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COBEM 2017
24th ABCM International Congress of Mechanical Engineering
MATHEMATICAL MODELING AND SIMULATION OF THE RHEOLOGICAL BEHAVIOR OF AN ELASTIC LIQUID UNDERGOING DIFFERENT SHEAR FLOWS
Submission Author:
Álvaro Moreira Neto , DF
Co-Authors:
Álvaro Moreira Neto, Igor Dal Osto Pereira, Yuri Dumaresq Sobral, Francisco Ricardo Cunha
Presenter: Álvaro Moreira Neto
doi://10.26678/ABCM.COBEM2017.COB17-2531
Abstract
In this work the rheological behavior of an elastic liquid composed of an ambient Newtonian fluid and a dilute polymeric is examined under steady and unsteady shear flows. The elastic liquid is described by a standard FENE-Dumbbell model of two equations under conditions of different flows: steady simple shear and oscillatory shear. The governing equations are non-dimensionalized based on the relaxation time of the elastic liquid and the viscosity of the ambient Newtonian fluid. The Deborah number (De) is the relevant non-dimensional physical parameter which measures the relative importance between the fluid relaxation time and a typical flow time. We investigate different quantities such as the first normal stress difference as a function of the Deborah number in steady shear. We show the typical dependence of the first normal stress with the square of the Deborah number for small value of this parameter. An asymptotic solution for small De (i.e., De << 1) is also presented under condition of the macromolecules close to the equilibrium and a constant spring function. This behavior O(De²) is also observed experimentally with an aqueous solution of anionic polyacrylamide under steady simple shear. A very good agreement is observed between the numerical solution based on a Runge-Kutta integration, the asymptotic solution and experimental data. The elastic and viscous modules as a function of frequency and De for both linear and nonlinear viscoelastic regimes are also obtained numerically in this work by calculating the Fourier coefficient of the stress. Again, we proposed an asymptotic solution for De << 1 for the elastic liquid experimenting an oscillatory shear. Finally a brief analysis of non-dimensional first normal stress difference N1 is presented where we estimate the output of this function from the asymptotic limit De << 1. The Fourier coefficients of this second normal stress are also examined in this work.
Keywords
Elastic Liquids, Dumbell model, Frequency response
