has mainly concentrated on a sudden increase in pressure drop over arrays when the flow rate is increased beyond a critical value [5][6][7], which has been attributed to elastic instabilities that cause the flow to become three-dimensional [8,9]. The corresponding critical value of the Deborah number De = λU/a (where λ is the fluid relaxation time, U is the cell-averaged velocity and a is the cylinder radius) is usually in the range 0·1-1.…”

Boger Fluids

“…Because sidewalls have much less influence with an array, one can create a nearly uniform flow, and Boger fluids have made it possible to distinguish the onset and magnitude of elastic effects. Experiments from two laboratories clearly show that (a) elasticity causes the pressure drop or flow resistance to rise, not dip, starting at a Weissenberg number of the order of unity and (b) flow resistance increases with We and can be an order of magnitude greater than that for Newtonian fluids (Chmielewski & Jayaraman 1992, Chmielewski et al 1990b, Khomami & Moreno 1997. The fluids in these studies were typical PIB-PB solutions, and the findings are similar to those found earlier for aqueous dragreducing fluids in packed beds of spheres (Durst & Haas 1981, James & McLaren 1975.…”