European Journal of Mechanics B/Fluids 29 (2010) 285–294 Contents lists available at ScienceDirect European Journal of Mechanics B/Fluids journal homepage: www.elsevier.com/locate/ejmflu Effect of momentum transfer condition at the interface of a model of creeping flow past a spherical permeable aggregate Anindita Bhattacharyya ∗ Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata - 700108, India article info Article history: Received 10 March 2009 Received in revised form 13 January 2010 Accepted 5 March 2010 Available online 18 March 2010 Keywords: Stokes flow Brinkman equation Porous sphere Stress jump boundary condition Stress jump co-efficient abstract Creeping flow past an isolated, spherical and permeable aggregate has been studied adopting the Stokes equation to model the fluid external to the aggregate and the Brinkman equation for the internal flow. At the interface of the clear fluid and porous region stress jump boundary condition for tangential stresses is used along with the continuity of velocity components and continuity of the normal stress. Using Faxen’s laws, drag and torque are calculated for different flow conditions and it is observed that drag and torque not only change with the permeability of the porous region, but as stress jump coefficient increases, the rate of change in behavior of drag and torque increases. © 2010 Elsevier Masson SAS. All rights reserved. 1. Introduction Flow through a porous media has been a topic of longstanding interest in many areas of science and engineering. Engineering systems based on fluidized bed combustion, enhance oil reservoir recovery, combustion in an inert porous matrix, underground spreading of chemical waste and chemical catalytic reactors are just a few examples of application of the study of flow through porous media. Due to its broad range of applications in science and industry this interdisciplinary field has gained extensive attention lately. In a broader sense, the study of porous media embraces fluid and thermal sciences, geothermal, petroleum and combustion engineering. In chemical engineering, mainly in industry one word used often is chemical agglomeration. From a material handling standpoint, agglomeration generally refers to the process of making larger particles (agglomerates) from smaller particles. It is used for duties as diverse as the formation of carbon black and, in the extreme, the production of scrap metal bales. Agglomerates can take the form of sheets or briquettes from an extruder or roll press process or pills and caplets from pill press operations. Other forms include prills and pearls. Many reasons for agglomeration of materials exist. These include increasing a material’s bulk density, decreasing dust concentration during feeding, reducing segregation of material (and thus product uniformity), improving the flow rate of material and making an end product such as ∗ Tel.: +91 33 25753030; fax: +91 33 25773026. E-mail addresses: su_ani@yahoo.co.in, ani_r@isical.ac.in. a briquette or pill. Immersion of permeable agglomerates in their processing media results in their progressive infiltration by the fluid. This phenomenon was observed and monitored earlier in the case of silica, calcium carbonate, carbon black and titanium dioxide agglomerates [1,2]. Matrix infiltration affects the dispersion property of agglomerates [3]. Hydrodynamic analysis of porous spheres with infiltrated peripheral shells in linear flow fields was discussed by Levresse et al. [4]. Such physical problems formulated would lead to solving a mathematical model subject to proper boundary conditions at the liquid–porous interface. To study the creeping flow past porous aggregates, the usual macroscopic continuum approach is to neglect the inertial and volume forces and treat the problem as a boundary value problem. In practical situations, the porous aggregate may be like a solid core covered with a porous layer, a porous shell or a porous sphere with uniform or varying permeability. Interest in flow past spherical boundaries began with the pioneering work of Hasimoto [5] who discussed an axisymmetric flow past a rigid sphere and after that several studies came up on this topic [6,7]. The steady flow of a Newtonian fluid past a solid sphere, liquid drop at low Reynolds number have been studied extensively by Happel and Brenner [8]. An interesting review on Stokes flow past spherical boundaries was given recently by Hasimoto [9]. Jones [10] studied the fluid flow of low Reynolds number past a porous spherical shell. Neale et al. [11] discussed a problem of creeping flow relative to a permeable sphere. The problem of Stokes flow past porous particles using Brinkman’s equation began with the work of Higdon and Kojima [12]. Also Qin and Kaloni [13] have discussed the creeping flow past a porous spherical shell. But, a majority of the study was on 0997-7546/$ – see front matter © 2010 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.euromechflu.2010.03.002