Hydrodynamical changes due to polymer migration in very dilute solutions

The slip hypothesis, based on thermodynamical arguments, has been extended to obtain the flow characteristics of polymer solutions flowing in a nonhomogeneous flow field. An asymptotic analysis, valid for both channel and falling film flows, is presented that predicts the flow enhancement due to polymer migration. Concentration-viscosity coupling is shown to be a critical factor in the hydrodynamic analysis. The analysis, which essentially provides an upper bound on flow enhancement, explicitly accounts for the influence of wall shear stress, initial polymer concentration etc. A comparison with the pertinent experimental data shows reasonable agreement. c concentration - c ₀ concentration in shear-free region - c _i initial concentration - d rate of deformation tensor - g acceleration due to gravity - g ₁ function defined in eq. 13] or 15] - g ₂ function defined in eq. 18] or 20] - H half-channel thickness or film thickness - K gas law constant - L length of the channel or film - q flow rate per unit width - q ^* normalized flow rate - T temperature - v velocity - V mean velocity - y transverse distance - y _c location of solvent layer - _w /µ _s - _w /c ₀ KT - /t convected derivative - dimensionless cenentration,c/c ₀ - _c dimensionless interface concentration - _w dimensionless wall concentration - relaxation time - µ _eff effective viscosity - µ _s solvent viscosity - dimensionless transverse distance,y/H - _c dimensionless interface location - density - stress tensor - _w wall shear stress - c _i KT/ _w - ns no slip NCL-Communication No. 3155