ON THE MODELING OF A MICROSTRUCTURAL PAIR OF CONSTITUTIVE EQUATIONS TO DESCRIBE THE MOTION OF ELASTIC FLUIDS

Abstract

SCALING ARGUMENTS BASED ON A BALANCE BETWEEN VISCOUS DRAG AND RESTORING BROWNIAN FORCES ARE USED IN ORDER TO GENERATE A NONLINEAR DUMBBELL MODEL WITH FINITE SPRING CORRECTION AND A DRAG CORRECTION FOR A DILUTE POLYMER SOLUTION. THE MICROSTRUCTURE COUPLED EQUATIONS LEADS TO THE MOST COMMONLY OLDROYD-LIKE CONSTITUTIVE EQUATION. WE SHOW THAT THE INVESTIGATED MODEL IS ABLE TO CAPTURE GENERALIZED NONLINEAR RESPONSE OF VISCOELASTIC FLUIDS. THE APPROACH IS USED TO INVESTIGATE THE NONLINEAR RESPONSE OF AN ELASTIC LIQUID UNDER STRONG EXTENSIONAL FLOWS. WE CHARACTERIZE THE NONLINEAR E®ECT OF THE °UID IN TERMS OF AN EXTENSIONAL VISCOSITY THAT IS FOUND TO BE A FUNCTION OF THREE RELEVANT PARAMETERS OF THE PROBLEM: DEBORAH NUMBER, THE MACROMOLECULE EXTENSIBILITY (OR ANISOTROPY) AND THE MACROMOLECULE VOLUME FRACTION. WE VERIFY THE PREDICTIONS OF THE MODEL WITH BATCHELOR'S CALCULATION OF EXTENSIONAL VISCOSITY BASED ON A SLENDER BODY THEORY FOR SUSPENSIONS COMPOSED OF LONG RIGID RODS. THE ANALYSIS MAY EXPLAIN FROM A PHENOMENOLOGICAL POINT OF VIEW WHY FEW PPMS OF MACROMOLECULES OF HIGH MOLECULE WEIGHT OR A SMALL CONCENTRATION OF LONG ¯BERS MAY PRODUCE DRASTIC CHANGES IN THE PRESSURE DROP OF ROBUST TURBULENT °OWS. IN ADDITION, THE PROPOSED ANALYSIS MAY BE USEFUL FOR DIRECT COMPUTER SIMULATIONS OF TURBULENT FLOWS IN THE PRESENCE OF MACROMOLECULE.