Flow of a Casson ¯uid in a narrow tube with a side branch J.C. Misra * , S.K. Ghosh Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India Received 5 February 1999; received in revised form 30 July 1999; accepted 29 September 1999 (Communicated by E.S. S ßUHUB _ I) Abstract Development of a mathematical model suitable for studying the mass-¯ux and hematocrit reduction due to plasma skimming in a capillary emerging from an artery making an angle a with the parent artery is of primary concern in the paper. The ¯ow is considered to have three phases ± the peripheral plasma layer, the cell depleted middle layer and the core region where the concentration of erythrocytes is highest. Both steady and pulsatile ¯ow situation are studied. The analysis for pulsatile ¯ow has been carried out by considering the pressure gradient as a periodic function of time and the inertial eects as negligibly small. A perturbation technique is employed to solve the resulting quasi-steady non-linear system of equations that are considered to govern the ¯ow. Basing upon relevant experimental data available for coronary arteries as well as very small vessels of the circulatory system, the study has been performed by considering Wo- meresely parameter to be small (less than unity). The theoretical estimates computed under the purview of the present mathematical analysis reveal that hematocrit in the branch capillary decreases with an increase in the yield stress of blood, both in steady and pulsatile ¯ows for any branching angle. Further, erythrocytes entrainment from the parent artery to the branch capillary is least when the branch is perpendicular to the parent artery. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Casson ¯uid; Erythrocytes; Branch capillary; Non-Newtonian ¯uid 1. Introduction One of the principal causes for the reduction of hematocrit in the microcirculatory system is the so-called plasma skimming, that is the fact that blood enters the branch capillary of the parent www.elsevier.com/locate/ijengsci International Journal of Engineering Science 38 (2000) 2045±2077 * Corresponding author. Fax: +91-03222-55303. E-mail address: jcm@maths.iitkgp.ernet.in (J.C. Misra). 0020-7225/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII:S0020-7225(00)00008-2