Miscible displacement flows in near-horizontal ducts at low Atwood number

Abstract

We study buoyant displacement flows with two miscible fluids of equal viscosity in the regime of low Atwood number and in ducts that are inclined close to horizontal. Using a combination of experimental, computational and analytical methods, we characterize the transitions in the flow regimes between inertial- and viscous-dominated regimes, and as the displacement flow rate is gradually increased. Three dimensionless groups largely describe these flows: densimetric Froude number $\mathit{Fr}$, Reynolds number $\mathit{Re}$ and duct inclination $\ensuremath{\beta} $. Our results show that the flow regimes collapse into regions in a two-dimensional $(\mathit{Fr}, \mathit{Re}\cos \ensuremath{\beta} / \mathit{Fr})$ plane. These regions are qualitatively similar between pipes and plane channels, although viscous effects are more extensive in pipes. In each regime, we are able to give a leading-order estimate for the velocity of the leading displacement front, which is effectively a measure of displacement efficiency.

A study of pressure-driven displacement flow of two immiscible liquids using a multiphase lattice Boltzmann approach

“…Our results predict the front velocity of the "lock-exchange flow" of two immiscible fluids in the exchange flow dominated regime. This is also consistent with the finding of Taghavi et al 61,62 for the exchange flow of miscible fluids at high Peclet number. A linear stability analysis of a three-layer system predicts the behavior of the numerical simulation qualitatively.…”

“…14 The first and second terms on the right hand side correspond to the buoyancy and imposed pressure forces, respectively. The leading term in the best fit curve compares well with that of Sahu et al, 43 who studied the buoyancy-driven "lock-exchange flow" of two immiscible fluids in an inclined channel and that of Taghavi et al 61 for miscible displacement flow in a near horizontal channel. However, in a purely buoyancy-driven flow of two miscible fluids in an inclined pipe, Séon et al 62 determined the leading term (=0.7) by balancing the buoyancy with the inertial force.…”

“…Thus, the trailing front has a tendency to move in the downstream direction (back flow) for χ > χ cr , whereas it moves only in the positive axial direction for χ < χ cr (no back flow). In the case of miscible displacement flows in a near horizontal pipe, Taghavi et al 61 found the value of χ cr to be 116.32. This difference is also due to the cylindrical geometry considered by these authors.…”

Capillary Model of Gravity Elution of High Viscosity Liquid from a Porous Bed with a Low-Viscosity Liquid

“…However, in the immiscible flow only the dynamics of flowing liquids are considered. The phenomena accompanying miscible flow in a single channel were discussed and supported by relevant numerical simulations provided by Sahu et al (2009a, b), Talon and Meiburg (2011), Talon et al (2013), Taghavi et al (2012). The various systems of channels with different initial conditions were analyzed there.…”

CFD simulation and experimental study of water-oil displacement flow in an inclined pipe

“…Flow pattern transition, interface instability, and displacement efficiency are the focus of many research papers. The miscible displacement flows are always associated with molecular diffusion [1]. For the miscible displacements of a more viscous fluid by a less viscous one, in most cases the less viscous fluid may finger into the more viscous one, thus forming a two or three-layer flow structure [2][3].…”