Molten polymer solutions are shear-thinning fluids where the viscosity is described by the following power- law...

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Molten polymer solutions are shear-thinning fluids where the viscosity is described by the following power- law expression: n T = k dy/ where k is the 'consistency index' (with units of Pa-s") andn is the flow behaviour index' (dimensionless). The equation for pressure-driven flow of a shear-thinning fluid between two parallel plates separated by distance 2b (as shown in accompanying figure) is given below:: avx (1 ΔΡ' УЛ y = +b y ду \k L y = 0 y =-b a) Solve this equation, using the appropriate boundary condition(s), to get the velocity profile v,(y) in terms of n, b, k, y, AP, and L. b) Show that for n 1 and k = , the equation simplifies to that given in the lecture notes for pressure- driven flow of an incompressible Newtonian fluid (INF) between two parallel plates (separated by distance 2b). Molten polymer solutions are shear-thinning fluids where the viscosity is described by the following power- law expression: n T = k dy/ where k is the 'consistency index' (with units of Pa-s") andn is the flow behaviour index' (dimensionless). The equation for pressure-driven flow of a shear-thinning fluid between two parallel plates separated by distance 2b (as shown in accompanying figure) is given below:: avx (1 ΔΡ' УЛ y = +b y ду \k L y = 0 y =-b a) Solve this equation, using the appropriate boundary condition(s), to get the velocity profile v,(y) in terms of n, b, k, y, AP, and L. b) Show that for n 1 and k = , the equation simplifies to that given in the lecture notes for pressure- driven flow of an incompressible Newtonian fluid (INF) between two parallel plates (separated by distance 2b).