Date

2013

Document Type

Dissertation

Degree

Doctor of Philosophy

Department

Chemical Engineering

First Adviser

Chaudhury, Manoj K.

Other advisers/committee members

Kothare, Mayuresh V.; Silebi, Cesar A.; Snyder, Mark A.; Rickman, Jeffrey M.

Abstract

There are enumerable examples of natural processes which fall in the class of non-equilibrium stochastic dynamics. In the literature it is prescribed that such a process can be described completely using transition probability that satisfy the Fokker Planck equation. The analytical solutions of transition probability density function are difficult to obtain and are available for linear systems along with few first order nonlinear systems. We studied such nonlinear stochastic systems and tried to identify the important parameters associated with the dynamics and energy dissipative mechanism using statistical tools.We present experimental study of macroscopic systems driven away far from equilibrium with an applied bias and external mechanical noise. This includes sliding of small solid object, gliding of a liquid drop or a rolling of a rigid sphere. We demonstrated that the displacement statistics are non-Gaussian at short observation time, but they tend towards a Gaussian behavior at long time scale. We also found that, the drift velocity increases sub-linearly, but the diffusivity increases super-linearly with the strength of the noise. These observations reflect that the underlying non-linear friction controls the stochastic dynamics in each of these cases. We established a new statistical approach to determine the underlying friction law and identified the operating range of linear and nonlinear friction regime.In all these experiments source of the noise and the origin of the energy dissipation mechanism (i.e. friction) are decoupled. Naturaly question arises whether the stochastic dynamics of these athermal systems are amenable to Einstein's Fluctuation dissipation theorem which is valid strictly for a closed thermodynamic system. We addressed these issues by comparing Einstein's ratio of Diffusivity and mobility which are measurable quantities in our experimental systems. As all our experimental systems exhibit substantial negative fluctuations of displacement that diminishes with observation time scale, we used another approach of integrated fluctuation theorem to identify athermal temperature of the system by characterizing a persistence time of negative fluctuations in terms of the measurable quantity. Specific experiments have also been designed to study the crossing of a small object over a physical barrier assisted by an external noise and a bias force. These results mimic the classical Arrhenius behavior from which another effective temperature may be deduced. All these studies confer that the nonlinear system does not possess any unique temperature.Detachment of a solid sphere as well as a liquid drop from a structured rubber surface during subcritical motion in presence of external noise was examined in the light of Arrhenius' activated rate equation. Drift velocity of small drops of water-glycerin solution behaves nonlinearly with viscosity which is reminiscence of Kramers' turn over theory of activated rate. In a designed experiment of barrier crossing of liquid drops we satisfactorily verified the Kramers' formalism of activated rate at the low friction limit.

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