Thermocapillary migration of a spherical drop in an arbitrary transient Stokes flow

2015 ◽  
Vol 27 (6) ◽  
pp. 063104 ◽  
Author(s):  
V. Sharanya ◽  
G. P. Raja Sekhar
Keyword(s):  
Stokes Flow ◽  
Spherical Drop ◽  
Thermocapillary Migration ◽  
Transient Stokes Flow

Recriprocal theorem for concentric compound drops in arbitrary Stokes flows

1993 ◽  
Vol 252 ◽  
pp. 265-277 ◽  
Author(s):  
H. Haj-Hariri ◽  
A. Nadim ◽  
A. Borhan
Keyword(s):  
Reynolds Number ◽  
Stokes Flow ◽  
Reciprocal Theorem ◽  
Stokes Flows ◽  
Thermocapillary Migration ◽  
Compound Drops ◽  
Migration Velocities

The Lorentz reciprocal theorem is generalized and applied to the study of the quasisteady motion of a concentric spherical (CS) compound drop at zero Reynolds number. Using this result, the migration velocities of a force-free CS compound drop placed in a general ambient Stokes flow, as well as the forces on each drop when subjected to specified migration velocities, are calculated. The latter constitutes a generalization of Faxén's law to the case of a CS compound drop. Also some earlier results on the thermocapillary migration of such drops (Borhan et al. 1992) are rederived more simply and in greater generality.

The effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow

1997 ◽  
Vol 341 ◽  
pp. 165-194 ◽  
Author(s):  
XIAOFAN LI ◽  
C. POZRIKIDIS
Keyword(s):  
Surface Tension ◽  
Stokes Flow ◽  
Capillary Number ◽  
Surfactant Concentration ◽  
Drop Deformation ◽  
Main Body ◽  
Incident Flow ◽  
Spherical Drop ◽  
Convection Diffusion ◽  
Elasticity Number

The effect of an insoluble surfactant on the transient deformation and asymptotic shape of a spherical drop that is subjected to a linear shear or extensional flow at vanishing Reynolds number is studied using a numerical method. The viscosity of the drop is equal to that of the ambient fluid, and the interfacial tension is assumed to depend linearly on the local surfactant concentration. The drop deformation is affected by non-uniformities in the surface tension due to the surfactant molecules convection–diffusion. The numerical procedure combines the boundary-integral method for solving the equations of Stokes flow, and a finite-difference method for solving the unsteady convection–diffusion equation for the surfactant concentration over the evolving interface. The parametric investigations address the effect of the ratio of the vorticity to the rate of strain of the incident flow, the Péclet number expressing the ability of the surfactant to diffuse, the elasticity number expressing the sensitivity of the surface tension to variations in surfactant concentration, and the capillary number expressing the strength of the incident flow. At small and moderate capillary numbers, the effect of a surfactant in a non-axisymmetric flow is found to be similar to that in axisymmetric straining flow studied by previous authors. The accumulation of surfactant molecules at the tips of an elongated drop decreases the surface tension locally and promotes the deformation, whereas the dilution of the surfactant over the main body of the drop increases the surface tension and restrains the deformation. At large capillary numbers, the dilution of the surfactant and the rotational motion associated with the vorticity of the incident flow work synergistically to increase the critical capillary number beyond which the drop exhibits continuous elongation. The numerical results establish the regions of validity of the small-deformation theory developed by previous authors, and illustrate the influence of the surfactant on the flow kinematics and on the rheological properties of a dilute suspension. Surfactants have a stronger effect on the rheology of a suspension than on the deformation of the individual drops.

Equivalent Inclusion Method for the Stokes Flow of Drops Moving in a Viscous Fluid

2014 ◽  
Vol 81 (7) ◽  
Author(s):  
H. M. Yin ◽  
P.-H. Lee ◽  
Y. J. Liu
Keyword(s):  
Viscous Fluid ◽  
Stokes Flow ◽  
The Body ◽  
Function Technique ◽  
Elongation Ratio ◽  
Spherical Drop ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix

The equivalent inclusion method is presented to derive the Stokes flow of multiple drops moving in a viscous fluid at a small Reynolds number. The drops are replaced by inclusions with the same viscosity as the fluid, but an eigenstrain rate field that is a fictitious nonmechanical strain rate field is introduced to represent the viscosity mismatch between each drop and the matrix fluid. The velocity and pressure fields can be solved by considering the body force and eigenstrain rate on the inclusions with the Green's function technique. When one spherical drop is considered, the solution recovers the closed-form classic solution. This method is versatile and can be used in the simulation of a many-body system with different drop size, elongation ratio, and viscosity. Numerical examples demonstrate the capability and accuracy of the proposed formulation and illustrate particles' rotation and motion caused by particle interactions.

scholarly journals Surfactant-induced migration of a spherical drop in Stokes flow

2010 ◽  
Vol 22 (1) ◽  
pp. 013102 ◽  
Author(s):  
James A. Hanna ◽  
Petia M. Vlahovska
Keyword(s):  
Stokes Flow ◽  
Spherical Drop
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