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Résumé |
Modeling fluid flows in channels is a general problem in science and engineering. For ideal liquids, the situation is simple: there is no dissipation due to fluid movement. For real liquids, some energy is lost. Navier, in his pioneering work on fluid mechanics identified two possible sources of dissipation: bulk dissipation, associated to the viscosity and the friction of the last layer of liquid molecules sliding on the solid surface. For surface dissipation, a classical assumption of fluid dynamics is that a liquid element adjacent to the surface is equal to the velocity of the surface, i.e. a non-slip boundary condition, which leads to no surface dissipation. This is not the only possibility. Navier, postulating the existence of a slip velocity at the surface, introduced the possibility of surface dissipation. He proposed a linear relation between the shear stress at the solid-liquid interface and the slip velocity: σ=kV, where k is the interfacial friction coefficient. Indeed, it is also possible to define the slip length b as the distance from the solid surface where the fluid velocity profile extrapolates linearly to zero.
During this presentation, I will briefly review what we know on the boundary condition for simple Newtonian liquids and show that polymers, due to their entanglements present a unique tool to study and understand the Navier condition. Based on a setup using the photobleaching of fluorescent polymers, I will present our last results on the slip of polymer melts and polymer solutions. |
