Slip and friction of liquid flow over solid surfaces: On the validity of the no slip condition in hydrodynamic systems

In the first chapter a review is presented of the existing ideas on surfactant dynamics, and irreversible thermodynamics is introduced as a tool of reference for different models. The two examples of lubrication and detergency are used to survey the implications of specific boundary conditions in dissipative processes. The second chapter gives a review of some published results and reinterprets those in terms of entropy production. The concept of a critical capillary radius, for which liquid flow with slip in the interface would be the thermodynamically favoured mode is discussed. This discussion leads to a new interpretation of the slip length : as a measure for the interfacial viscosity. To investigate this concept, Newtonian surfactant solutions are subjected to oscillating flow through a membrane. Phase differences between the flows and their driving forces are recorded as a function of the stress. The observations are attributed to the complexity of the pore/solution interface, where surfactant adsorption is taking place. The experiment indicates viscoelastic interfacial behaviour. With low shear stress as the driving force surface elasticity is predominant and the no slip boundary condition applies for the flow pattern. At higher stresses, surface motion is allowed. In the fourth chapter an expression is worked out for the momentum transfer from the bulk of a flowing liquid to the interface. This equation allows the calculation of the slip length as a function of the relevant driving forces. Two linear regimes are observed in flows through a membrane of surfactant solutions with different concentrations. The difference between these two regimes is described in terms of a stick to slip transition. In the following chapter, the mathematical description is extended to consider both the stick to slip transition and the e¤ect of coupled hydrodynamic and electroosmotic flows. This extended model is then applied to, as yet, unexplained observations of regime transitions in the electroosmotic flow through porous plugs. It follows from the analysis that the slip length (i.e. the interfacial viscosity) should depend on surface forces, which are characterized by the zeta potential. In the sixth chapter our mathematical models are applied to describe the flow of various surfactants at different concentrations through porous membranes. A definition of the deceivingly simple concept of a slip length as the sum of interfacial effects is suggested. These effects can then be lumped together in a new interfacial excess function for the fluid flow over a solid surface (the viscoelastic interfacial flow). A description in terms of a (complex) interfacial viscosity is preferred over the concept of a slip length. The last chapter summarizes our results in succinct statements about the physical chemistry of surfactant solutions, which flow over solid pore walls of membranes, textiles and sorbent materials.Applied Science