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A theoretical study is presented of the flow of viscoplastic fluid through a Hele-Shaw cell that contains various kinds of obstructions. Circular and elliptical blockages of the cell are considered together with stepwise contractions or expansions in slot width, all within the simplifying approximation of a narrow gap. Specific attention is paid to the flow patterns that develop around the obstacles, particularly any stagnant plugged regions, and the asymptotic limits of relatively small or large yield stress. Periodic arrays of circular contractions or expansions are studied to explore the interference between obstructions. Finally, viscoplastic flow through a cell with randomly roughened walls is examined, and it is shown that constructive interference of local contractions and expansions leads to a pronounced channelization of the flow. An optimization algorithm based on minimization of the pressure drop is derived to construct the path of the channels in the limit of relatively large yield stress or, equivalently, relatively slow flow. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

We study buoyant displacement flows with two miscible fluids of equal viscosity in ducts that are inclined at angles close to horizontal (β≈90°). As the imposed velocity (V⁁0) is increased from zero, we change from an exchange flow dominated regime to a regime in which the front velocity (V⁁f) increases linearly with V⁁0. During this transition, we observed an interesting phenomenon in which the layer of displaced fluid remained at the top of the pipe (diameter D⁁) during the entire duration of the experiment, apparently stationary for times t⁁>=103D⁁/V⁁0 (the stationary residual layer). Our investigation revealed that this flow marks the transition between flows with a back flow, counter to the imposed flow, and those that displace instantaneously. The same phenomena are observed in pipes (experiments) and in plane channels (two-dimensional numerical computations). A lubrication/thin-film model of the flows also shows the transition from back flow to instantaneous displacement. At long times, this model has a stationary residual layer solution of the type observed, which is found at a unique ratio χ of the axial viscous velocity to the imposed velocity. The prediction of the stationary residual layer from the lubrication model is compared with the transition in observed behavior in our pipe flow experiments and our 2D numerical displacements in the channel. Reasonable agreement is found for the pipe and excellent agreement for the channel. Physically, in either geometry at transition, the upper layer of the fluid is in a countercurrent motion with zero net volumetric flux; the velocity at the interface is positive, but the velocity of the interface is zero. This results from a delicate balance between buoyancy forces against the mean flow and viscous forces in the direction of the mean flow. [ABSTRACT FROM AUTHOR]

We present an experimental study of slow laminar miscible displacement flows in vertical narrow eccentric annuli. We demonstrate that for suitable choices of viscosity ratio, density ratio and flow rate, we are able to find steady travelling wave displacements along the length of the annulus, even when strongly eccentric. Small eccentricity, increased viscosity ratio, increased density ratio and slower flow rates all appear to favour a steady displacement for Newtonian fluids. Qualitatively similar effects are found for non-Newtonian fluids, although the role of flow rate is less clear. These results are largely in line with predictions of a Hele-Shaw style of displacement model (Bittleston et al., J. Engng Math., vol. 43, 2002, pp. 229-253). The experiments also reveal interesting phenomena caused largely by secondary flows and dispersion. In the steady displacements, eccentricity drives a strong azimuthal counter-current flow above/below the advancing interface. This advects displacing fluid to the wide side of the annulus, where it focuses in the form of an advancing spike. On the narrow side we have also observed a spike, but only in Newtonian fluid displacements. For unsteady displacements, the azimuthal currents diminish as the interface elongates. With a strong enough yield stress and with a large enough eccentricity, unyielded fluid remains behind on the narrow side of the annulus. [ABSTRACT FROM AUTHOR]

We study experimentally the effect of a mean flow imposed on a buoyant exchange flow of two miscible fluids of equal viscosity in a long tube oriented close to horizontal. We measure the evolution of the front velocity Vf as a function of the imposed velocity V0. At low V0, an exchange-flow dominated regime is found, as expected, and is characterized here by Kelvin–Helmholtz-like instabilities. With increasing V0 we observed that the flow becomes stable. Here also Vf increases linearly with V0 with slope of >1. At large V0 we find Vf∼V0. [ABSTRACT FROM AUTHOR]

The motion of tracer fibers settling in a suspension made optically transparent using an index-of refraction matching technique is studied as a function of concentration, aspect ratio, fluid viscosity, and fiber length distribution. At Re ∼ O(1), two different regimes of sedimentation are clearly identified. For small volume fractions we find that fibers settle with their long-axis preferentially in the horizontal state. With increasing volume fraction, fibers settle preferentially with their long-axis aligned in the direction of gravity. These findings are strikingly different than for those conducted with Re → 0 and qualitatively support the numerical simulations reported by Kuusela et al. [ABSTRACT FROM AUTHOR]