A dynamic slip velocity model for molten polymers based on a network kinetic theory

In this paper the slip phenomenon is considered as a stochastic process where the polymer segments (taken as Hookean springs) break off the wall due to the excessive tension imposed by the bulk fluid motion. The convection equation arising in network theories is solved for the special case of a polymer/wall interface to determine the time evolution of the configuration distribution function (Q, t). The stress tensor and the slip velocity are calculated by averaging the proper relations over a large number of polymer segments. Due to the fact that the model is probabilistic and time dependent, dynamic slip velocity calculations become possible for the first time and therefore some new insight is gained on the slip phenomenon. Finally, the model predictions are found to match macroscopic experimental data satisfactorily.Nomenclature rate of creation of polymer segments - g(Q) constant of rate of creation of polymer segments - rate of loss of polymer segments - h(Q) constant of rate of loss of polymer segments - h(Q) constant of rate of loss of polymer segments due to destruction of its B-link - H Hookean spring constant - k Boltzmann's constant - n unit vector normal to the polymer/wall interface - n ₀ number density of polymer segments - n ₀ surface number density of polymer segments - Q vector defining the size and orientation of a polymer segment - Q ^* critical length of a segment beyond which the tension may overcome the W _adh - t time - t _h howering time of broken polymer segments - T absolute temperature - W _adh work of adhesion Greek Letters _n nominal strain - strain - _n nominal shear rate - shear rate - dimensionless constant in the expressions of h(Q), g(Q) - viscosity - ^T velocity gradient tensor - ₀ time constant - standard deviation of vectors Q at equilibrium - _w wall shear stress - stress tensor - ₀ equilibrium configuration distribution function of Q - configuration distribution function of Q