Contact and coalescence of viscous drops

When two fluid drops come into contact, surface tension quickly pulls the drops together into a single larger drop. This coalescence process is an example of a singular flow resulting from a topological transition, in this case between the disjoint and connected drops. In this thesis, we consider theoretically the flow in two viscous drops with inertia either side of this topological transition. The deformation of drops prior to contact sets the initial shape of the drops for the subsequent coalescence. We consider a mechanism for contact between nearby, effectively stationary drops: when such drops are in sufficiently close proximity, van der Waals attraction between the drops overcomes surface tension and deforms the surfaces into contact. We solve for the viscous dynamics of this deformation both with and without inertia and find in each case a self-similar solution. The self-similar surface evolution determines the initial surface profile, and therefore the strength of the singularity in surface curvature, for the subsequent coalescence. At sufficiently early times, coalescence is described geometrically by a small fluid bridge over which the touching drops are in contact. At the edge of the fluid bridge the surface is tightly curved. The corresponding surface tension drives an expansion of the fluid bridge and consequently coalescence. We solve for the dynamics of viscous coalescence for general initial surface profiles set by a contact process. The strength of the singularity in surface curvature at contact determines the initial rate of coalescence at leading order. For drops with both viscosity and inertia, the early-time coalescence dynamics transitions between several regimes that are determined by the relative strengths of viscosity and inertia on the different length scales of the problem. We identify regimes in which the momentum imparted on the fluid by surface tension is confined to a viscous wake over the fluid bridge. Entrainment into the wake alters the drop profile ahead of the fluid bridge and subsequently alters the rate of coalescence.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2023

Author dc:creator

• Beaty, Edward

Advisor dc:contributor.advisor

• Lister, John

• Coalescence of drops
• Fluid dynamics
• Interfacial dynamics

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/d025f2d0-1708-4126-a5a7-f2a4e77a01e3/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

Author Identifier

0000-0001-6995-8645

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/361576