Dear Arshan,

as far as I know, the Couette flow is used by NASA in rotating bioreactor for cartilage tissue engineering applications (a good resource for a start could be this https://smartech.gatech.edu/handle/1853/18174 or this http://ajprenal.physiology.org/content/281/1/F12). Also, the Magnus effect on a cylinder has been used for an exotic type propulsion, called "Flettner rotors" (http://en.wikipedia.org/wiki/Rotor_ship). 

Finally, I believe page 1 of this (ftp://ftp.nist.gov/pub/itl/div891/thesis-final.pdf) thesis contains all the information you need. I quote: "applications include rotary fractionation columns (Willingham et al. 1947; Macleod & Matterson 1959), heat transfer (Gazley 1958; Kaye & Elgar 1958; Becker & Kaye 1962; Kataoka, Doi & Komai 1977), electrochemical reactors using rotating cylinder electrodes (Gabe 1974; Legrand, Dumargue & Coeuret 1980; Coeuret & Legrand 1981; Gu & Fahidy 1982; Gabe & Walsh 1983; Eklund & Simonsson 1988; Gabe et al. 1998; Gao, Scheeline & Pearlstein 2002), membrane oxygenation and filtration devices (Strong & Carlucci 1976; Moore & Cooney 1995), and so-called "vortex flow reactors" (Giordano et al. 1998, 2000; Resende et al. 2001).

Other applications include continuous-flow photochemical reactors (Haim & Pismen 1994; Sczechowski, Koval & Noble 1995), and reactors for certain classes of chemical reactions in which a nearly uniform residence-time distribution is desired (Kataoka et al. 1975; Cohen & Marom 1983; Haim & Pismen 1994; Giordano et al. 1998). When the inner shaft has either an axisymmetric axially-periodic radius variation or has helical symmetry (e.g., a screw), applications include screw extruders (Griffith 1962; Kroesser & Middleman 1965; Tung & Laurence 1975; Choo, Neelakantan & Pittman 1980; Booy 1981; Choo, Hami & Pittman 1981; Elbirli & Lindt 1984; Bruker, Miawl, Hasson & Balch 1987; B¨ohme & Broszeit 1997; Broszeit 1997) used in polymer processing, and viscoseals or labyrinth pumps and seals (Stoff 1980; Rhode et al. 1986). Other applications include "through-hole" Schwartz et al. (1992) and "blind-hole" plating processes, and microfluidic applications of static mixers with helical elements (cf. Bertsch et al. 2001)."

Regards,

Andrea Antonello

Dear Arshan,

There are several applications of Taylor Couette flow through porous medium. I recommend the following interesting papers.

Bhargava, S. K. (1989), "Heat transfer in generalized Couette flow of two immiscible Newtonian fluids through a porous channel: Use of Brinkman model," Indian journal of technology 27, 211.

Channabasappa, M. N., G. Ranganna, and B. Rajappa (1983), "Stability of Couette flow between rotating cylinders lined with porous material. I," Indian J. Pure Appl. Math. 14, 741-56.

Channabasappa, M. N., G. Ranganna, and B. Rajappa (1984), "Stability of viscous flow in a rotating porous medium in the form of an annulus: the small-gap problem," Int. J. Numer. Methods Fluids 4, 803-11.

Daskalakis, J. (1990), "Couette Flow Through a Porous Medium of a High Prandtl Number Fluid with Temperature Dependent Viscosity," Int. J. Energy Res. 14, 21.

Gupta, S. C. and P. C. Jain (1981), "Couette flow of a viscous electrically conducting fluid in a porous annulus," Def. Sci. J. 31, 53-61.

Morel, J., Z. Lavan, and B. Bernstein (1977), "Flow through rotating porous annuli," Phys. Fluids 20, 726-733.

Nakayama, A. (1992), "Non-Darcy Couette Flow in a Porous Medium Filled With an Inelastic Non-Newtonian Fluid," Journal of fluids engineering 114, 642.

Narasimhacharyulu, V. and N. C. Pattabhi Ramacharyulu (1978), "Steady flow through a porous region contained between two cylinders," J. Indian Inst. Sci. 60, 37-42.

With my best regards

Prof. Bachir ACHOUR

Thanks respected Prof. Bachir ACHOUR and  Andrea Antonello.

Dear Arshan,

Notwithstanding the papers which have been published on Darcy-Brinkman convection in the presence of a moving surface, such as the Taylor-Couette problem you are interested in, or stretching surfaces which others study, I am not yet convinced that these situations are physically realistic.

If the porous medium consists of particles, such as sand, then these need to be increasingly widely-spaced as the Brinkman term becomes significant. I don't know of a mechanism by which the particles are able to remain stationary or to move with the boundary if they are separate from one another.

If the porous medium consists of pores in an otherwise fully-connected solid matrix, then it must be the case that the solid matrix is attached to the bounding surfaces, and therefore it has to stretch when surfaces move. If it is not attached to the moving bounding surface (for example, a Taylor-Couette flow with a stationary inner cylinder and a rotating outer cylinder), then how is the presence of the moving surface felt by the fluid in the stationary porous matrix?

Perhaps there is an easy answer to my doubts, and I would be very glad to know how a practical example of a moving surface bounding or within a porous medium could affect the flow. So my question is: how can one set up a practical Taylor-Couette problem where the annular cavity is filled with a porous medium and where the Darcy-Brinkman equations are valid?

Andrew

Dear Andrew,

I read your conclusion. What about a 2D case in which the inner cylinder and the porous medium are attached and stationary. The outer cylinder rotates with a very small gap from the porous medium. The outer cylinder as well as the inner cylinder can be held by their ends out of the 2D plane far from the plane cut of the study. The rotation of the outer cylinder can be controlled at the ends. This way, the effect of the outer cylinder rotation can be seen in some layers of the porous medium, and the porous medium can be consists of fully connected pores. If I am ignoring something, please let me know.

Dear Mohammad,

What you suggest can certainly be done practically. If the porous medium is attached to the inner cylinder, which is stationary as you suggest, and the outer one rotates with a small gap between it and the porous medium, then there will be Taylor-Couette flow set up in that gap. But this situation is quite different from what one would compute if, say, it is assumed that a Darcy-Brinkman medium occupies the region between the two surfaces. If one had a Darcy-Brinkman medium of this type then it is assumed subconsciously that it is attached somehow to both surfaces. So what is happening to the solid matrix?

Andrew