If the interplay between capillary and centrifugal forces makes the fluid-fluid interface unstable and gives rise to the fingering patterns, can these patterns be unique within the same fluids and constant experimental situations?
Can we expect a uniform pattern within Hele-Shaw cells repeatedly?
Dear Hanie
Yes, it is interesting that the viscous fingering pattern is an important factor in fuild dynamics.
Dear all,
just to add something where the fingering occurs in real and practical systems. This situation is well seen in the secondary oil recovery process, in which water is injected to restore pressure and to sweep some of the oil in place. This is done until water flow fingering occurs where water mobility relatively increases with respect to oil, so water surpasses oil. To correct this problem water soluble polymers are used to thicken water to reduce its high mobility with respect to oil.
The point I want to stress is that fingering occurs even in discontinuous media (porous medium for example).
I hope this contribution will bring some additional information to the question. Regards
Dear Hanie,
although viscous fingering patterns appearing either in Hele-Shaw cells or in porous media during the dispplcement of a viscous fluid by a less viscous one are indeed unique, there are some parameter of this instability with can be predicted. The phenomena is called Saffman-Taylor instability, please refer to the pioneering study by P. G. Saffman and G. Taylor, The Penetration of a Fluid into a Porous Medium or Hele-Shaw Cell Containing a More Viscous Liquid, Proceedings of the Royal Society A, 1958, V. 245, Iss. 1242. The main theoretical result for displacement of immiscible fluids is that the wavelength of a disturbance to the interface beteween the fluids with maximum growth rate is inversely proportional to the Capillary number Ca, so that, in the limit of small surface tension (large Ca), the smaller the wave length, the larger its growth rate. This poses serious problems for modeling of S-T instability by direct numerical methods ignoring the pressure jump at the interface between the fluids (the finer the mesh, the thinner the fingers). The similar result applies for discplacement of miscible fluids, so both surface tension and molecular diffusion tend to dump small wavelenght disturbances. The topic is really interesting and has many important applications. Hope this helps.
Kind regards,
Sergei
- Badges
- Science topic
- Similar topics
- Engineering
- Thermal Engineering
- Thermofluid
- Fluid Mechanics