The effect of shear thinning and differential viscoelasticity on mixing in a model 2D mixer as determined using FEM with particle tracking

Abstract In order to determine the mechanism of mixing and evaluate its effectiveness in a model mixer, FEM flow profiles generated for a series of purely viscous, shear thinning inelastic and viscoelastic fluids using the techniques previously described in Connelly and Kokini (2003) [31] were used to find trajectories for material points with random initial positions. The mixing mode was shown to be primarily laminar shear using the Manas-Zloczower mixing index [10] . The mixing was analyzed statistically using the segregation scale [5] and cluster distribution index [41] , demonstrating its cyclic nature in the model mixer with the type of rheology studied effecting the period of the cycles. Length of stretch and efficiency of mixing was evaluated using the method of Ottino (1989) [18] . They showed some stretching near the walls but overall the efficiency decayed as t −1 , with the effect of the rheology evident in the speed of the decay and the negative values in the viscoelastic model results.

[1]  J. Kokini,et al.  2-D Numerical Simulation of Differential Viscoelastic Fluids in a Single-Screw Continuous Mixer: Application of Viscoelastic Finite Element Methods , 2003 .

[2]  Heh Han Meijer,et al.  Transient phenomena in dispersive mixing , 1993 .

[3]  R. Saxton,et al.  Mixing in Laminar-Flow Systems , 1957 .

[4]  T. Jongen,et al.  Characterization of batch mixers using numerical flow simulations , 2000 .

[5]  I. Manas‐Zloczower,et al.  Influence of design on dispersive mixing performance in an axial discharge continuous mixer—LCMAX 40 , 1998 .

[6]  I. Manas‐Zloczower,et al.  Analysis of Mixing Performance in a VIC Mixer , 1994 .

[7]  Patrick D. Anderson,et al.  Chaotic fluid mixing in non-quasi-static time-periodic cavity flows , 2000 .

[8]  P. V. Danckwerts.  The Definition and Measurement of Some Characteristics of Mixtures , 1952 .

[9]  Julio M. Ottino,et al.  CHAOTIC MIXING OF SHEAR-THINNING FLUIDS , 1994 .

[10]  J. J. Elmendorp.  A study on polymer blending microrheology , 1986 .

[11]  I. Manas‐Zloczower,et al.  Hydrodynamic analysis of a Banbury mixer-2-D-flow simulations for the entire mixing chamber , 1989 .

[12]  Julio M. Ottino,et al.  A comparative computational and experimental study of chaotic mixing of viscous fluids , 1990, Journal of Fluid Mechanics.

[13]  J. Ottino.  The Kinematics of Mixing: Stretching, Chaos, and Transport , 1989 .

[14]  Jozef L. Kokini,et al.  Determination of mixing efficiency in a model food mixer , 1999 .

[15]  Ottino,et al.  Increase in regularity by polymer addition during chaotic mixing in two-dimensional flows. , 1990, Physical review letters.

[16]  Julio M. Ottino,et al.  Experiments on mixing due to chaotic advection in a cavity , 1989, Journal of Fluid Mechanics.

[17]  Jozef L. Kokini,et al.  Estimation and prediction of shear rate distribution as a model mixer , 2000 .

[18]  M. Crochet,et al.  A new mixed finite element for calculating viscoelastic flow , 1987 .

[19]  Nhan Phan-Thien,et al.  A numerical study of viscoelastic effects in chaotic mixing between eccentric cylinders , 2000, Journal of Fluid Mechanics.

[20]  Ica Manas-Zloczower,et al.  Flow field analysis of the kneading disc region in a co‐rotating twin screw extruder , 1992 .

[21]  I. Manas‐Zloczower,et al.  Study of mixing efficiency in kneading discs of co‐rotating twin‐screw extruders , 1997 .

[22]  H. Aref.  Stirring by chaotic advection , 1984, Journal of Fluid Mechanics.

[23]  R. S. Spencer,et al.  The mixing of very viscous liquids , 1951 .

[24]  R. Tanner,et al.  A new constitutive equation derived from network theory , 1977 .

[25]  M. F. Edwards,et al.  Mixing in the Process Industries: Second Edition , 1997 .

[26]  W. Ranz,et al.  A lamellar model for analysis of liquid-liquid mixing , 1979 .

[27]  Patrick Patrick Anderson,et al.  Mixing of non-Newtonian fluids in time-periodic cavity flows , 2000 .

[28]  I. Manas‐Zloczower,et al.  Analysis of Agglomerate Rupture in Linear Flow Fields , 1989 .

[29]  Julio M. Ottino,et al.  A framework for description of mechanical mixing of fluids , 1981 .

[30]  Marcel Crochet,et al.  Numerical-simulation of Viscoelastic Flow - a Review , 1989 .

[31]  Gianni Astarita,et al.  Objective and generally applicable criteria for flow classification , 1979 .

[32]  J. Oldroyd.  On the formulation of rheological equations of state , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[33]  J. Dooley,et al.  On the development of secondary motions in straight channels induced by the second normal stress difference: experiments and simulations , 1997 .

[34]  J. Ottino,et al.  Mixing of a viscoelastic fluid in a time-periodic flow , 1993, Journal of Fluid Mechanics.

[35]  G. K. Patterson,et al.  Mixing of liquids by mechanical agitation , 1985 .

[36]  George M. Homsy,et al.  Chaotic advection in creeping flow of viscoelastic fluids between slowly modulated eccentric cylinders , 1996 .

[37]  Julio M. Ottino,et al.  Chaotic mixing of viscous fluids by periodic changes in geometry: Baffled cavity flow , 1994 .