The temperature dependence of the hydrodynamic boundary condition between a PDMS melt and two different non-attractive surfaces made of either an OTS (octadecyltrichlorosilane) self-assembled monolayer (SAM) or a grafted layer of short PDMS chains has been characterized. A slip length proportional to the fluid viscosity is observed on both surfaces. The slip temperature dependence is deeply influenced by the surfaces. The viscous stress exerted by the polymer liquid on the surface is observed to follow exactly the same temperature dependences as the friction stress of a crosslinked elastomer sliding on the same surfaces. Far above the glass transition temperature, these observations are rationalized in the framework of a molecular model based on activation energies: increase or decrease of the slip length with increasing temperatures can be observed depending on how the activation energy of the bulk viscosity compares to that of the interfacial Navier's friction coefficient.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 [1] identified two possible sources of dissipation: bulk dissipation, associated to the friction between layers of liquid, and surface dissipation, associated to the friction of the last layer of liquid molecules sliding on the solid surface. The bulk dissipation can be obtained assuming a linear relation between the shear stress and the velocity gradient, which, for incompressible fluids, gives the Navier-Stokes equation. For surface dissipation, a classical assumption is that a liquid element adjacent to the surface assumes the velocity of the surface, i.e. a non-slip boundary condition, which leads to no surface dissipation. Indeed, Navier, postulated the existence of a slip velocity at the surface. He proposed a linear relation between the shear stress at the solid-liquid interface and the slip velocity: σ fluid→surface = kV , where k is the interfacial friction coefficient, sometimes called the Navier's coefficient, assumed to be independent of the shear rate, and V is the slip velocity. It is thus possible to define the slip length as the distance from the solid surface where the fluid velocity profile extrapolates linearly to zero (see Figure 1a). Balancing the viscous stress exerted by the fluid on the solid σ = ηγ, where η is the fluid viscosity andγ is the shear rate, to the friction stress proposed by Navier gives:The slip length, if it exists, is thus the ratio of two quantities characterizing respectively bulk and surface dissipation mechanisms. In this equation, both η and k should depend on the temperature.Slip length determination in the case of simple fluids has been the subject of intensive experimental [2][3][4][5][6][7] and theoretical/numerical [8][9][10][11][12] research over the last 20 years. Despite this strong activity, there is still no quantitative agreement between experiments and numerical simulatio...

The macroscopic viscosity of polymer solutions in general differs strongly from the viscosity at the nanometer scale, and the relation between the two can be complicated. To investigate this relation, we use a fluorescent molecular rotor that probes the local viscosity of its molecular environment. For a range of chain lengths and concentrations, the dependence of the fluorescence on the macroscopic viscosity is well described by the classical Förster–Hoffmann (FH) equation, but the value of the FH exponent depends on the polymer chain length. We show that all data can be collapsed onto a master curve by plotting the fluorescence versus polymer concentration, which we explain in terms of the characteristic mesh size of the polymer solution. Using known scaling laws for polymers then allows us to quantitatively explain the relation between the FH exponent and the polymer chain length, allowing us to link the nano- to the macroviscosity.

We investigate the local viscosity of a polymer glass around its glass transition temperature using environment-sensitive fluorescent molecular rotors embedded in the polymer matrix. The rotors' fluorescence depends on the local viscosity, and measuring the fluorescence intensity and lifetime of the probe therefore allows to measure the local free volume in the polymer glass when going through the glass transition. This also allows us to study the local viscosity and free volume when the polymer film is put under an external stress. We find that the film does not flow homogeneously, but undergoes shear banding that is visible as a spatially varying free volume and viscosity.

The progressive onset of slip at the wall, which corresponds to a slip length increasing with the solicitation time before reaching a plateau, has been investigated for model viscoelastic polymer solutions, allowing one to vary the longest relaxation time while keeping constant solid–fluid interactions. A hydrodynamic model based on a Maxwell fluid and the classical Navier’s hypothesis of a linear response for the friction stress at the interface fully accounts for the data. In the limit of the linear viscoelasticity of the fluid, we could postulate a Newtonian response for the interfacial friction coefficient, reflecting the local character of solid–liquid friction mechanisms. Deviations between the experiments and our model are observed when the fluid is far from its linear viscoelastic behavior.