Pressure-driven flow of wormlike micellar solutions in rectilinear microchannels

Journal of Non-Newtonian Fluid Mechanics

Volumn 166, Issue 3-4, 2011, Pages 180-193

  Cromer, Michael ^a   Cook, L Pamela ^a   McKinley, Gareth H ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Constitutive modeling; Non Newtonian fluids; Rheology; Spectral methods; Viscoelasticity; Wormlike micelles

Indexed keywords

APPARENT SLIP; BROWNIAN MOTION; CHANNEL WALL; CONSTITUTIVE MODELING; CRITICAL PRESSURES; DIFFUSION PARAMETERS; FINITE LENGTH; FLOW CURVES; FLOW EXPERIMENTS; HIGH SHEAR RATE; HOMOGENEOUS FLOW; MICELLAR SYSTEMS; MICRO-STRUCTURAL; MICROFLUIDIC GEOMETRY; MODEL FORMULATION; NETWORK CONNECTION; NETWORK MODELS; NEWTONIAN FLUIDS; NON-LOCAL EFFECT; NON-NEWTONIAN FLUIDS; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; NONLOCAL; PARABOLIC PROFILES; PRESSURE-DRIVEN; PRESSURE-DRIVEN FLOWS; SHEAR BANDING; SHEAR-INDUCED DIFFUSION; SMALL CHANNELS; SPATIAL STRUCTURE; SPECTRAL METHODS; VELOCITY PROFILES; WORM-LIKE MICELLES; WORMLIKE MICELLAR SOLUTIONS;

BOUNDARY CONDITIONS; BROWNIAN MOVEMENT; ELASTICITY; FLOW MEASUREMENT; FLUIDS; MICELLES; NON NEWTONIAN LIQUIDS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RHEOLOGY; SHEAR DEFORMATION; SPECTROSCOPY; VISCOELASTICITY; VISCOSITY; VISCOUS FLOW; WALLS (STRUCTURAL PARTITIONS);

NON NEWTONIAN FLOW;

EID: 78651429878     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2010.11.007     Document Type: Article

References (39)

1. Hu Y., Lips A. Kinetics and mechanism of shear banding in entangled micellar solutions. J. Rheol. 2005, 49:1027-1101.
2. Miller E., Rothstein J. Transient evolution of shear banding in wormlike micelle solutions. J. Non-Newtonian Fluid Mech. 2007, 143:22-37.
3. Boukany P., Wang S. Use of particle-tracking velocimetry and flow birefringence to study nonlinear flow behavior of entangled wormlike micellar solution: From wall slip, bulk disentanglement to chain scission. Macromolecules 2008, 41:1455-1464.
4. Callaghan P. Rheo NMR and shear banding. Rheol. Acta 2008, 47:243-255.
5. Cates M. Reptation of living polymers: dynamics of entangled polymers in the presence of reversible chain-scission reactions. Macromolecules 1987, 20:2289-2296.
6. Cates M. Flow behavior of entangled surfactant micelles. J. Phys. Condens. Matter 1996, 8:9167-9176.
7. Olmsted P., Radulescu O., Lu C. Johnson-Segalman model with a diffusion term in cylindrical Couette flow. J. Rheol. 2000, 44:257-275.
8. Vasquez P., McKinley G., Cook L. A network scission model for wormlike micellar solutions. I. Model formulation and homogeneous flow predictions. J. Non-Newtonian Fluid Mech. 2007, 144:122-139.
9. Zhou L., Vasquez P., Cook L., McKinley G. Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids. J. Rheol. 2008, 52:591-623.
10. Cates M., Fielding S. Rheology of giant micelles. Adv. Phys. 2006, 55:799-879.
11. Fielding S. Complex dynamics of shear banded flows. Soft Matter 2007, 2:1262-1279.
12. Olmsted P. Perspectives on shear banding in complex fluids. Rheol. Acta 2008, 47:283-300.
13. Lerouge S., Berret J.-F. Shear-induced transitions and instabilities in surfactant wormlike micelles. Advances in Polymer Science 2009, Springer-Verlag.
14. L. Zhou, L. Cook, G. McKinley, Probing shear-banding transition of a model of entangled wormlike micellar solutions using large amplitude oscillatory shearing (LAOS) deformation, J. Non-Newtonian Fluid Mech. 165 (2010) 1462-1472.
15. Cromer M., Cook L., McKinley G. Extensional flow of wormlike micellar solutions. Chem. Eng. Sci. 2009, 64:4588-4596.
16. Lu C.-Y.D., Olmsted P., Ball R. Effects of nonlocal stress on the determination of shear banding flow. Phys. Rev. Lett. 2000, 84:642-645.
17. Méndez-Sánchez A., López-González M., Rolón-Garrido V., Pérez-González J., de Vargas L. Instabilities of micellar systems under homogeneous and non-homogeneous flow conditions. Rheol. Acta 2003, 42:56-63.
18. Yamamoto T., Hashimoto T., Yamashita A. Flow analysis for wormlike micellar solutions in an axisymmetric capillary channel. Rheol. Acta 2008, 34:963-974.
19. Marín-Santibáñez B., Pérez-González J., de Vargas L., DeCruppe J., Huelsz G. Visualization of shear banding and entry Poiseuille flow oscillations in a micellar aqueous solution. J. Non-Newtonian Fluid Mech. 2009, 157:117-125.
20. Masselon C., Colin A., Olmsted P. Influence of boundary conditions and confinement on non local effects in flows of wormlike micellar systems. Phys. Rev. E 2010, 81:021502.
21. Masselon C., Salmon J.-B., Colin A. Nonlocal effects in flows of wormlike micellar solutions. Phys. Rev. Lett. 2008, 100:038301.
22. Nghe P., Degre G., Tabeling P., Ajdari A. High shear rheology of shear banding fluids in microchannels. Appl. Phys. Lett. 2008, 93:204102.
23. Radulescu O., Olmsted P. Matched asymptotic solutions for the steady banded flow of the diffusive Johnson-Segalman model in various geometries. J. Non-Newtonian Fluid Mech. 2000, 91:143-164.
24. Adams J., Fielding S., Olmsted P. The interplay between boundary conditions and flow geometries in shear banding: hysteresis, band configurations and surface transitions. J. Non-Newtonian Fluid Mech. 2008, 151:101-118.
25. M. Helgeson, Private communications.
26. Pipe C., Kim N., Vasquez P., Cook L., McKinley G. Wormlike micellar solutions. II. Comparison between experimental data and scission model predictions. J. Rheol. 2010, 54:881-913.
27. Black W., Graham M. Slip, concentration fluctuations, and flow instability in sheared polymer solutions. Macromolecules 2001, 34:5731-5733.
28. Mavrantzas V., Beris A. Theoretical study of wall effects on rheology of dilute polymer solutions. J. Rheol. 1992, 36:175-213.
29. Bhave A., Armstrong R., Brown R. Kinetic theory and rheology of dilute, non-homogeneous polymer solutions. J. Chem. Phys. 1991, 95:2988-3000.
30. Cook L., Rossi L. Slippage and migration in models of dilute wormlike micellar solutions and polymeric fluids. J. Non-Newtonian Fluid Mech. 2004, 116:347-369.
31. Beris A., Mavrantzas V. On the compatibility between various macroscopic formalisms for the concentration and flow of dilute polymer solutions. J. Rheol. 1994, 38:1235-1250.
32. Iserles A. A First Course in the Numerical Analysis of Differential Equations 1996, Cambridge University Press.
33. Radulescu O., Olmsted P., Decruppe J., Lerouge S., Berret J.-F., Porte G. Time scales in shear banding of wormlike micelles. Europhys. Lett. 2003, 62:230.
34. Orszag S. Spectral methods for problems in complex geometries. J. Comput. Phys. 1980, 37:70-92.
35. Berrut J.-P., Trefethen L. Barycentric Lagrange interpolation. SIAM Rev. 2004, 46:501-517.
36. Canuto C., Hussaini Y., Quarteroni A., Zang T. Spectral Methods in Fluid Dynamics 1987, Springer-Verlag.
37. Brenan K., Campbell S., Petzold L. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations 1989, Elsevier Science.
38. L. Zhou, Private communications.
39. Adams J., Olmsted P. Nonmonotonic models are not necessary to obtain shear banding phenomena in entangled polymer solutions. Phys. Rev. Lett. 2009, 102:067801.