An Analysis of the effect of the peripheral viscosity on bile flow characteristics through cystic duct with stone: Study of two-layer model with squeezing

  IJETT-book-cover  International Journal of Engineering Trends and Technology (IJETT)          
  
© 2016 by IJETT Journal
Volume-32 Number-7
Year of Publication : 2016
Authors : Suchi Agarwal, S.P.Singh

Citation 

Suchi Agarwal, S.P.Singh"An Analysis of the effect of the peripheral viscosity on bile flow characteristics through cystic duct with stone: Study of two-layer model with squeezing", International Journal of Engineering Trends and Technology (IJETT), V32(7),309-314 February 2016. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group

Abstract
Bile flow in the human biliary system plays a vital role in the pathogenesis of biliary diseases. In the present study, the effect of an overlapping stone in the cystic duct on the flow characteristics of bile is observed. The mathematical model here, considers a two-fluid model of bile, consisting of a core region of suspension of bile salts, cholesterol and bilirubin and peripheral layer of mucosa. The expression for the flow characteristics like the resistance, the wall shear stress, and the stress at the throat and at the critical height of stone is studied. It is observed that as the peripheral viscosity decreases the resistance to flow and the shear stress also decreases.

 References

[1] Jungst D, Lang T, Huber P, Lang V and Paumgartner G. Effect of phospholipids and bile acids on cholesterol nucleation time and vesicular/micellar cholesterol in gallbladder bile of patients with cholesterol stones. Journal of lipid research. Vol.34, 1993.
[2] Ooi R, Luo XY, Chin S, Johnson A and Bird NC. The flow of bile in the human cystic duct. Journal of biomechanics. 37: 1913-1922.(2004)
[3] Al-Atabi M, Chin SB, Al-Zuhair S and Luo XY. Pressure drop in laminar and turbulent flows in circular pipe with baffles – An experimental and analytical study. International Journal of Fluid Mechanics Research. Vol. 33, No. 4,(2006).
[4] Bird N C, Ooi R, Chin SB and Johnson A. Investigation of the functional three-dimensional anatomy of the human cystic duct: A single helix. ClinAnat. 19(6); 528-534, 2006.
[5] Li W G, Luo XY, Bird N and Johnson A. Correlation of mechanical factors and gallbladder pain.,J of Computational and Mathematical methods in Medicine.
[6] Li W, Chin SB, Johnson A and Bird NC. One dimensional models of the human biliary system.J of Biomechanics. Vol.129, 2007.
[7] Luo XY, Li W, Bird N, Chin SB and Johnson A.On the mechanical behavior of the human biliary system. World J. Gastroentero. March 7; 13(9):1384- 1392(2007).
[8] Li W, Luo XY, Chin SB, Hill NA, Johnson A and Bird NC. Non- Newtonian bile flow in elastic cystic duct: one and three dimensional modeling.Annals of Biomedical Engineering, Vol.36, No.11, 2008.
[9] Srivastava V P,Vishnoi R,Mishra S and Sinha P.A two layered Non-Newtonian arterial blood flow through an overlapping constriction.Applications and Applied Mathematics:An International Journal.Vol.6,Issue 11(june 2011)pp. 1781- 1797.
[10] Shukla JB,Parihar RS and Gupta SP.Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis.Bulletin of Mathematical Biology,Vol 42,pp. 797- 805.Pergamon Press Ltd.1980.
[11] Agarwal.S, Sinha A.K and Singh SP. A theoretical analysis of the effect of the non- newtonian bile flow on the flow characteristics in the diseased cystic duct. Int. J. of Appl. Math and Mech. 8(16): 92-103, 2012.
[12] Agarwal.S, Sinha A.K and Singh SP. Effect of the plug flow on the flow characteristics of bile through diseased cystic duct: Casson Model Analysis Advances in Applied Science Research, 2012, 3 (2):1098-1106
[13] Agarwal.S, Sinha A.K and Singh SP. Effect on the Flow of Bile Due to Radially Varying Viscosity in the Cystic Duct International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 2, Issue 2, March 2014, PP 180-185.

Keywords
Bile, Cystic duct, Gallstone, Shear stress, Gallstone.