F. Restagno – 02 Octobre

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: , 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.

Figure 1: Definition of the slip length.

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 [1], I will present our last results on the slip of polymer melts [2,3] and polymer solutions [4].

[1] M. Hénot, A. Chennevière, E. Drockenmuller, L. Léger, F. Restagno, Comparison of the Slip of a PDMS Melt on Weakly Adsorbing Surfaces Measured by a New Photobleaching-Based Technique, Macromolecules. (2017). doi:10.1021/acs.macromol.7b00601.
[2] M. Hénot, É. Drockenmuller, L. Léger, F. Restagno, Friction of Polymers: from PDMS Melts to PDMS Elastomers, ACS Macro Lett. 7 (2018) 112–115. doi:10.1021/acsmacrolett.7b00842.
[3] M. Hénot, E. Drockenmuller, L. Léger, F. Restagno, Sensing adsorption kinetics through slip velocity measurements of polymer melts, Eur. Phys. J. E. 41 (2018). doi:10.1140/epje/i2018-11697-4.
[4] C. Barraud, B. Cross, C. Picard, F. Restagno, L. Léger, E. Charlaix, Boundary flow of viscoelastic polyelectrolyte solutions, ArXiv180303440 Cond-Mat Physicsphysics. (2018). http://arxiv.org/abs/1803.03440 (accessed June 5, 2018).