Abstract
The present article deals with theoretical analysis on the peristaltic transport of a couple stress fluid with lubrication on the walls of the channel. The walls are coated with thin layer of power-law lubricant and the condition arised by the coating is modelled by taking the continuity of velocity and shear stresses of both the fluids at the fluid–fluid interface. The flow problem is discussed in two-dimensional asymmetric medium assuming long wavelength and low Reynolds number. Closed form solutions for velocity, stream function and flow rate are discussed. The numerical solutions for pressure rise, trapping and reflux are discussed. The effects of lubricant parameter, couple stress parameter, phase difference, wave amplitudes and flow rate are discussed for symmetric and asymmetric channels. It is observed that by increasing the lubrication effects, pressure rise increases in the pumping region and for trapping, boluses disappear and streamlines become parallel to the walls of the channel. From the given flow problem, the limiting cases of no-slip and viscous flow are presumed and found to be in excellent agreement with the existing literature.
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References
V K Stokes, Phys. Fluids 9(9), 1709 (1966)
T W Latham, Fluid motion in peristaltic pump, MS Thesis (Massachusetts Institute of Technology, Cambridge, 1966)
A M Siddiqui and W H Schwarz, J. Non-Newtonian Fluid Mech. 53, 257 (1994)
A M Siddiqui, A Provost and W H Schwarz, Rheol. Acta 30(3), 249 (1991)
M H Haroon, Comm. Non-linear Sci. Numer. Simul. 12(8), 1464 (2007)
T Hayat, Y Wang, A M Siddiqui, K Hutter and S Asghar, Math. Models Meth. Appl. Sci. 12(12), 1691 (2002)
T Hayat, F Mahmood and S Asghar, Non-linear Dynam. 40(4), 375 (2005)
T Hayat, Y Wang, S Asghar, K Hutter and A M Siddiqui, Math. Problems Eng. 4, 347 (2004)
K S Makheimer, Biorheology 39(6), 755 (2002)
L M Srivastava, Rheol. Acta 25(6), 638 (1986)
A M Siddiqui, T Hayat and M Khan, J. Phys. Soc. Jpn 73(8), 2142 (2004)
M Elshahed and M H Haroun, Math. Problems Eng. 6, 663 (2005)
K S Makheimer, Phys. Lett. A 372(23), 4271 (2008)
D D Joseph, Phys. Fluids 23(12), 2356 (1980)
H I Anderson and O A Valnes, Fluid Dynam. Res. 24(4), 211 (1999)
B Santra, B S Dandapat and H I Anderson, Acta Mech. 194(1–4), 1 (2007)
M Sajid, K Mahmood and Z Abbas, Chin. Phys. Lett. 29(2), 024702 (2012)
M Sajid, T Javed, Z Abbas and N Ali, Int. J. Nonlinear Sci. Numer. Simul. 14(5), 285 (2013)
K Mahmood, M Sajid, N Ali and F Labropulu, J. Appl. Mech. Technol. Phys. 58(2), 224 (2017)
K Mahmood, M Sajid, N Ali and M N Sadiq, Eur. Phys. J. Plus 132(7), 297 (2017)
K Mahmood, M Sajid, M N Sadiq and N Ali, Phys. Astron. Int. J. 2, 389 (2018)
K Mahmood, M N Sadiq, M Sajid and N Ali, J. Braz. Soc. Mech. Sci. Eng. 41(2), 65 (2019)
M Sajid, M N Sadiq, K Mahmood and N Ali, Sadhana 44, 136 (2019)
M N Sadiq, M Sajid, N Ali and T Javed, J. Braz. Soc. Mech. Sci. Eng. 42, 390 (2020)
A H Shapiro, M Y Jaffrin and S L Weinberg, J. Fluid Mech. 37(4), 799 (1969)
P Tong and D Vawter, J. Appl. Mech. 39(4), 857 (1972)
M Mishra and A R Rao, ZAMP 54(3), 532 (2003)
N Ali, T Hayat and M Sajid, Biorheology 44(2), 125 (2007)
H S Lew, Y C Fung and C B Lowenstein, J. Biomech. 4(4),297 (1971)
T Hayat, M Iqbal, H Yasmin, F E Alsaadi and H Gao, Pramana – J. Phys. 85(1), 125 (2015)
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Mahmood, W., Sajid, M., Sadiq, M.N. et al. Lubrication effects on the peristaltic motion of a couple stress fluid in an asymmetric channel. Pramana - J Phys 95, 7 (2021). https://doi.org/10.1007/s12043-020-02055-z
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DOI: https://doi.org/10.1007/s12043-020-02055-z
Keywords
- Peristaltic motion
- couple stress fluid
- interfacial boundary condition
- asymmetric channel
- exact solution
- pumping
- trapping
- reflux