Fluid-solid interfaces friction

The above remarks point out the interest of direct measurements of the boundary condition (BC) for the fluid velocity at a fluid solid interface. To obtain reliable information on the flow velocity BC of a fluid, with a spatial resolution from the wall down to molecular sizes, is a particularly difficult challenge. Conventional velocimetry techniques (even laser velocimetry) are far from such a resolution. We have developed a near field laser velocimetry technique which allows to increase significantly the spatial resolution compared to more conventional velocimetry techniques. This technique has been used to characterize the friction between a polymer melt and a solid wall and to understand how surface modifications weakening the interactions between a solid and a given simple fluid affected the fluid -- wall friction. 

Boundary lubrication is characterized by film thicknesses of < 0.025 pm, which is less than the height of the asperity contacts. Mixed film, or EHD boundary lubrication, occurs at the transition from boundary to EHD lubrication. For comparison, the relative sizes of various components of a wear contact are provided in Figure 4.3.9 Because the solids are not separated by a lubricant, fluid film effects are negligible and there is considerable asperity contact. The contact lubrication mechanism is dominated by the physical and chemical properties of thin surface films of molecular proportions. The properties of the bulk lubricant are of minor importance, and the friction coefficient is essentially independent of fluid viscosity. The frictional characteristics are determined by the properties of the solids and the lubricant film at the common interfaces. 

Indeed, the shear stress at the solid surface is txz=T (S 8z)z=q (where T (, is the melt viscosity and (8USz)z=0 the shear rate at the interface). If there is a finite slip velocity Vs at the interface, the shear stress at the solid surface can also be evaluated as txz=P Fs, where 3 is the friction coefficient between the fluid molecules in contact with the surface and the solid surface [139]. Introducing the extrapolation length b of the velocity profile to zero (b=Vs/(8vy8z)z=0, see Fig. 18), one obtains (3=r bA). Thus, any determination of b will yield (3, the friction coefficient between the surface and the fluid. This friction coefficient is a crucial characteristics of the interface it is obviously directly related to the molecular interactions between the fluid and the solid surface, and it connects these interactions at the molecular level to the rheological properties of the system. 

The flow of a viscous fluid generates heat throughout the fluid. This should not be confused with frictional heating, which occurs at the interface between two solids in relative motion. The power dissipated in a small cube of melt in a shear flow, is the product of the shear force on the top and bottom surfaces and the velocity difference between these surfaces. When this quantity is divided by the volume of the cube, the power dissipated per unit volume W is found to be... 

The essential point is that such an adsorption process markedly influences the hydrodynamic and electrical properties of the interface. Figure 3.16 is a schematic representation of the structure formed polymer chains with fixed charges extend out of the solid surface to an average distance d = b — a in this region, the fluid can move, although with an increased viscosity because of the hydrodynamic resistance of the polyelectrolyte layer (also called hydrogel layer). To take this into account, a friction term — yv is included in the Navier-Stokes equation. 

In fact, b is directly related to the friction coefficient between the fluid and the surface. This can be easily seen by evaluating the friction force transmitted to the solid by the sheared fluid, either as the product of the velocity at the interface. Vs, by friction coefficient between the solid and the fluid, k, or as the product of the fluid viscosity by the velocity gradient at the surface, i.e. Ff =kVs =ti9V/3z q H s/b One sees... 

---