Mathematical justification and computation of slip lengths
With the recent development of micro- and nanofluidics, drag reduction for low Reynolds number flows, notably at solid walls, has become a stimulating issue. Therefore, the interaction between a fluid and a solid boundary has been investigated thoroughly, both at the experimental and theoretical levels.
At the nanoscale, viscous flows present some striking features, such as the capacity for the material to slip much more easily that one would expect. The origin of this slip is the subject of current debate in the physics community.
Lots of models have been proposed to describe the interaction between the fluid and the solid wall. Some of them rely on a fine description of the surface geometry, whose tiny irregularities are suspected to have an impact on the apparent contact.
Homogenization is a powerful tool to analyze the effect of such small scales, which are filtered out by asymptotic analysis to derive an effective system that keeps track of the main order effect of the small parameter.
One typical effect that models need to explain is the appearance of a so-called "slip length", defined as the ratio between the viscosity of the fluid and a friction coefficient associated with tangential slippage. This concept is illustrated below in the simple case of a Couette flow.
Main fields of application
My research interests in this field include:
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superhydrophobicity, which is observed when chemical properties of the surfaces are combined with rough patterns to create large slip lengths;
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depletion layer models, based on the hypothesis of a drop of viscosity in a very narrow vicinity of the wall;
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lubrication with non-Newtonian fluids;
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models from cellular biology involving ionic exchanges at the nanoscale, such as aquaporin models.
Illustration by Couette flow
Couette flow describes the steady state of a viscous flow between two parallel plates, one being in motion with respect to the other. On the lower boundary, one considers either no-slip boundary condition, meaning that the fluid velocity is equal to the velocity of the plate (left picture), or slip conditions associated with a positive friction coefficient β and slip length l (right).
