An arbitrary Stokes flow of a viscous, incompressible fluid inside a sphere with internal singularities, enclosed by a porous spherical shell, using Brinkman's equation for the flow in the porous region is discussed. At the interface of the clear fluid and porous region stress jump boundary condition for tangential stresses is used. The drag and torque are found by deriving the corresponding Faxen's laws. It is found that drag and torque not only change with the varying permeability, but also change for different values of stress jump coefficient. Critical permeability is found for which drag and torque change their behavior. As a limiting case the corresponding Faxen's laws for the rigid spherical shell with internal singularities has been obtained.
Mathematics Subject Classification (2000). 76xx, 76D07, 76S05
Visceral leishmaniasis, also known as kala-azar (KA) is generally caused by Leishmania donovani. Organic pentavalent antimonials (SbV) is the first line of treatment for KA. However, the number of KA patients unresponsive to treatment with Sb(V) is steadily increasing in India and elsewhere. The primary objective of this work is to determine the factor(s) associated with the rise of unresponsiveness. Analysis of the clonal population of parasites clearly indicated that wild type parasites isolated from KA patients who were clinically cured after treatment with Sb(V), were a mixture of resistant and sensitive cells. The resistant promastigotes were also resistant as amastigotes in vivo. It was further observed that Stibanate sensitive parasites can be made resistant to the drug by repeated passages in experimental animals followed by incomplete treatment with suboptimal doses of the drug. These results suggest that the steady rise in Sb(V) unresponsiveness of KA patients in India is due to infection with resistant parasites, generated as a result of irregular and often incomplete treatment of the patients
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