Leela Rakesh

The random parking of spheres on spheres

Given a ‘‘target’’ sphere of radius r1 and ‘‘probe’’ spheres of radius r2, we consider, as a function of r2/r1, how many probe spheres, on average, can be attached to the target sphere if (1) the attachment sites are chosen at random, (2) the probe spheres are not permitted to overlap, and (3) each attachment is irreversible. We also consider two separate extremes for selecting new attachment sites: Each probe sphere is either permitted to diffuse into place from a large distance, or the attachment site is chosen completely at random. Diffusion‐controlled attachment produces a slightly higher packing density than completely random attachment.

Phase behavior of concentrated hydroxypropyl methylcellulose solution in the presence of mono and divalent salt

Thermo reversible sol-gel transitions of hydroxypropylmethylcellulose (HPMC) are critical for many pharmaceutical, cosmetic, and food applications. This study examined the effects of salt (NaCl and CaCl₂) on the viscoelastic properties of concentrated low molecular weight HPMC solutions and found that the gelation temperature decreased linearly as a function of salt concentrations, independent of valency of cations and the mole concentration of anions. Thermal analysis showed that the depression of melting temperature can be fitted for both NaCl and CaCl₂ as a function of the total number of ions by a single linear curve, which was consistent with the melting point depression of pure water by NaCl and CaCl₂, but with a higher linear slope.

Limit cycles for successive projections onto hyperplanes in Rn

Abstract In this paper we consider successive orthogonal projections onto m hyperplanes in R n, where m ⩾ 2 and n ⩾ 2. A limit cycle is defined to be a sequence of points formed by projecting onto each of the hyperplanes once in a prescribed order, with the last projection giving the starting point. Several examples, including triangles, quadrilaterals, regular polygons, and arbitrary collections of lines in R 2, are solved for the limit cycle. Limit cycles are found in various ways, including by a limiting process and by solving an mn × mn linear system of equations. The latter approach will produce all the limit cycles for an arbitrary ordered set of m hyperplanes in R n.

Rheological Study of Time/Temperature Dependent Viscosity Curves of Mayonnaise

The shelf-life of mayonnaise is a major concern for manufacturers and restaurateurs especially in regions where adequate refrigeration is scrace. Temperature, climate and food additives affect the properties of mayonnaise. When subjected to torsional flow at constant temperature and stress, mayonnaise reveals a quasi-exponential time-dependent viscosity curve, with a shere thinning and temperature dependent phenomena. These behaviors cannot be characterized by a single well-known mathematical equation and thus must be fitted with additional piecewise functions.© 2003 ASME

Viscoelastic properties of konjac glucomannan in the presence of salts

Viscoelastic properties of konjac glucomannan (KGM) were studied in the entanglement region using steady and small-amplitude oscillatory rheological measurements in order to probe the role of salts on gel–sol transition temperature. It was found that gel–sol transition temperature, Theat (

A conservative and variation preserving finite volume method for non-overlapping meshes of reaction and diffusion in angiogenesis

G^{\prime } = G^{\prime \prime }

Rheological Study of Steady Shear and Linear Viscoelastic Characteristics of Polyethylene and Polycarbonate Nanocomposites

G′=G″), as a function of KGM concentration increased linearly with increasing salt concentration and independent of salt type. However, at higher KGM concentration, in the presence of CaCl2, the gel–sol transition temperature is higher than that of native KGM, NaCl, and KCl due to the effect of bivalent salt (Ca2+) of CaCl2 compared to the univalent salts of NaCl and KCl. The zero shear viscosity (η0) and specific viscosity are scaled as C4.0 with concentration and are also independent of the type of salt used, which confirms that KGM and salt have very minimal interaction and the viscoelastic properties are mainly due to the salting-out effect.

Solution Rheology of Saline and Polysaccharide Systems

The issue of long-term incompatible interactions associated with the permanent implants can be eliminated by using various biodegradable metal implants. The recent research is focusing on the use of degradable stents to restore most of the hindrances of capillaries, and coronary arteries by supplying instant blood flow with constant mechanical and structural support. However, internal endothelialization and infection due to the corrosion of implanted stents are not easy to diagnose in the long run. In the recent past, magnesium (Mg) has been widely investigated for the cardiovascular stent applications. Here we made an attempt to understand the biodegradation process of Mg alloy stent by studying the degradation of Mg alloy AZ31 (3 wt% Aluminum, 1 wt% Zn) powder at various time-intervals in simulated blood fluid using the Rheological methods. The degradability of the Mg stent in the arteries affects the stress-strain properties of blood plasma and the subsequent flow conditions. Blood and plasma viscosities alter due to the degradation of Mg resulting from the stress-strain experienced in the blood vessels, in which the stent is inserted. Here our objective was to explore the influence of Mg degradation on the blood plasma viscosity by studying the viscoelastic properties. In this work, the effect of dissolution of Mg alloy AZ31 on the rheological properties of Phosphate Buffer Saline (PBS) at various time intervals have been investigated. The viscosity of the PBS-AZ31 solution increased with the dissolution of both slurries and percolated clear solution. The only exception was day-7 of the percolated clear solution, where viscosity was decreased showing a reduction in viscosity at initial stages of dissolution. The frequency sweep showed the tendency of the PBS-AZ31 gelation up to 100 rad/s frequency.