D. M. Martinez

Settling of an isolated spherical particle in a yield stress shear thinning fluid

We visualize the flow induced by an isolated non-Brownian spherical particle settling in a shear thinning yield stress fluid using particle image velocimetry. With Re<1, we show a breaking of the fore-aft symmetry and relate this to the rheological properties of the fluid. We find that the shape of the yield surface approximates that of an ovoid spheroid with its major axis approximately five times greater than the radius of the particle. The disagreement of our experimental findings with previous numerical simulations is discussed.

Buoyancy-dominated displacement flows in near-horizontal channels: the viscous limit

We consider the viscous limit of a plane channel miscible displacement flow of two generalized Newtonian fluids when buoyancy is significant. The channel is inclined close to horizontal. A lubrication/thin-film approximation is used to simplify the governing equations and a semi-analytical solution is found for the flux functions. We show that there are no steady travelling wave solutions to the interface propagation equation. At short times the diffusive effects of the interface slope are dominant and there is a flow reversal, relative to the mean flow. We are able to find a short-time similarity solution governing this initial counter-current flow. At longer times the solution behaviour can be predicted from the associated hyperbolic problem (where diffusive effects are set to zero). Each solution consists of a number N ≥ 1 of steadily propagating fronts of differing speeds, joined together by segments of interface that are stretched between the fronts. Diffusive effects are always present in the propagating fronts. We explore the effects of viscosity ratio, inclinations and other rheological properties on the front height and front velocity. Depending on the competition of viscosity, buoyancy and other rheological effects, it is possible to have single or multiple fronts. More efficient displacements are generally obtained with a more viscous displacing fluid and modest improvements may also be gained with slight positive inclination in the direction of the density difference. Fluids that are considerably shear-thinning may be displaced at high efficiencies by more viscous fluids. Generally, a yield stress in the displacing fluid increases the displacement efficiency and yield stress in the displaced fluid decreases the displacement efficiency, eventually leading to completely static residual wall layers of displaced fluid. The maximal layer thickness of these static layers can be directly computed from a one-dimensional momentum balance and indicates the thickness of static layer found at long times.

Stationary residual layers in buoyant Newtonian displacement flows

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 (V0) is increased from zero, we change from an exchange flow dominated regime to a regime in which the front velocity (Vf) increases linearly with V0. 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/V0 (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 h...

Influence of an imposed flow on the stability of a gravity current in a near horizontal duct

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.

The orientation of semidilute rigid fiber suspensions in a linearly contracting channel

We measure the spatial evolution of the orientation distribution of a semidilute rigid fiber suspension in the contraction plane of a linear contracting channel. We fit these data with a Fokker–Plank type equation using equations for rotary diffusion coefficient advanced by either (i) Folgar and Tucker [J. Reinf. Plast. Compas. 3, 98 (1984)] or (ii) Koch [Phys. Fluids 7, 2086 (1995)]. Both models of the diffusion coefficient were found to first increase with increasing suspension concentration up to a maximum and then decrease with concentrations above this point. This nonmonotonic behavior was attributed to fiber clumping or flocculation, a mechanism not considered in the closure relationships.We measure the spatial evolution of the orientation distribution of a semidilute rigid fiber suspension in the contraction plane of a linear contracting channel. We fit these data with a Fokker–Plank type equation using equations for rotary diffusion coefficient advanced by either (i) Folgar and Tucker [J. Reinf. Plast. Compas. 3, 98 (1984)] or (ii) Koch [Phys. Fluids 7, 2086 (1995)]. Both models of the diffusion coefficient were found to first increase with increasing suspension concentration up to a maximum and then decrease with concentrations above this point. This nonmonotonic behavior was attributed to fiber clumping or flocculation, a mechanism not considered in the closure relationships.

Stability and instability of Taylor-Couette flows of a Bingham fluid

We consider in detail the Taylor–Couette problem for a Bingham fluid, presenting a range of analytical and computational results. First, for co-rotating cylinders it is known that the critical inner cylinder Reynolds number

Observation of laminar-turbulent transition of a yield stress fluid in Hagen-Poiseuille flow

\hbox{\it Re}_{1,c}

An experimental study of laminar displacement flows in narrow vertical eccentric annuli

, does not increase monotonically with the Bingham number

DISPLACEMENT FLOW OF SHEAR THINNING FLUIDS IN TUBE: THE EFFECT OF DENSITY AND VISCOSITY RATIO

B

Experimental Studies of Visco-Elastic Flow Using Visco-Plastic Lubricant

, over a range of small to moderate