FLOW OF ELLIPTICAL PARTICLE SUSPENSIONS THROUGH A CONVERGING-DIVERGING CHANNEL
DOI:
https://doi.org/10.26512/ripe.v2i34.21807Palavras-chave:
Elliptical particle suspensions. Particle migration. Particle alignment. Finite Element Method.Resumo
This work analyzes the flow of elliptical particle suspensions through a convergingdiverging channel. The model considers rigid elliptical particles dispersed in a Newtonian liquid, and the suspension viscosity is given by a function of the local particle concentration and particle axis aspect ratio. Shear-induced particle migration phenomena is described by the well-known Diffusive Flux Model, and the average particle orientation is given by the principal direction of a particle conformation tensor. The conformation evolution in the flow and the constitutive equation for the resulting complex liquid are adapted from classical models used to describe the behavior of suspensions of spheroids, cylinders and fibers and polymeric solutions of rod-like molecules that are almost or completely rigid. The resulting set of fully coupled, nonlinear equations is solved using a slightly variation of the DEVSS-TG/SUPG Finite Element Method. The results show the local particle concentration and average particle orientation in the flow domain, highlighting the behavior of the suspension microstructure near sheardominated and extensional-dominated regions.
Downloads
Referências
Abbott, J. R., Tetlow, N., Graham, A. L., Altobelli, S. A., Fukushima, E., Mondy, L. A., & Stephens, T. S., 1991. Experimental observations of particle migration in concentrated sus pensions: Couette flow. Journal of Rheology, vol. 35, pp. 773-797.
Ahmed, G. M. Y. & Singh, A., 2011. Numerical simulation of particle migration in asymmetric bifurcation channel. Journal of Non-Newtonian Fluid Mechanics, vol. 166, pp. 42-51.
Altobelli, S. A. & Givler, R. C., 1991. Velocity and concentration measurements of suspensions by nuclear magnetic resonance imaging. Journal of Rheology, vol. 35, 721-734.
Bicerano, J., Douglas, J. F., & Brune, D. A., 1999. Model for the viscosity of particle dispersions. Journal of Macromolecular Science C, vol. 39, pp. 561-642.
Brady, J. F., 1993. The rheological behavior of concentrated colloidal dispersions. Journal of Chemical Physics, vol. 99, pp. 567-581.
Chow, A. W., Sinton, S. W., Iwamiya, J. H., & Stephens, T. S., 1994. Shear-induced migration in Couette and parallel-plate viscometers: NMR imaging and stress measurements. Physics of Fluids, vol. 6, pp. 2561-2576.
Donev, A., Connelly, R., Stillinger, F. H., & Torquato, S., 2007. Under constrained jammed packings of non-spherical hard particles: Ellipses and ellipsoids. Physical Review E, vol. 75, pp. 051304 1-32.
Donev, A., Sachs, I. C. D., Variano, E. A., Stillinger, F. H., & Connelly, R., 2004. Improving the density of jammed disordered packings using ellipsoids. Science, vol. 303, pp. 990-993.
Einstein, A., 1911. Berichtigung zu meiner arbeit: Eine nene bestimmung der molekuldimension. Annalen der Physik, vol. 34, pp. 591-592.
Gadala-Maria, F. & Acrivos, A., 1980. Shear-induced structure in a concentrated suspension of solid spheres. Journal of Rheology, vol. 24, pp. 799-814.
Graham, A. L. & Altobelli, S.A, 1991. NMR imaging of shear-induced diffusion and structure in concentrated suspensions. Journal of Rheology, vol. 35, pp. 191-201.
Gu´enette, R. & Fortin, M., 1995. A new mixed finite element method for computing viscoelastic flows. Journal of Non-Newtonian Fluid Mechanics, vol. 60, pp. 27-52.
Hampton, R. E., Mammoli, A. A., Graham, A. L., Tetlow, N., & Altobelli, S. A., 1997. Migration of particles undergoing pressure-driven flow in a circular conduit. Journal of Rheology, vol. 41, pp. 621-640.
Han, M., Kim, C., Kim, M., & Lee, S., 1999. Particle migration in tube flow of suspensions. Journal of Rheology, vol. 43, pp. 1157-1174.
Jeffery, G. B., 1922. The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society of London A, vol. 102, pp. 161-179.
Karnis, A., Goldsmith, A. L., & Mason, S. G., 1966. The kinetics of flowing dispersions: Concentrated suspensions of rigid particles. Journal of Colloid and Interface Science, vol. 22, pp. 531-553.
Kim, J. M., Lee, S. G., & Kim, C., 2008. Numerical simulations of particle migration in suspension flows: Frame-invariant formulation of curvature-induced migration. Journal of Non-Newtonian Fluid Mechanics, vol. 150, pp. 162-176.
Kistler, S. F. & Schweizer, P. M., 1997. Liquid film coating. Chapman & Hall.
Koh, C. J., Hookham, P., & Leal, L. G., 1994. An experimental investigation of concentrated suspension flows in a rectangular channel. Journal of Fluid Mechanics, vol. 266, pp. 1-32.
Krieger, I. M., 1972. Rheology of monodisperse latices. Advances in Colloid and Interface Science, vol. 3, pp. 111-136.
Krieger, I. M. & Dougherty, T. J., 1959. A mechanism for non-Newtonian flow in suspensions of rigid spheres. Transactions of The Society of Rheology, vol. 3, pp. 137-152.
Kulshreshtha, A. K., Singh, O. N., & Wall, G. M., 2010. Pharmaceutical Suspensions: From Formulation Development to Manufacturing. Springer.
Landau, L. D., Lifshitz, E. M., & Pitaevskii, L. P., 1984. Electrodynamics of Continuous Media. Pergamon Press.
Larson, R. G., 1988. Constitutive equations for polymer melts and solutions. Butterworths Books.
Larson, R. G., 1999. The Structure and Rheology of Complex Fluids. Oxford University Press.
Leighton, D. & Acrivos, A., 1987. The shear-induced migration of particles in concentrated suspensions. Journal of Fluid Mechanics, vol. 181, pp. 415-439.
Lyon, M. K. & Leal, L. G., 1998. An experimental study of the motion of concentrated suspensions in two-dimensional channel flow Part 1 : Monodisperse systems. Journal of Fluid Mechanics, vol. 363, pp. 25-56.
Miller, R. M. & Morris, J. F., 2006. Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions. Journal of Non-Newtonian Fluid Mechanics, vol. 135, pp. 149-165.
Oumer, A. N. & Mamat, O., 2013. A review of effects of molding methods, mold thickness and other processing parameters on fiber orientation in polymer composites. Asian Journal of Scientific Research, vol. 6, pp. 401-410.
Pasquali, M. & Scriven, L. E., 2002. Free surface flows of polymer solutions with models based on the conformation tensor. Journal of Non-Newtonian Fluid Mechanics, vol. 108, pp. 363-409.
Pasquali, M. & Scriven, L. E., 2004. Theoretical modeling of microstructured liquids: a simple thermodynamic approach. Journal of Non-Newtonian Fluid Mechanics, vol. 120, pp. 101-135.
Phillips, R. J., Armstrong, R. C., Brown, R. C., Graham, A. L., & Abbott, J. R., 1992. A constitutive equation for concentrated suspensions that accounts for shear-induced particle migrations. Physics of Fluids, vol. 4, pp. 30-40.
Rebouc¸as, R. B., Siqueira, I. R., de Souza Mendes, P. R., & Carvalho, M. S., 2016. On the pressure-driven flow of suspensions: particle migration in shear sensitive liquids. Journal of Non-Newtonian Fluid Mechanics, vol. 234, pp. 178”“187.
Santamar´Ä±a-Holek, I. & Mendoza, C. I., 2009. The rheology of hard sphere suspensions at arbitrary volume fractions: an improved differential viscosity model. Journal of Chemical Physics, vol. 130, pp. 044904 1-7.
Santamar´Ä±a-Holek, I. & Mendoza, C. I., 2010. The rheology of concentrated suspensions of arbitrarily-shaped particles. Journal of Colloid and Interface Science, vol. 346, pp. 118-126.
Schramm, L. L., 1996. Suspensions: Fundamentals And Applications In The Petroleum Industry. American Chemical Society.
Shewan, H. M. & Stokes, J. R., 2015. Analytically predicting the viscosity of hard sphere suspensions from the particle size distribution. Journal of Non-Newtonian Fluid Mechanics, vol. 222, pp. 72-81.
Sinton, S. A. &Chow, A., 1991. NMR flow imaging of fluids and solid suspensions in Poiseuille flow. Journal of Rheology, vol. 35, pp. 735-772.
Subia, S. R., Ingber, M. S., Mondy, L. A., Altobelli, S. A., & Graham, A. L., 1998. Modelling of concentrated suspensions using a continuum constitutive equation. Journal of Fluid Mechanics, vol. 373, pp. 193-219.
Szady, M. J., Salamon, T. R., Liu, A.W., Armstrong, R. C., & Brown, R. A., 1995. A new mixed finite element method for viscoelastic flows governed by differential constitutive equations. Journal of Non-Newtonian Fluid Mechanics, vol. 59, pp. 215-243.
Trados, T. F., 2011. Rheology of Dispersions: Principles and Applications. JohnWiley & Sons.
Trados, T. F., 2012. Dispersion of Powders in Liquids and Stabilization of Suspensions. John Wiley & Sons.
Trebbin, M., Steinhauser, D., Perlich, J., Buffet, A., Roth, S. V., Zimmermann, W., Thiele, J., & Frster, S., 2013. Anisotropic particles align perpendicular to the flow direction in narrow microchannels. Proceedings of the National Academy of Sciences, vol. 110, pp. 6706-6711.
Downloads
Publicado
Como Citar
Edição
Seção
Licença
Autores que publicam nesta revista concordam com os seguintes termos:
Autores mantém os direitos autorais e concedem à revista o direito de primeira publicação, sendo o trabalho simultaneamente licenciado sob a Creative Commons Attribution License o que permite o compartilhamento do trabalho com reconhecimento da autoria do trabalho e publicação inicial nesta revista.
Autores têm autorização para assumir contratos adicionais separadamente, para distribuição não-exclusiva da versão do trabalho publicada nesta revista (ex: publicar em repositório institucional ou como capítulo de livro), com reconhecimento de autoria e publicação inicial nesta revista.
Autores têm permissão e são estimulados a publicar e distribuir seu trabalho online (ex: em repositórios institucionais ou na sua página pessoal) a qualquer ponto antes ou durante o processo editorial, já que isso pode gerar alterações produtivas, bem como aumentar o impacto e a citação do trabalho publicado.
