Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-13T22:39:56.124Z Has data issue: false hasContentIssue false
  • English
  • Français

On the effect of coalescence on the rheology of emulsions

Published online by Cambridge University Press:  18 October 2019

Francesco De Vita Open the ORCID record for Francesco De Vita [Opens in a new window] ,
Marco Edoardo Rosti Open the ORCID record for Marco Edoardo Rosti [Opens in a new window] ,
Sergio Caserta  and
Luca Brandt Open the ORCID record for Luca Brandt [Opens in a new window]
Francesco De Vita*
Affiliation:
Linné Flow Center and SeRC (Swedish e-Science Reseach Center), KTH Mechanics, S-100 44 Stockhom, Sweden
Marco Edoardo Rosti
Affiliation:
Linné Flow Center and SeRC (Swedish e-Science Reseach Center), KTH Mechanics, S-100 44 Stockhom, Sweden
Sergio Caserta
Affiliation:
University of Naples ‘Federico II’, Department of Chemical, Materials and Industrial Production Engineering, Piazzale V. Tecchio 80, 80125 Napoli, Italy
Luca Brandt
Affiliation:
Linné Flow Center and SeRC (Swedish e-Science Reseach Center), KTH Mechanics, S-100 44 Stockhom, Sweden
*
†Email address for correspondence: fdv@mech.kth.se
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a numerical study of the rheology of a two-fluid emulsion in dilute and semidilute conditions. The analysis is performed for different capillary numbers, volume fractions and viscosity ratios under the assumption of negligible inertia and zero buoyancy force. The effective viscosity of the system increases for low values of the volume fraction and decreases for higher values, with a maximum for approximately 20 % concentration of the disperse phase. When the dispersed fluid has lower viscosity, the normalised effective viscosity becomes smaller than 1 for high enough volume fractions. To single out the effect of droplet coalescence on the rheology of the emulsion we introduce an Eulerian force which prevents merging, effectively modelling the presence of surfactants in the system. When the coalescence is inhibited the effective viscosity is always greater than 1 and the curvature of the function representing the emulsion effective viscosity versus the volume fraction becomes positive, resembling the behaviour of suspensions of deformable particles. The reduction of the effective viscosity in the presence of coalescence is associated with the reduction of the total surface of the disperse phase when the droplets merge, which leads to a reduction of the interface tension contribution to the total shear stress. The probability density function of the flow topology parameter shows that the flow is mostly a shear flow in the matrix phase, with regions of extensional flow when the coalescence is prohibited. The flow in the disperse phase, instead, always shows rotational components. The first normal stress difference is positive, except for the smallest viscosity ratio considered, whereas the second normal difference is negative, with their ratio being constant with the volume fraction. Our results clearly show that the coalescence efficiency strongly affects the system rheology and that neglecting droplet merging can lead to erroneous predictions.

JFM classification

Complex Fluids: Emulsions Multiphase and Particle-laden Flows: Multiphase flow Non-Newtonian Flows: Rheology
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 880 , 10 December 2019 , pp. 969 - 991
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albadawi, A., Donoghue, D. B., Robinson, A. J., Murray, D. B. & Delauré, Y. M. C. 2013 Influence of surface tension implementation in volume of fluid and coupled volume of fluid with level set methods for bubble growth and detachment. Intl J. Multiphase Flow 53, 11–28.Google Scholar
Batchelor, G. K. 1970 Stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Batchelor, G. K. & Green, J. T. 1972 Hydrodynamic interaction of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56 (2), 375–400.Google Scholar
Bolotnov, I. A., Jansen, K. E., Drew, D. A., Oberai, A. A., Lahey, R. T. & Podowski, M. Z. 2011 Detached direct numerical simulations of turbulent two-phase bubbly channel flow. Intl J. Multiphase Flow 37 (6), 647–659.10.1016/j.ijmultiphaseflow.2011.03.002Google Scholar
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335–354.Google Scholar
Caserta, S. & Guido, S. 2012 Vorticity banding in biphasic polymer blends. Langmuir 28 (47), 16254–16262.Google Scholar
Caserta, S., Sabetta, L., Simeone, M. & Guido, S. 2005 Shear-induced coalescence in aqueous biopolymer mixtures. Chem. Engng Sci. 60 (4), 1019–1027.Google Scholar
Chesters, A. K. 1991 The modelling of coalescence process in fluid-liquid dispersions: a review of current understanding. Chem. Engng Res. Des. 69 (4), 259–270.Google Scholar
Choi, S. J. & Schowalter, W. R. 1975 Rheological properties of nondilute suspensions of deformable particles. Phys. Fluids 18 (4), 420–427.10.1063/1.861167Google Scholar
De Vita, F., Rosti, M. E., Izbassarov, D., Du, L., Tammisola, O., Hormozi, S. & Brandt, L. 2018 Elastoviscoplastic flows in porous media. J. Non-Newtonian Fluid Mech. 258 (April), 10–21.Google Scholar
Eilers, V. H. 1941 Die Viskositat von Emulsionen hochviskoser Stoffe als Funktion der Konzentration. Kolloidn. Z. 97, 313–321.10.1007/BF01503023Google Scholar
Einstein, A. 1906 Eine neue Bestimmung der Molekuldimensionen. Ann. Phys. 19, 289–306.Google Scholar
Einstein, A. 1911 Berichtingung zu meiner Arbeit: ‘Eine neue Bestimmung der Molekuldimensionen’. Ann. Phys. 34, 591–592.Google Scholar
Foudazi, R., Qavi, S., Masalova, I. & Malkin, A. Y. 2015 Physical chemistry of highly concentrated emulsions. Adv. Colloid Interface Sci. 220, 78–91.Google Scholar
Guazzelli, E. & Pouliquen, O. 2018 Rheology of dense granular suspensions under extensional flow. J. Fluid Mech. 852 (P1), 1–73.Google Scholar
Guido, S. & Simeone, M. 1998 Binary collision of drops in simple shear flow. J. Fluid Mech. 357, 1–20.Google Scholar
Hudson, S. D. 2003 Wall migration and shear-induced diffusion of fluid droplets in emulsions. Phys. Fluids 15 (5), 1106–1113.Google Scholar
Ii, S., Sugiyama, K., Takeuchi, S., Takagi, S. & Matsumoto, Y. 2012 An interface capturing method with a continuous function: the THINC method with multi-dimensional reconstruction. J. Comput. Phys. 231 (5), 2328–2358.Google Scholar
Khatri, S. & Tornberg, A.-K. 2011 Computers and fluids a numerical method for two phase flows with insoluble surfactants. Comput. Fluids 49 (1), 150–165.Google Scholar
Kulkarni, P. M. & Morris, J. F. 2008 Suspension properties at finite Reynolds number from simulated shear flow. Phys. Fluids 20, 040602.Google Scholar
Loewenberg, M. & Hinch, E. J. 1996 Numerical simulations of a concentrated emulsion in shear flow. J. Fluid Mech. 321, 395–419.Google Scholar
Mari, R., Seto, R., Morris, J. F. & Denn, M. M. 2014 Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions. J. Rheol. 58, 1693.Google Scholar
Matsunaga, D., Imai, Y., Yamaguchi, T. & Ishikawa, T. 2015 Rheology of a dense suspension of spherical capsules under simple shear flow. J. Fluid Mech. 786, 110–127.Google Scholar
Pal, R. 2002 Novel shear modulus equations for concentrated emulsions of two immiscible elastic liquids with interfacial tension. J. Non-Newtonian Fluid Mech. 105 (1), 21–33.10.1016/S0377-0257(02)00058-7Google Scholar
Pal, R. 2003 Viscous behavior of concentrated emulsions of two immiscible Newtonian fluids with interfacial tension. J. Colloid Interface Sci. 263 (1), 296–305.Google Scholar
Pal, R. 2011 Rheology of simple and multiple emulsions. Curr. Opin. Colloid Interface Sci. 16 (1), 41–60.Google Scholar
Picano, F., Breugem, W. P., Mitra, D. & Brandt, L. 2013 Shear thickening in non-Brownian suspensions: an excluded volume effect. Phys. Rev. Lett. 111 (9), 2–6.Google Scholar
Rosti, M. E. & Brandt, L. 2018 Suspensions of deformable particles in a Couette flow. J. Non-Newtonian Fluid Mech. 262 (C), 3–11.Google Scholar
Rosti, M. E., Brandt, L. & Mitra, D. 2018 Rheology of suspensions of viscoelastic spheres: Deformability as an effective volume fraction. Phys. Rev. Fluids 3 (1), 012301.Google Scholar
Rosti, M. E., De Vita, F. & Brandt, L. 2019 Numerical simulations of emulsions in shear flows. Acta Mechanica 230 (2), 667–682.Google Scholar
Russo, G. & Smereka, P. 2000 A remark on computing distance functions. J. Comput. Phys. 163 (1), 51–67.Google Scholar
Schowalter, W. R., Chaffey, C. E. & Brenner, H. 1968 Rheological behavior of a dilute emulsion. J. Colloid Interface Sci. 26 (2), 152–160.Google Scholar
Sega, M., Sbragaglia, M., Kantorovich, S. S. & Ivanov, A. O. 2013 Mesoscale structures at complex fluid-fluid interfaces: a novel lattice Boltzmann/molecular dynamics coupling. Soft Matt. 9 (42), 10092–10107.Google Scholar
Shardt, O., Derksen, J. J. & Mitra, S. K. 2013 Simulations of droplet coalescence in simple shear flow. Langmuir 29 (21), 6201–6212.Google Scholar
Sibillo, V., Pasquariello, G., Simeone, M., Cristini, V. & Guido, S. 2006 Drop deformation in microconfined shear flow. Phys. Rev. Lett. 97 (5), 1–4.Google Scholar
Soligo, G., Roccon, A. & Soldati, A. 2019 Coalescence of surfactant-laden drops by phase field method. J. Comput. Phys. 376, 1292–1311.Google Scholar
Srivastava, P., Malipeddi, A. R. & Sarkar, K. 2016 Steady shear rheology of a viscous emulsion in the presence of finite inertia at moderate volume fractions: sign reversal of normal stress differences. J. Fluid Mech. 805, 494–522.Google Scholar
Taylor, G. I. 1932 The viscosity of a fluid containig small drops of another fluid. Proc. R. Soc. Lond. A 138, 41–48.Google Scholar
Vananroye, A., Van Puyvelde, P. & Moldenaers, P. 2006 Structure development in confined polymer blends: steady-state shear flow and relaxation. Langmuir 22 (5), 2273–2280.Google Scholar
Xia, Y., Gates, B., Yin, Y. & Lu, Y. 2000 Monodispersed colloidal spheres: old materials with new applications. Adv. Mater. 12, 693–713.Google Scholar
Yang, M., Krishnan, S. & Shaqfeh, E. S. G. 2016 Numerical simulations of the rheology of suspensions of rigid spheres at low volume fraction in a viscoelastic fluid under shear. J. Non-Newtonian Fluid Mech. 233, 181–197.Google Scholar
Zhou, H. & Pozrikidis, C. 1993 The flow of ordered and random suspensions of two-dimensional drops in a channel. J. Fluid Mech. 255, 103–127.10.1017/S0022112093002411Google Scholar