OJAppS  Vol.3 No.4 , August 2013
A Laminar Flow Model for Mucous Gel Transport in a Cough Machine Simulating Trachea: Effect of Surfactant as a Sol Phase Layer

In this paper, a planar three layer quasisteady laminar flow model is proposed in a cough machine which simulates mucous gel transport in model trachea due to mild forced expiration. The flow is governed by the time dependent pressure gradient generated in trachea due to mild forced expiration. Mucous gel is represented by a viscoelastic Voigt element whereas sol phase fluid and air are considered as Newtonian fluids. For fixed airflow rate, it is shown that when the viscosity of mucous gel is small, mucous gel transport decreases as the elastic modulus increases. However, elastic modulus has negligible effect on large gel viscosity. It is also shown that for fixed airflow rate and fixed airway dimension, mucous gel transport increases with the thickness of sol phase fluid and this increase is further enhanced as the viscosity of sol phase fluid decreases. The effect of surfactant is studied by considering sol phase as surfactant layer which causes slip at the wall and interface of sol phase and mucous gel. It is found that in the presence of surfactant mucous gel transport is enhanced.


Cite this paper
D. Satpathi and A. Ramu, "A Laminar Flow Model for Mucous Gel Transport in a Cough Machine Simulating Trachea: Effect of Surfactant as a Sol Phase Layer," Open Journal of Applied Sciences, Vol. 3 No. 4, 2013, pp. 312-317. doi: 10.4236/ojapps.2013.34040.
[1]   Wanner, “Clinical Aspects of Mucociliary Transport,” American Review of Respiratory Disease, Vol. 116, No. 1, 1977, pp. 73-125.

[2]   L. Allegra, R. Bossi and P. Barga, “Influence of Surfac tant on Mucociliary Transport,” European Journal of Re spiratory Diseases, Vol. 67, Suppl. 142, 1985, pp. 71-76.

[3]   H. Kai, M. Saito, K. Furuswa, Y. Oda, Y. Okano, K. Ta kahama and T. Miyata, “Protective Effect of Surface Ac tive Phospholipids against the Acid inducing Inhibitions of the Tracheal Mucociliary Transport,” The Japanese Journal of Pharmacology, Vol. 49, No. 3, 1989, pp. 375-380. doi:10.1254/jjp.49.375

[4]   Lachmann, “Possible Function on Bronchial Surfactant,” European Journal of Respiratory Diseases, Vol. 67, No. 142, 1985, pp. 49-60.

[5]   K. Rubin, O. Ramirez and M. King, “Mucus Rheology and Transport in Neonatal Respiratory Distress Syndrome and the Effect of Surfactant Therapy,” Chest, Vol. 101, No. 4, 1992, pp. 1080-1085. doi:10.1378/chest.101.4.1080

[6]   M. Agarwal, M. King, B. K. Rubin and J. B. Shukla, “Mucus Transport in a Miniaturized Simulated Cough Machine: Effect of Constriction and Serous Layer Simu lant,” Biorheology, Vol. 26, No. 6, 1989, pp. 977-988.

[7]   P. W. Scherer and L. Burtz, “Fluid Mechanical Experi ments Relevant to Coughing,” Journal of Biomechanics, Vol. 11, No. 4, 1978, pp. 183-187. doi:10.1016/0021-9290(78)90011-8

[8]   P. W. Scherer, “Mucus Transport by Cough,” Chest, Vol. 80, Suppl. 6, 1981, pp. 830-833. doi:10.1378/chest.80.6.830

[9]   M. King, “The role of Mucus Viscoelasticity in Cough Clearance,” Biorheology, Vol. 24, No. 6, 1987, pp. 589 597.

[10]   M. King, G. Brock and C. Lundell, “Clearance of Mucus by Simulated Cough,” Journal of Applied Physiology, Vol. 58, No. 6, 1985, pp. 1176-1182.

[11]   M. King, J. M. Zahm, D. Pierrot, S. Vaquez-Girod and E. Puchelle, “The Role of Mucus Gel Viscosity, Spinability and Adhesive Properties in Clearance by Simulated Cough,” Biorheology, Vol. 26, No. 4, 1989, pp. 737-745.

[12]   J. M. Zahm, D. Pierrot, C. Duvivier, M. King and E. Puchelle, “Influence of Airway Surface Liquid (Sol Phase) on Clearance by Cough,” Biorheology, Vol. 26, No. 4, 1989, pp. 747-752.

[13]   M. Agarwal, M. King and J. B. Shukla, “Mucous Gel Transport in a Simulated Cough Machine: Effects of Lon gitudinal Grooves Representing Spacing between Arrays of Cilia,” Biorheology, Vol. 31, No. 1, 1994, pp. 11-19.

[14]   W. L. Wilkinson, “Non-Newtonian Fluids,” Pergamon Press, London, 1960.

[15]   A. H. P. Skelland, “Non-Newtonian Flow and Heat Trans fer,” John Wiley and Sons Inc., New York, 1967.

[16]   S. S. Davis and J. E. Dippy, “The Rheological Properties of Sputum,” Biorheology, Vol. 6, No. 1, 1969, pp. 11-21.

[17]   S. M. Ross and S. Corssin, “Results of an Analytical Model of Mucociliary Pumping,” Journal of Applied Physiology, Vol. 37, No. 3, 1974, pp. 333-340.

[18]   A. Silberberg, “Biorheological Matching: Mucociliary In teraction and Epithelial Clearance,” Biorheology, Vol. 20, No. 2, 1983, pp. 215-222.

[19]   B. Yeates, “Mucus Rheology,” In: R. G. Crystal and J. B. West, Eds., The lung: Scientific Foundations, Raven, New York, 1991, pp. 197-203.

[20]   D. K. Satpathi, B. V. Rathish Kumar and P. Chandra, “Unsteady Sate Laminar Flow of Viscoelastic Gel and Air in a Channel: Application to Mucus Transport in a Cough Machine Simulated Trachea,” Mathematical and Com puter Modeling, Vol. 38, No. 1-2, 2003, pp. 63-75. doi:10.1016/S0895-7177(03)90006-9

[21]   D. K. Satpathi, “Mathematical Modeling of Mucus Trans port in the Lung under Pathological and Normal Condi tions,” PhD thesis, Indian Institute of Technology, Kan pur, 1998.

[22]   P. Camner, B. Mossberg, K. Philipson and G. Strandberg, “Elimination of Test Particles from Human Tracheo bronchial Tract by Voluntary Coughing,” Scandinavian Journal of Respiratory Diseases, Vol. 60, No. 2, 1979, pp. 56 62.

[23]   A. Saxena, A. P. Tyagi and R. Saxena, “Mathematical Modeling of Mucus Transport in the Lung Due to Pro longed Cough: Effect of Resistance to Flow by Serous Fluid in Cilia Bed,” International Journal of Mathemati cal Science, Vol. 10, No. 1-2, 2011, pp. 9-20.

[24]   H. Rensch and H. Von Seefeld, “Surfactant Mucus Inter action in Pulmonary Surfactant,” In: B. Robertson, L. M. G. Von Golde and J. J. Batunberg, Eds., Pulmonary Sur factant: From Molecular Biology to Clinical Practice, Elsevier Science Publishers, Amsterdam, 1984, pp. 203 214.

[25]   R. Banerjee and R. R. Puniyani, “Analysis of Dynamic Surface Properties of Therapeutic Surfactants and Lung Phospholipids,” Journal of Biomaterials Applications, Vol. 14, No. 3, 2000, pp. 243-272. doi:10.1106/9D4B-L6PP-7CTF-BY8G