Viscosity, two immicible phase flow, wettabilility

[Jabbar_B]

If the single phase flows on the inclined surface and this phase (let's say water) is wetting the surface then closest layer to the surface will be bounded and will not move. And velocity of flow will be in inverse proportion with viscosity of the fluid.
If now the second phase is introduced, immicible and non-wetting phase (lets say oil), it flow on top of the wetting phase. So non-wetting phase will flow on top of the thin film of wetting phase which is bounded to the surface. So now, would velocity of the non-wetting phase be dependent on the Viscosity similarly as in single wetting phase case?
thanks in advance,
J

 

[Chestermiller]

Yes. It would be dependent on the viscosity.

 

[Jabbar_B]

non-wetting fluid (oil) flows on top of the wetting fluid (water film on top of the surface). And because these two fluids do not mix that mean oil is "ice skate" on top of the water. In that case velocity will not merely depend on viscosity unlike the case when oil is wetting the surface and outer most layer is attached to surface.

is there any study on friction between immiscible fluids in flow condition?

Thanks for reply
J

 

[Andy Resnick]

non-wetting fluid (oil) flows on top of the wetting fluid (water film on top of the surface). And because these two fluids do not mix that mean oil is "ice skate" on top of the water. In that case velocity will not merely depend on viscosity unlike the case when oil is wetting the surface and outer most layer is attached to surface.

is there any study on friction between immiscible fluids in flow condition?

Thanks for reply
J

There are entire books on the subject. You are asking for the jump momentum balance condition across the deformable boundary, first written out by Scriven in 1960:

http://www.sciencedirect.com/science/article/pii/0009250960870030

 

[Chestermiller]

Bird, Stewart, and Lightfoot, Transport Phenomena, solve the problem of two fluids in contact with one another of different viscosities flowing through a flow channel. Across the interface, the shear stress and normal stress are continuous.

 

[Andy Resnick]

Bird, Stewart, and Lightfoot, Transport Phenomena, solve the problem of two fluids in contact with one another of different viscosities flowing through a flow channel. Across the interface, the shear stress and normal stress are continuous.

They don't have to be continuous- the interface may be separately modeled (Boussinesq surface fluid) with properties distinct from bulk phases. Similarly, the Laplace equation ΔP=2σκ is a jump condition across a deformed interface.

 

[Chestermiller]

They don't have to be continuous- the interface may be separately modeled (Boussinesq surface fluid) with properties distinct from bulk phases. Similarly, the Laplace equation ΔP=2σκ is a jump condition across a deformed interface.

Good point. Thanks.