MODEL FOR HYDRODYNAMIC THICKNESS OF THIN POLYMER LAYERS AT SOLID LIQUID INTERFACES

If the length scale of an adsorbed polymer layer is small relative to the length scale relevant to the flow about the solid, i.e., the local radius of curvature of the solid surface or the spacing between solid surfaces, then the hydrodynamic thickness of the polymer (L(H)) is a local property of the layer and is independent of geometry. Flow within the polymer layer couples to only the shear components, and not the diagonal (extensional) components, of the velocity gradient of the external flow; therefore the local curvature of the solid surface does not play a role in determining the flow within the polymer layer. Furthermore, if the external flow does not perturb the structure of the polymer layer, L(H) is a material property of the layer, independent of the external flow. The hydrodynamic thickness can be interpreted in two ways: as the coefficient relating the apparent "slip velocity" of the fluid at the solid surface to the shear rate at the surface or, equivalently, as a displacement of the "no-slip" boundary condition from the actual surface into the fluid phase. Sample calculations are presented to illustrate application of the model derived here.