scholarly journals Fluid dynamics of the slip boundary condition for isothermal rimming flow with moderate inertial effects

2019 ◽  
Vol 31 (3) ◽  
pp. 033602 ◽  
Author(s):  
J. M. P. Nicholson ◽  
H. Power ◽  
O. Tammisola ◽  
S. Hibberd ◽  
E. D. Kay
Keyword(s):  
Fluid Dynamics ◽  
Boundary Condition ◽  
Slip Boundary Condition ◽  
Inertial Effects ◽  
Slip Boundary ◽  
Rimming Flow

scholarly journals The appearance of boundary layers and drift flows due to high-frequency surface waves

2012 ◽  
Vol 707 ◽  
pp. 482-495 ◽  
Author(s):  
Ofer Manor ◽  
Leslie Y. Yeo ◽  
James R. Friend
Keyword(s):  
Boundary Layer ◽  
Surface Waves ◽  
High Frequency ◽  
Slip Boundary Condition ◽  
Inertial Effects ◽  
Velocity Amplitude ◽  
Slip Boundary ◽  
Long Period ◽  
Bulk Waves ◽  
Schlichting Streaming

AbstractThe classical Schlichting boundary layer theory is extended to account for the excitation of generalized surface waves in the frequency and velocity amplitude range commonly used in microfluidic applications, including Rayleigh and Sezawa surface waves and Lamb, flexural and surface-skimming bulk waves. These waves possess longitudinal and transverse displacements of similar magnitude along the boundary, often spatiotemporally out of phase, giving rise to a periodic flow shown to consist of a superposition of classical Schlichting streaming and uniaxial flow that have no net influence on the flow over a long period of time. Correcting the velocity field for weak but significant inertial effects results in a non-vanishing steady component, a drift flow, itself sensitive to both the amplitude and phase (prograde or retrograde) of the surface acoustic wave propagating along the boundary. We validate the proposed theory with experimental observations of colloidal pattern assembly in microchannels filled with dilute particle suspensions to show the complexity of the boundary layer, and suggest an asymptotic slip boundary condition for bulk flow in microfluidic applications that are actuated by surface waves.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

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