Bharadwaj model

Similar to the Nielsen model, the Bharadwaj model is based strictly on tortuosity arguments. The main difference is the consideration of the orientation and 

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Sewell and co workers [145-148] have performed molecular dynamics simulations using the HMX model developed by Smith and Bharadwaj [142] to predict thermophysical and mechanical properties of HMX for use in mesoscale simulations of HMX-containing plastic-bonded explosives. Since much of the information needed for the mesoscale models cannot readily be obtained through experimental measurement, Menikoff and Sewell [145] demonstrate how information on HMX generated through molecular dynamics simulation supplement the available experimental information to provide the necessary data for the mesoscale models. The information generated from molecular dynamics simulations of HMX using the Smith and Bharadwaj model [142] includes shear viscosity, self-diffusion [146] and thermal conductivity [147] of liquid HMX. Sewell et al. have also assessed the validity of the HMX flexible model proposed by Smith and Bharadwaj in molecular dynamics studies of HMX crystalline polymorphs. 

For diffusion of liquid through rubbery polymer composites, Fickian and non-Fickian diffusion theories are frequently used to describe the mechanism of transport, but for gas or vapour, other models have been developed to fit experimental data of diffusion profiles. The models of gas transport include Maxwell s model," free volume increase mechanism," solubility increase mechanism," nanogap hypothesis," Nielsen model, " " Bharadwaj model, ° Cussler model " " and Gusev and Lusti model, " etc. 

Bharadwaj model was modified from Nielsen model by incorporating an orientation parameter, S. The range of relative orientations of the clay sheets with respect to each other is represented by 9, the angle between the direction of preferred orientation and the normal sheet. 

The Bharadwaj model expresses the equation accompanied by orientation parameter as shown in Equation (27.11) ... 

R. K. Bharadwaj, Modeling the barrier properties of polymer layered silicate nanocomposites. Macromo/ecMtei, 34 (2001), 1989-92. 

Bharadwaj A., Archer D.H., Rubin E.S. (2005) Modeling the performance offlattened tubular solid oxide fuel cell. Journal of Fuel Cell Science and Technology 2, 52-59. 

The PASS model requires description of electromigration, diffusion, and advection of sample ions as well as BGE ions. The general system of equations is highly coupled and nonlinear and, therefore, difficult to solve. However, the concentration of sample ions is much smaller than the buffer ions (typically p,M sample ions concentration or less versus order 1 mM buffer ion concentrations). Therefore, we can decouple the buffer and sample ion concentration fields. Using this approach, Bharadwaj and Santiago [4] have developed a dynamic model for PASS in a flat-plate... 

S.C. Roy, J.V. Sonawane, N.S. Rathore, A.K. Pabby, P. Janardan, R.D. Changrani, P.K. Dey, S.R. Bharadwaj, Pseudo-emulsion based hollow fibre strip dispersion, technique (PEHFSD) Optimization, modelling and application of PEHFSD for recovery of U(VI) from process effluent, Sep. Sci. Technol. 43 (2008) 3305-3332. 

Bharadwaj Rishikesh, K., Boyd Richard, H. (1999). Diffusion of Low-Molecular Penetrant into the Aromahc Polyesters Modeling with Method of Molecular Dynamics. Polymer, 40(15), 4229 236. 

Bharadwaj, R. K. 2001. Modelling the barrier prop>erties of jxjlymer-layered sihcate nanocomposites. Macromolecules 34 9189-9192. 

Bharadwaj, R.K. Modeling the barrier properties of polymtrt-laytaed silicate nanocomposites. Macromolecules 34, 9189-9192 (2001)... 

An exception to difficult-to-model filled systems is provided by the norbomene-POSS pol5miers studied by Bharadwaj and co-workers (278). POSS is polyhedral oligomeric silseqiuoxane—groups that are pendant from the poly(norbornene) chains of the model. This can be viewed as a filled system, but one in which the filler is nanoscopic and chemically bonded to the chains. The simulations were done to determine Tg, density, thermal expansion, solubility parameter, POSS mobilities, and elastic moduli in a wide-ranging study. They conclude that the ponderous nature of the POSS moieties is largely responsible for the reinforcing effect. 

The density and temperature dependence of some of the slow relaxations in PE were studied by Bharadwaj and Boyd (369) using NVT simulations with a relatively simple united atom model of the polsrmer. Runs of six nanoseconds for each of several conditions were performed, resulting in a comprehensive view of how relaxation processes depend on p and T. One insight provided by this work is that reorientation motion of the chains seems to require barrier crossings rather than free-volume adjustments. This result suggests that there is a need for analysis tools that are capable of cross-correlating different types of motions with structural or packing aspects of amorphous polymers so as to unravel the complex interplay of phenomena that determine the dominant motions in these systems. 

Kodam, M. Bharadwaj, R. Curtis, J. Hancock, B. Wassgren, C. (2009) Force model considerations for glued-sphere discrete element method simulations. Chemical Engineering Science 64, 3466-3475. 

Park Dae Soon, Kim Seong Hun. (2003). Miscibility Study on Blend of Thermotropic Liquid Crystalline Polymers and Polyester. J. Appl. Polym. Sci, 87(11), 1842-1851. Bharadwaj Rishikesh, K. Boyd Richard, H. (1999). Diffusion of Low-Molecular Penetrant into the Aromatic Polyesters Modeling with Method of Molecular Dynamics. Polymer, 40(15), 4229 236. 

The mentioned approach has been used in (Bharadwaj et al., 2007) which describes a simple probabilistic damage model for general corrosion of the tower structure. Assuming this to be the only damage mechanism causing failure of the structure, the remaining lifetime of the structure is calculated by the following model ... 

Heitemeyer, C., Kirby, J., Labaw, B., Archer, M., Bharadwaj, R. Using Abstraction and Model Checking to Detect Safety Violations in Requirements Specifications. IEEE Transactions on Software Engineering 24(11) (November 1998)... 

One of the principal assumptions of the Nielsen model is that the plates are oriented parallel to the polymer surface. In literature some results where the plates are randomly oriented along the film thickness are reported. In order to overcome this problem, Bharadwaj proposed an extension of the Nielsen model able to describe the effects of the sheet orientation on the relative permeability. The new study addressed both of these issues by modifying a simple model developed to describe permeability in filled polymers on the basis of tortuosity arguments. The tortuosity factor is modified to include the orientational order, and the relative permeability is given by Equation (11.5) ... 

Osman M A, Mittal V, Lusti H R, The aspect ratio and gas permeation in polymerlayered silicate nanocomposites , Macromol. Rapid Commun., 2004 25 1145—9. Bharadwaj R K, Modeling the Barrier Properties of Polymer-Layered Silicate Nanocomposites , Macromolecules, 2001 34 9189—92. 

Bharadwaj, R.K., Bunning, T.J., and Farmer, B.L. (2000). A mesoscale modelling study of nematic liquid crystals confined to ellipsoidal domains, Liq. Cryst. 27 591-603. 

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