Research Interests 

Highlighted Current Research 
Buoyant miscible displacement flows in rectangular channels
Abstract: Buoyant displacement flows of two miscible fluids in rectangular channels are studied, theoretically and experimentally. The scenario considered involves the displacement of a fluid by a slightly heavier one in nearlyhorizontal channel inclinations, where inertial effects are weak and laminar stratified flows may be expected. In the theoretical part, a lubrication approximation model is developed to simplify the displacement flow governing equations and furnish a semianalytical solution for the heavy and light fluid flux functions. Three key dimensionless parameters govern the fluid flow motion, i.e., a buoyancy number, the viscosity ratio and the channel cross section aspect ratio. When these parameters are specified, the reduced model can deliver the interface propagation in time, leading and trailing front heights, shapes and speeds, cross sectional velocity fields, etc. In addition, the model can be exploited to provide various classifications such as single or multiple fronts as well as main displacement flow regimes at long times such as nosustainedbackflows, stationary interface flows and sustainedbackflows. Focusing on the variation of the buoyancy number, a large number of isoviscous displacement experiments are performed in a square duct and the results are compared with those of the lubrication model. Qualitative displacement flow features observed in the theory and experiments are in good agreement, in particular, in terms of the main displacement flow regimes. The quantitative comparisons are also reasonable for small and moderate imposed displacement flow velocities. However, at large flow rates, a deviation of the experimental results from the model results is observed, which may be due to the presence of nonnegligible inertial effects. 
Displacement flows in moving geometry
Abstract: In the present work, we experimentally study displacement flows of two Newtonian, miscible fluids in a long, vertical moving pipe while comparing the results with the corresponding displacement flows in a stationary pipe. When in motion, the pipe slowly oscillates like an inverted pendulum. The two fluids have a small density difference and a nearlyidentical viscosity. The denser displacing fluid is placed above the displaced fluid. Overall, our buoyant displacement flows in a moving pipe are at least controlled by three dimensionless groups, namely the Reynolds number, the densimetric Froude number, and the Rossby number. Experimental images of the penetrating front of the heavy displacing fluid into the light displaced one have been analyzed for a wide range of the dimensionless groups. In particular, three different flow regimes are observed for displacement flows in a moving pipe: a stable flow that is nondiffusive (for Re/Ro ≲ O(10^{2}) & Re/Fr^{2}<35), a stablediffusive flow (for Re/Ro≳ O(10^{2}) & Re/Fr^{2}<35) and an unstablediffusive flow (for Re/Fr^{2} >35). Collaborators: Professor F. Larachi at Laval. 
Buoyant displacement flows in slightly nonuniform channels
Abstract: We consider displacement flows in slightly diverging or converging plane channels. The two fluids are miscible and buoyancy is significant. We assume that the channel is oriented close to horizontal. Employing a classical lubrication approximation, we simplify the governing equations to furnish a semianalytical solution for the flux functions. Then, we demonstrate how the nonuniformity of the displacement flow geometry can affect the propagation of the interface between the heavy and light fluids in time, for various parameters studied, e.g. the viscosity ratio, a buoyancy number and rheological features. By setting diffusion effects to zero, certain solution behaviours at longer times can be practically predicted through the associated hyperbolic problem, using which it becomes possible to directly compute the interfacial features of interest, e.g. leading and trailing front heights and speeds. 
A model for nanofibre formation in centrifugal spinning methods
Abstract: We develop a general regularized thinfibre (string) model to predict the properties of nonNewtonian fluid fibres generated by centrifugal spinning. In this process the fibre emerges from a nozzle of a spinneret that rotates rapidly around its axis of symmetry, in the presence of centrifugal, Coriolis, inertial, viscous/shearthinning, surface tension and gravitational forces. We analyse the effects of five important dimensionless groups, namely, the Rossby number (Rb), the Reynolds number (Re), the Weber number (We), the Froude number (Fr) and a powerlaw index (m), on the steady state trajectory and thinning of fibre radius. In particular, we find that the gravitational force mainly affects the fibre vertical angle at small arc lengths as well as the fibre trajectory. We show that for small Rb, which is the regime of nanofibre formation in centrifugal spinning methods, rapid thinning of the fibre radius occurs over small arc lengths, which becomes more pronounced as Re increases or m decreases. At larger arc lengths, a relatively large We results in a spiral trajectory regime, where the fibre eventually recovers a corresponding inviscid limit with a slow thinning of the fibre radius as a function of the arc length. Viscous forces do not prevent the fibre from approaching the inviscid limit, but very strong surface tension forces may do so as they could even result in a circular trajectory with an almost constant fibre radius. We divide the spiral and circular trajectories into zones of no thinning, intense thinning and slow or ceased thinning, and for each zone we provide simple expressions for the fibre radius as a function of the arc length. Collaborators: Professor R.G. Larson at University of Michigan and Dr. W. Arne at Fraunhofer Institute for Industrial Mathematics. 
Viscous fingering regimes in elastoviscoplastic fluids
Abstract: We experimentally study the SaffmanTaylor instability of air invasion into a nonNewtonian fluid (i.e., Carbopol solution) in a rectangular HeleShaw cell. In addition to viscous features, the nonNewtonian fluid used exhibits yield stress, shearthinning as well as elastic behaviors. The key dimensionless parameters that govern the various flow regimes are the Bingham number (Bn), the capillary number (Ca), the Weber number (We), the Weissenberg number (Wi), the channel aspect ratio (δ ≫ 1), and the shear thinning powerlaw index (n). Three main flow regimes are observed, i.e., a yield stress regime, a viscous regime and an elastoinertial regime. We present a detailed description for each regime and quantify their transition boundaries versus dimensionless groups. Some of the secondary flow aspects, e.g., the wall residual layer thickness and a network structure regime, have been also studied. 
A microfluidic model for nonintrusive biofilm viscosity measurements
Abstract: Straight, lowaspect ratio micro flow cells are used to support biofilm attachment and preferential accumulation at the short sidewall, which progressively reduces the effective channel width. The biofilm shifts downstream at measurable velocities under the imposed force from the constant laminar coflowing nutrient stream. The dynamic behaviour of the biofilm viscosity is modeled semianalytically, based on experimental measurements of biofilm dimensions and velocity as inputs. The technique advances the study of biofilm mechanical properties by strongly limiting biases related to nonNewtonian biofilm properties (e.g., shear dependent viscosity) with excellent time resolution. To demonstrate the proof of principle, young Pseudomonas sp. biofilms were analyzed under different nutrient concentrations and constant microflow conditions. The striking results show that large initial differences in biofilm viscosities grown under different nutrient concentrations become nearly identical in less than one day, followed by a continuous thickening process. The technique verifies that in 50 h from inoculation to early maturation stages, biofilm viscosity could grow by over 2 orders of magnitude. The approach opens the way for detailed studies of mechanical properties under a wide variety of physiochemical conditions, such as ionic strength, temperature, and shear stress. Collaborators: Professor J. Greener at Laval. 