THE INSTABILITY OF SLIPPING FLOW IN A CURVILINEAR POROUS MICROCHANNEL
The hydrodynamic instability of flow with slippage in a curvilinear porous microchannel between two stationary concentric cylinders is investigated. Unperturbed velocity profiles for a flow with slip are obtained. The problem of linear instability is solved numerically, using the collocation method.
Calculations showed that an increase in the coefficient of slippage, the porosity of the medium and the width of the channel leads to an increase in the occupancy of the velocity profile of the undisturbed flow (the profile becomes more flat). This, in turn, leads to an increase in the critical values of Dean number and the critical wave length of the perturbation, which determine the instability criteria for the flow. It is also shown that for σ> 0 the dependences of the critical Dean number on the parameter η have a minimum observed at η = 0.5. With decrease in channel width and permeability, this effect is leveled.
2. Bhagat A.A., Kuntaegowdanahalli S.S., Papautsky I. Continuous particle separation in spiral microchannels using dean flows and differential migration, Lab Chip, 2008, Vol.8, pp.1906–1914. (Eng)
3. Avramenko A. A., Kuznetsov A. V. Instability of a slip flow in a curved channel formed by two concentric cylindrical surfaces, European Journal of Mechanics B/Fluids, 2009, 28, Vol. 6, pp. 722–727. (Eng)
4. Avramenko A. A., Tyrinov A. I., Shevchuk I. V., Dmitrenko N. P. Centrifugal instability of nanofluids with radial temperature and concentration non-uniformity between co-axial rotating cylinders, European Journal of Mechanics B/Fluids, 2016, №60, pp. 90– 98. (Eng)
5. Avramenko A. A., Tyrinov A. I., Shevchuk I. V., Dmitrenko N. P. Dean instability of nanofluids with radial temperature and concentration non-uniformity, Phys. Fluids, 2016, №28, рр. 034104-1 - 034104-16. (Eng)
6. Avramenko A. A., Shevchuk I. V., Harmand S., Tyrinov A. I. Thermocapillary instability in an evaporating two-dimensional thin layer film, International Journal of Heat and Mass Transfer, 2015, №91, рр. 77 – 88. (Eng)
7. Avramenko A.A., Kuznetsov A.V., Basok B.I., Blinov D.G. Investigation of stability of a laminar flow in a parallel-plate channel filled with a fluid saturated porous medium, Phys. Fluids, 2005, №17, рр. 094102-1 - 094102-6. (Eng)
8. Avramenko A.A., Kuznetsov A.V., Nield D.A. Instability of slip-flow in a channel occupied by a hyper-porous medium, Journal of Porous Media, 2007, vol. 10, рр. 435 – 442. (Eng)
9. Avramenko A.A., Kuznetsov A.V. Renormalization group model of macroscopic turbulence in porous media, Transport in Porous Media, 2006, vol. 63, рр. 175 – 193. (Eng)
10. Avramenko A.A., Kuznetsov A.V. Flow in a Curved Porous Channel with a Rectangular Cross Section, Journal of Porous Media, 2008, vol. 11, рр. 241 – 246. (Eng)
11. Avramenko A.A., Kuznetsov A.V. Flow instability in a curved porous channel formed by two concentric cylindrical surfaces, Transport in Porous Media, 2007, vol. 69, рр. 373 – 381. (Eng)
Abstract views: 103 PDF Downloads: 80
This work is licensed under a Creative Commons Attribution 4.0 International License.
If the article is accepted for publication in the journal «Industrial Heat Engineering» the author must sign an agreementon transfer of copyright. The agreement is sent to the postal (original) or e-mail address (scanned copy) of the journal editions.
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License International CC-BY that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.