S. M. Taghavi

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.

Miscible density-unstable displacement flows in inclined tube

Miscible density-unstable displacement flows in inclined tube K. Alba,1 S. M. Taghavi,2 and I. A. Frigaard1,3,a) 1Department of Mechanical Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, British Columbia V6T 1Z4, Canada 2Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA 3Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia V6T 1Z2, Canada

In Vivo Predictive Dissolution: Transport Analysis of the CO2, Bicarbonate In Vivo Buffer System

Development of an oral in vivo predictive dissolution medium for acid drugs with a pKa in the physiological range (e.g., Biopharmaceutics Classification System Class IIa) requires transport analysis of the complex in vivo CO2 /bicarbonate buffering system. In this report, we analyze this buffer system using hydrodynamically defined rotating disk dissolution. Transport analysis of drug flux was predicted using the film model approach of Mooney et al based on equilibrium assumptions as well as accounting for the slow hydration reaction, CO2 + H2 O → H2 CO3 . The accuracy of the models was compared with experimentally determined results using the rotating disk dissolution of ibuprofen, indomethacin, and ketoprofen. The equilibrium and slow hydration reaction rate models predict significantly different dissolution rates. The experimental results are more accurately predicted by accounting for the slow hydration reaction under a variety of pH and hydrodynamic conditions. Although the complex bicarbonate buffering system requires further consideration given its dynamic nature in vivo, a simplifying irreversible reaction (IRR) transport analysis accurately predicts in vitro rotating disk dissolution rates of several carboxylic acid drugs. This IRR transport model provides further insight into bicarbonate buffer and can be useful in developing more physiologically relevant buffer systems for dissolution testing.

In Vivo Predictive Dissolution: Comparing the Effect of Bicarbonate and Phosphate Buffer on the Dissolution of Weak Acids and Weak Bases

Bicarbonate is the main buffer in the small intestine and it is well known that buffer properties such as pKa can affect the dissolution rate of ionizable drugs. However, bicarbonate buffer is complicated to work with experimentally. Finding a suitable substitute for bicarbonate buffer may provide a way to perform more physiologically relevant dissolution tests. The dissolution of weak acid and weak base drugs was conducted in bicarbonate and phosphate buffer using rotating disk dissolution methodology. Experimental results were compared with the predicted results using the film model approach of (Mooney K, Mintun M, Himmelstein K, Stella V. 1981. J Pharm Sci 70(1):22-32) based on equilibrium assumptions as well as a model accounting for the slow hydration reaction, CO2 + H2 O → H2 CO3 . Assuming carbonic acid is irreversible in the dehydration direction: CO2 + H2 O ← H2 CO3 , the transport analysis can accurately predict rotating disk dissolution of weak acid and weak base drugs in bicarbonate buffer. The predictions show that matching the dissolution of weak acid and weak base drugs in phosphate and bicarbonate buffer is possible. The phosphate buffer concentration necessary to match physiologically relevant bicarbonate buffer [e.g., 10.5 mM (HCO3 (-) ), pH = 6.5] is typically in the range of 1-25 mM and is very dependent upon drug solubility and pKa .

Miscible heavy-light displacement flows in an inclined two-dimensional channel: A numerical approach

We numerically study the displacement flow of two iso-viscous Newtonian fluids in an inclined two-dimensional channel, formed by two parallel plates. The results are complementary to our previous studies on displacement flows in pipes and channels. The heavier displacing fluid moves the lighter displaced fluid in the downward direction. Three dimensionless groups largely describe these flows: the densimetric Froude number (Fr), the Reynolds number (Re), and the duct inclination (β). As a first order approximation, we are able to classify different flow regimes phenomenologically in a two-dimensional (Fr; Recosβ/Fr)-plane and provide leading order expressions for the transitions between different regimes. The stabilizing and/or de-stabilizing effects of the imposed mean flow on buoyant exchange flows (zero imposed velocity) are described for a broad range of dimensionless parameters.

Live-streaming: Time-lapse video evidence of novel streamer formation mechanism and varying viscosity.

Time-lapse videos of growing biofilms were analyzed using a background subtraction method, which removed camouflaging effects from the heterogeneous field of view to reveal evidence of streamer formation from optically dense biofilm segments. In addition, quantitative measurements of biofilm velocity and optical density, combined with mathematical modeling, demonstrated that streamer formation occurred from mature, high-viscosity biofilms. We propose a streamer formation mechanism by sudden partial detachment, as opposed to continuous elongation as observed in other microfluidic studies. Additionally, streamer formation occurred in straight microchannels, as opposed to serpentine or pseudo-porous channels, as previously reported.

Buoyant miscible displacement flows in vertical pipe

The displacement flow of two miscible Newtonian fluids is investigated experimentally in a vertical pipe of long aspect ratio (δ−1 ≈ 210). The fluids have a small density difference and they have the same viscosity. The heavy displacing fluid is initially placed above the light displaced fluid. The displacement flow is downwards. The experiments cover a wide range of the two dimensionless parameters that largely describe the flow: the modified Reynolds number (0 ≤ Ret⪅800) and the densimetric Froude number (0 ≤ Fr ≤ 24). We report on the stabilizing effect of the imposed flow and uncover the existence of two main flow regimes at long times: a stable displacement flow and an unstable displacement flow. The transition between the two regimes occurs at a critical modified Reynolds number RetCritical, as a function of Fr. We study in depth the stable flow regime: First, a lubrication model combined with a simple initial acceleration formulation delivers a reasonable prediction to the time-dependent penetratin...

Roles of chemical and physical crosslinking on the rheological properties of silica-doped polyacrylamide hydrogels

This paper examines the nanoparticle (NP) influence on energy storage and dissipation in hydrogel nanocomposites (HNCs). To obtain fundamental insights into mechanical enhancement, a model system involving the in situ free-radical polymerization of acrylamide with bis-acrylamide (bis) and silica NPs is adopted. The loss tangents of the unmodified polymer networks span three orders of magnitude, and the weak attraction between silica and poly(acrylamide) (PA)—as compared to composites with a stronger NP-polymer interaction—makes these HNCs particularly sensitive to systematic variations in (i) NP size and concentration and (ii) monomer and crosslinker concentrations. From the dynamic shear moduli during polymerization, and their spectra at steady-state, silica NPs in PA behave as multi-functional, physical crosslinking centers that increase the storage modulus, particularly in very weakly bis-crosslinked PA (in which NP aggregates are proposed to form elastically effective clusters). The loss modulus for HNCs reflects adsorption/desorption and friction at the NP surfaces, varying with the NP, monomer and crosslinker concentrations. Silica NPs were also found to slow the polymerization and crosslinking of acrylamide according to the specific NP surface area (set by the NP size and concentration), suggesting that silica NPs reduce the free-radical concentration.