On the effect of coalescence on the rheology of emulsions

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 fraction and viscosity ratio 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 about 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 vs. 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 to 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 neglecting droplet merging can lead to erroneous predictions. † Email address for correspondence: fdv@mech.kth.se

Turbulent Flows With Drops and Bubbles: What Numerical Simulations Can Tell Us—Freeman Scholar Lecture

“…Acting on the first two issues, interface merging and smaller droplets, through models or AMR strategies comes however at a cost: the free parameters of the various approaches need to be carefully selected. For coalescence models, the choice of the parameters modifies the drop-drop collision outcome: for instance, the magnitude of the repulsive forcing determines whether the interfaces will merge upon collision [235]. Furthermore, the grid resolution has a negligible effect in certain film drainage models [231,261], while it is more important in others [233].…”

“…Alternative to the use of lubrication models, a possible solution is to employ macroscopic models. Their general framework is based on a localized forcing [235][236][237], which is added at the interface in the collision region (i.e., where two separate interfaces are closer than a certain imposed threshold), thus repelling the interfaces. This repulsive force is a mesoscale representation of near-contact forces [236], which cannot be actually resolved as they act at a length scale much smaller than the resolved ones.…”

“…Another possibility is to use a short-range repulsive force as a mesoscale representation of near-contact forces [235][236][237], as, for instance, van der Waals or electrostatic forces. The short-range repulsive force acts only in the close proximity of the interface, usually in a halo few grid cells thick surrounding the drop, and is only active in the area where halos belonging to different drops superpose, as shown in the scheme in Fig.…”

Global and local statistics in turbulent emulsions

“…Numerical studies of Rosti, Brandt & Mitra (2018) show that the Eilers formula is a good description also for suspensions of viscoelastic spheres, provided that the volume fraction φ is replaced by the effective volume fraction. Among the studies of the effective viscosity, various types of dispersed entities have been investigated, such as deformable particles in suspensions and droplets in emulsions (Tadros 1994;Adams, Frith & Stokes 2004;Saiki, Prestidge & Horn 2007;Derkach 2009;Faroughi & Huber 2015;Rosti et al 2018;De Vita et al 2019;Villone & Maffettone 2019). The conventional way to measure the viscosity of a fluid is usually based on capillary tubes or rheometers, both of which only operate in the laminar regime (Pal et al 1992).…”

“…2018; De Vita et al. 2019; Villone & Maffettone 2019). The conventional way to measure the viscosity of a fluid is usually based on capillary tubes or rheometers, both of which only operate in the laminar regime (Pal et al.…”