On the Optimal Control of a Class of Non-Newtonian Fluids

We consider optimal control problems of systems governed by stationary, incompressible generalized Navier-Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of viscosity functions including shear-thinning and shear-thickening behavior. We prove an existence result for such class of optimal control problems

Preventing transition to turbulence: a viscosity stratification does not always help

In channel flows a step on the route to turbulence is the formation of streaks, often due to algebraic growth of disturbances. While a variation of viscosity in the gradient direction often plays a large role in laminar-turbulent transition in shear flows, we show that it has, surprisingly, little effect on the algebraic growth. Non-uniform viscosity therefore may not always work as a flow-control strategy for maintaining the flow as laminar.Comment: 9 pages, 8 figure

Microdevices for extensional rheometry of low viscosity elastic liquids : a review

Extensional flows and the underlying stability/instability mechanisms are of extreme relevance to the efficient operation of inkjet printing, coating processes and drug delivery systems, as well as for the generation of micro droplets. The development of an extensional rheometer to characterize the extensional properties of low viscosity fluids has therefore stimulated great interest of researchers, particularly in the last decade. Microfluidics has proven to be an extraordinary working platform and different configurations of potential extensional microrheometers have been proposed. In this review, we present an overview of several successful designs, together with a critical assessment of their capabilities and limitations

Constant depth microfluidic networks based on a generalised Murray’s law for Newtonian and power-law fluids

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Microfluidic bifurcating networks of rectangular cross-sectional channels are designed using a novel biomimetic rule, based on Murray’s law. Murray’s principle is extended to consider the flow of power-law fluids in planar geometries (i.e. of constant depth rectangular cross-section) typical of lab-on-a-chip applications. The proposed design offers the ability to control precisely the shear-stress distributions and to predict the flow resistance along the network. We use an in-house code to perform computational fluid dynamics simulations in order to assess the extent of the validity of the proposed design for Newtonian, shear-thinning and shear-thickening fluids under different flow conditions

Instability and morphology of polymer solutions coating a fiber

We report an experimental study on the dynamics of a thin film of polymer solution coating a vertical fiber. The liquid film has first a constant thickness and then undergoes the Rayleigh-Plateau instability which leads to the formation of sequences of drops, separated by a thin film, moving down at a constant velocity. Different polymer solutions are used, i.e. xanthan solutions and polyacrylamide (PAAm) solutions. These solutions both exhibit shear-rate dependence of the viscosity, but for PAAm solutions, there are strong normal stresses in addition of the shear-thinning effect. We characterize experimentally and separately the effects of these two non-Newtonian properties on the flow on the fiber. Thus, in the flat film observed before the emergence of the drops, only shear-thinning effect plays a role and tends to thin the film compared to the Newtonian case. The effect of the non-Newtonian rheology on the Rayleigh-Plateau instability is then investigated through the measurements of the growth rate and the wavelength of the instability. Results are in good agreement with linear stability analysis for a shear-thinning fluid. The effect of normal stress can be taken into account by considering an effective surface tension which tends to decrease the growth rate of the instability. Finally, the dependence of the morphology of the drops with the normal stress is investigated and a simplified model including the normal stress within the lubrication approximation provides good quantitative results on the shape of the drops.Comment: Accepted in Journal of Fluid Mechanic

Active colloids in complex fluids

We review recent work on active colloids or swimmers, such as self-propelled microorganisms, phoretic colloidal particles, and artificial micro-robotic systems, moving in fluid-like environments. These environments can be water-like and Newtonian but can frequently contain macromolecules, flexible polymers, soft cells, or hard particles, which impart complex, nonlinear rheological features to the fluid. While significant progress has been made on understanding how active colloids move and interact in Newtonian fluids, little is known on how active colloids behave in complex and non-Newtonian fluids. An emerging literature is starting to show how fluid rheology can dramatically change the gaits and speeds of individual swimmers. Simultaneously, a moving swimmer induces time dependent, three dimensional fluid flows, that can modify the medium (fluid) rheological properties. This two-way, non-linear coupling at microscopic scales has profound implications at meso- and macro-scales: steady state suspension properties, emergent collective behavior, and transport of passive tracer particles. Recent exciting theoretical results and current debate on quantifying these complex active fluids highlight the need for conceptually simple experiments to guide our understanding.Comment: 6 figure