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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
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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 

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