Abstract
The steadystate thermocapillary motion of a Newtonian droplet translating in an otherwise quiescent OldroydB fluid has been investigated analytically in the framework of a perturbation technique and in the limit of small Deborah numbers. The analysis has been carried out assuming the absence of convective transport effects and decoupling the solution of the energy equation from the velocity field. Specific nonNewtonian correction formulae for the droplet migration velocity have been obtained in the limit of small Capillary numbers, i.e., assuming a spherical drop, as well as in the presence of small boundary deformations (small but finite Capillary numbers). Equations describing the droplet shape have also been obtained. The results show that, in the absence of deformation, the migration speed decreases monotonically with the Deborah number irrespective of the other parameters. In particular, when the viscosity and thermal conductivity of the drop are much smaller than the corresponding values for the continuous phase, the effect of elasticity becomes increasingly more important and the migration velocity is significantly decreased. When shape deformations are allowed, the velocity, evaluated as a function of the Deborah number, either initially increases with respect to the Newtonian value, or takes a behavior qualitatively similar to that observed for the spherical particle depending on the specific value of the viscosity ratio.
Original language  English 

Publication status  Published  17 Jul 2019 
Event  8th International Symposium on Bifurcations and Instabilities in Fluid Dynamics  Limerick, Ireland Duration: 16 Jul 2019 → 19 Jul 2019 
Conference
Conference  8th International Symposium on Bifurcations and Instabilities in Fluid Dynamics 

Country/Territory  Ireland 
City  Limerick 
Period  16/07/19 → 19/07/19 
Keywords
 thermocapillary flow
 creeping flow
 oldroydB fluid
 droplet migration
 asymptotic analysis
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Thermocapillary motion of droplets in complex fluid flows
Author: Capobianchi, P., 22 Feb 2019Supervisor: Oliveira, M. (Supervisor) & Zhang, Y. (Supervisor)
Student thesis: Doctoral Thesis