On Fully Developed Flows of Fluids with a Pressure Dependent Viscosity in a Pipe

Stokes recognized that the viscosity of a fluid can depend on the normal stress and that in certain flows such as flows in a pipe or in channels under normal conditions, this dependence can be neglected. However, there are many other flows, which have technological significance, where the dependence of the viscosity on the pressure cannot be neglected. Numerous experimental studies have unequivocally shown that the viscosity depends on the pressure, and that this dependence can be quite strong, depending on the flow conditions. However, there have been few analytical studies that address the flows of such fluids despite their relevance to technological applications such as elastohydrodynamics. Here, we study the flow of such fluids in a pipe under sufficiently high pressures wherein the viscosity depends on the pressure, and establish an explicit exact solution for the problem. Unlike the classical Navier-Stokes solution, we find the solutions can exhibit a structure that varies all the way from a plug-like flow to a sharp profile that is essentially two intersecting lines (like a rotated V). We also show that unlike in the case of a Navier-Stokes fluid, the pressure depends both on the radial and the axial coordinates of the pipe, logarithmically in the radial coordinate and exponentially in the axial coordinate. Exact solutions such as those established in this paper serve a dual purpose, not only do they offer solutions that are transparent and provide the solution to a specific but simple boundary value problems, but they can be used also to test complex numerical schemes used to study technologically significant problems.     

Some polishing experiments on copper in a hyperbolic cell

Some polishing experiments have been carried out on copper anodes in a hyperbolic cell designed by Gilmont and Walton, using orthophosphoric acid as the electrolyte. The results obtained have been compared to those obtained in similar experiments in a Hull cell. It has been found that very similar bands of different reflectivity and polishes are found to form in both the cells. These bands shift with time and a study of such displacements has been made. The results are briefly discussed.     

Synthesis and antimicrobial study of linked heterocyclics containing Pyrazole-pyrimidine-thiazolidin-4-one

A new series of linked heterocyclics, 3-[4-(4-chlorophenyl)-6-(3,5-dimethyl-1-phenyl-1H-4-pyrazolyl)-2-pyrimidinyl]-2-(aryl/heteryl)-1,3-thiazolan-4-ones (6a-j), has been synthesized by the one-pot cyclo-condensation of 4-(4-chlorophenyl)-6-(3,5-dimethyl-1-phenyl-1H-4-pyrazolyl)-2-pyrimidinamine (5), aryl/heteroaryl aldehyde and thioglycolic acid. The structures of the synthesized compounds have been confirmed via IR, (1)H-NMR, (13)C-NMR, MS and elemental analyses. Further, all the newly synthesized compounds 6a-j have been assayed for their antimicrobial activity against Gram-positive and Gram-negative bacteria and fungi. The compounds containing moieties like 4-nitrophenyl (6c), 3-nitrophenyl (6d), 4-dimethylaminophenyl (6g), 2-furyl (6i) and 1,3-benzodioxole (6j), at 2-position of thiazolidin-4-one ring exhibited good inhibitory activity against all the tested organisms.     

Size effect study in magnetoelectric BiFeO3 system

In this paper, we report for the first time finite size effects on Néel temperature (T _N) of magnetoelectric BiFeO₃ system. Novel wet chemical route has been developed to produce fine particles of BiFeO₃ with controlled size and size distribution. Unlike other oxide systems, lattice volume contraction has been observed with decrease in particle size. The decrease in T _N is co-related to unit cell volume contraction occurring with reduction in particle size.     

Enantioselective total synthesis of (-)-Salinosporamide A (NPI-0052)

A novel enantioselective total synthesis of 20S proteasome inhibitor Salinosporamide A (NPI-0052; 1) is presented. Key features include intramolecular aldol cyclization of 6 to simultaneously generate the three chiral centers of advanced intermediate 5, cyclohexene ring addition using B-2-cyclohexen-1-yl-9-BBN, and inversion of the C-5 stereocenter by oxidation followed by enantioselective enzymatic reduction.     

Polarisation and polishing studies on copper in a Hull cell

In continuation of our previous work,^1–2 the effects of polishing time, sp. gr. of the electrolyte, addition of EDTA, electrolyte level, etc., on the position, size and shape of the variously polished bands obtained in a Hull cell have now been studied. I–V measurement when carried out showed that total cell voltage increases regularly with total cell current, thereby affording no explanation for the variously polished bands. However, with a specially designed probe electrode,³ it has been possible to study the current distribution as existing during polarisation at different points of the anode surface and thus offer some explanation for the appearance of variously polished bands which could not be interpreted earlier in terms of electrode potentials.