Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

Studies on Electrical and Thermal Properties of Certain Selected Photonic Materials

The present thesis is centered around the study of electrical and thermal properties of certain selected photonic materials.We have studied the electrical conduction mechanism in various phases of certain selected photonic materials and those associated with different phase transitions occurring in them. A phase transition leaves its own impressions on the key parameters like electrical conductivity and dielectric constant. However, the activation energy calculation reveals the dominant factor responsible for conduction process.PA measurements of thermal diffusivity in certain other important photonic materials are included in the remaining part of the research work presented in this thesis. PA technique is a promising tool for studying thermal diffusivities of solid samples in any form. Because of its crucial role and common occurrence in heat flow problems, the thermal diffusivity determination is often necessary and knowledge of thermal diffusivity can intum be used to calculate the thermal conductivity. Especially,knowledge of the thermal diffusivity of semiconductors is important due to its relation to the power dissipation problem in microelectronic and optoelectronic devices which limits their performances. More than that, the thermal properties, especially those of thin films are of growing interest in microelectronics and microsystems because of the heat removal problem involved in highly integrated devices. The prescribed chapter of the present theis demonstrates how direct measurement of thermal diffusivity can be carried out in thin films of interest in a simple and elegant manner using PA techniques. Although results of only representative measurements viz; thermal diffusivity values in Indium, Aluminium, Silver and CdS thin films are given here, evaluation of this quantity for any photonic and / electronic material can be carried out using this technique in a very simple and straight forward manner.