scholarly journals Numerical Approximation of a Quasi-Newtonian Stokes Flow Problem with Defective Boundary Conditions

2007 ◽  
Vol 45 (5) ◽  
pp. 2120-2140 ◽  
Author(s):  
Vincent J. Ervin ◽  
Hyesuk Lee
Keyword(s):  
Boundary Conditions ◽  
Stokes Flow ◽  
Numerical Approximation ◽  
Flow Problem ◽  
Defective Boundary Conditions

Stokes flow with slip and Kuwabara boundary conditions

2002 ◽  
Vol 112 (3) ◽  
pp. 463-475 ◽  
Author(s):  
Sunil Datta ◽  
Satya Deo
Keyword(s):  
Boundary Conditions ◽  
Stokes Flow

Slow steady rotation of axially symmetric bodies in a viscous fluid

1961 ◽  
Vol 10 (1) ◽  
pp. 17-24 ◽  
Author(s):  
R. P. Kanwal
Keyword(s):  
Angular Velocity ◽  
Flow Field ◽  
Viscous Fluid ◽  
Stokes Flow ◽  
Flow Problem ◽  
Analytic Solutions ◽  
The Body ◽  
Axially Symmetric ◽  
Steady Rotation ◽  
Axis Of Symmetry

The Stokes flow problem is considered here for the case in which an axially symmetric body is uniformly rotating about its axis of symmetry. Analytic solutions are presented for the heretofore unsolved cases of a spindle, a torus, a lens, and various special configurations of a lens. Formulas are derived for the angular velocity of the flow field and for the couple experienced by the body in each case.

scholarly journals From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

2021 ◽  
Vol 44 (1) ◽  
Author(s):  
Hendrik Ender ◽  
Jan Kierfeld
Keyword(s):  
Symmetry Breaking ◽  
Boundary Conditions ◽  
Spontaneous Symmetry Breaking ◽  
Stokes Flow ◽  
Peclet Number ◽  
Swimming Velocity ◽  
Marangoni Flow ◽  
Péclet Number ◽  
Constant Flux ◽  
Flux Boundary Conditions

AbstractWe present a theory for the self-propulsion of symmetric, half-spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air–water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion–advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient along the air–water–swimmer contact line and Marangoni flow forces. We unravel whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occur for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.

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