Dusty effects on pulsating viscous flow of two immiscible fluids between two parallel plates

1983 ◽  
Vol 92 (3) ◽  
Author(s):  
P K Jha ◽  
M P Pateriya
Keyword(s):  
Viscous Flow ◽  
Immiscible Fluids ◽  
Parallel Plates

scholarly journals On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders

Entropy ◽  
2007 ◽  
Vol 9 (3) ◽  
pp. 118-131 ◽  
Author(s):  
Haidong Liu ◽  
Prabhamani Patil ◽  
Uichiro Narusawa
Keyword(s):  
Viscous Flow ◽  
Brinkman Equation ◽  
Parallel Plates

The Steady Viscous Flow of Two Differentially Rotating Immiscible Fluids

1982 ◽  
Vol 67 (1) ◽  
pp. 63-71 ◽  
Author(s):  
Gregory R. Baker ◽  
Steven J. Mardeusz
Keyword(s):  
Viscous Flow ◽  
Immiscible Fluids

Miscible displacement between two parallel plates: BGK lattice gas simulations

1997 ◽  
Vol 338 ◽  
pp. 277-297 ◽  
Author(s):  
N. RAKOTOMALALA ◽  
D. SALIN ◽  
P. WATZKY
Keyword(s):  
Peclet Number ◽  
Lattice Gas ◽  
Viscosity Ratio ◽  
Flow Direction ◽  
Stokes Problem ◽  
Finite Difference Methods ◽  
Immiscible Fluids ◽  
Parallel Plates ◽  
Miscible Fluids ◽  
Péclet Number

We study the displacement of miscible fluids between two parallel plates, for different values of the Péclet number Pe and of the viscosity ratio M. The full Navier–Stokes problem is addressed. As an alternative to the conventional finite difference methods, we use the BGK lattice gas method, which is well suited to miscible fluids and allows us to incorporate molecular diffusion at the microscopic scale of the lattice. This numerical experiment leads to a symmetric concentration profile about the middle of the gap between the plates; its shape is determined as a function of the Péclet number and the viscosity ratio. At Pe of the order of 1, mixing involves diffusion and advection in the flow direction. At large Pe, the fluids do not mix and an interface between them can be defined. Moreover, above M∼10, the interface becomes a well-defined finger, the reduced width of which tends to λ∞=0.56 at large values of M. Assuming that miscible fluids at high Pe are similar to immiscible fluids at high capillary numbers, we find the analytical shape of that finger, using an extrapolation of the Reinelt–Saffman calculations for a Stokes immiscible flow. Surprisingly, the result is that our finger can be deduced from the famous Saffman–Taylor one, obtained in a potential flow, by a stretching in the flow direction by a factor of 2.12.

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