Articles written in Pramana – Journal of Physics

    • Macroscopic equation of motion in inhomogeneous media: A microscopic treatment

      A M Jayannavar Mangal C Mahato

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      The dynamical evolution of a Brownian particle in an inhomogeneous medium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative stability of states in nonequilibrium systems which has been a subject of debate for over several decades. The theoretical treatments adopted so far are mostly phenomenological in nature. In this work we give a microscopic treatment of this problem. We derive the Langevin equation of motion and the associated Fokker-Planck equation. The correct reduced description of the Kramers equation in the overdamped limit (Smoluchowski equation) is obtained. Our microscopic treatment may be helpful in understanding the working of thermal ratchets, a problem of much current interest.

    • An experimental study of recoil capillary waves and break up of vertically flowing down water jets


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      Break up of water jets under gravity is a ubiquitous phenomenon. The role of surface tension on the instability of uniform water jets was recognised long ago by Plateau and Rayleigh. According to the Plateau–Rayleigh theory, external (or internal) perturbation waves create necks and bulges all along the uniform jet length. The perturbation waves of wavelengths larger than a certain value keep growing with time and ultimately cause the continuous jet to break up into individual drops. The effect of external perturbation waves was investigated experimentally, in most cases under gravity, and found to confirm the essentials of the theory. Recently, the idea of recoil capillary waves as a possible internal source of perturbations was emphasised. According to this idea, immediately after the break up of the jet, the tip of the remaining continuous jet (after a drop is detached) recoils. Its effect travels upstream as a recoil capillary wave which gets reflected at the mouth of the jet-issuing nozzle. The reflected capillary wave travels downstream along the jet with its Doppler-shifted wavelength as a reinforcing perturbation wave and, as a result, affecting the break up length of the jet. We set up and perform an experiment to verify the existence of these tip contraction recoil capillary waves. The results of our experiment support the existence of these recoil capillary waves. However, the effect of these capillary waves on the jet break up length is found to be small.

    • Intermediate length scale of water jets under gravity: An experimental result


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      The profile of water jets along its length before breakup is indirectly inferred from the observation of surface waves created by the jet as it plunges into a reservoir of pure and contaminated water. The inference isdrawn based on the measurement of surface wavelengths as a function of jet length before it touches the reservoir surface. It is observed that the nature of variation of wavelength changes abruptly at a certain jet length L$_0$. It isfound that the dimensionless L$_0$ depends only on the local velocity and diameter of the jet at L = L$_0$ apart from the local acceleration due to gravity but is not a function of the surface tension of the reservoir; i.e., L$_0$ is a functionof the Froude number Fr at L = L$_0$. Our analysis suggests the existence of an intermediate length scale L$_0$ that demarcates the inertia-dominated region (L ${\le}$ L$_0$) of the jet from the gravity-dominated region (L > L$_0$).

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