Browsing by Author "Mukherjee, Saikat"

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    Front Propagation and Feedback in Convective Flow Fields
    Mukherjee, Saikat (Virginia Tech, 2020-05-28)
    This dissertation aims to use theory and numerical simulations to quantify the propagation of fronts, which consist of autocatalytic reaction fronts, fronts with feedback and pattern forming fronts in Rayleigh-Bénard convection. The velocity and geometry of fronts are quantified for fronts traveling through straight parallel convection rolls, spatiotemporally chaotic rolls, and weakly turbulent rolls. The front velocity is found to be dependent on the competing influence of the orientation of the convection rolls and the geometry of the wrinkled front interface which is quantified as a fractal having a non-integer box-counting dimension. Front induced solutal and thermal feedback to the convective flow field is then studied by solving an exothermic autocatalytic reaction where the products and the reactants can vary in density. A single self-organized fluid roll propagating with the front is created by the solutal feedback while a pair of propagating counterrotating convection rolls are formed due to heat release from the reaction. Depending on the relative change in density induced by the solutal and thermal feedback, cooperative and antagonistic feedback scenarios are quantified. It is found that front induced feedback enhances the front velocity and reactive mixing length and induces spatiotemporal oscillations in the front and fluid dynamics. Using perturbation expansions, a transition in symmetry and scaling behavior of the front and fluid dynamics for larger values of feedback is studied. The front velocity, flow structure, front geometry and reactive mixing length scales for a range of solutal and thermal feedback are quantified. Lastly, pattern forming fronts of convection rolls are studied and the wavelength and velocity selected by the front near the onset of convective instability are investigated. This research was partially supported by DARPA Grant No. HR0011-16-2-0033. The numerical computations were done using the resources of the Advanced Research Computing center at Virginia Tech.
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    Propagating fronts in fluids with solutal feedback
    Mukherjee, Saikat; Paul, Mark R. (American Physical Society, 2020-03-25)
    We numerically study the propagation of reacting fronts in a shallow and horizontal layer of fluid with solutal feedback and in the presence of a thermally driven flow field of counterrotating convection rolls. We solve the Boussinesq equations along with a reaction-convection-diffusion equation for the concentration field where the products of the nonlinear autocatalytic reaction are less dense than the reactants. For small values of the solutal Rayleigh number the characteristic fluid velocity scales linearly, and the front velocity and mixing length scale quadratically, with increasing solutal Rayleigh number. For small solutal Rayleigh numbers the front geometry is described by a curve that is nearly antisymmetric about the horizontal midplane. For large values of the solutal Rayleigh number the characteristic fluid velocity, the front velocity, and the mixing length exhibit square-root scaling and the front shape collapses onto an asymmetric self-similar curve. In the presence of counterrotating convection rolls, the mixing length decreases while the front velocity increases. The complexity of the front geometry increases when both the solutal and convective contributions are significant and the dynamics can exhibit chemical oscillations in time for certain parameter values. Last, we discuss the spatiotemporal features of the complex fronts that form over a range of solutal and thermal driving.
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    Review: Biofunctionalized Quantum Dots in Biology and Medicine
    Mazumder, Sonal; Dey, Rajib; Mitra, M. K.; Mukherjee, Saikat; Das, G. C. (Hindawi, 2009-11-04)
    Quantum dot (QD) nanocrystals which have important optical properties, in particular, the wavelength of their fluorescence, depend strongly on their size. Colloidal QDs once dispersed in a solvent are quite interesting fluorescence probes for all types of labelling studies because of their reduced tendency to photo bleach. In this review, we will give an overview on how QDs have been used so far in cell biology. In particular, we will discuss the biologically relevant properties of QDs and focus on four topics: labeling of cellular structures and receptors with QDs, incorporation of QDs by living cells, tracking the path and the fate of individual cells using QD labels, and QDs as contrast agents. QDs are seen to be much better in terms of efficacy over radioisotopes in tracing medicine in vivo. They are rapidly being applied to existing and emerging technologies but here this review deals with a comprehensive compilation of the biological relevance of quantum dots. It covers important information from 1999 till 2008 with few from 1982 to 1997.
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    Spiral defect chaos in Rayleigh-Benard convection: Asymptotic and numerical studies of azimuthal flows induced by rotating spirals
    Vitral, Eduardo; Mukherjee, Saikat; Leo, Perry H.; Vinals, Jorge; Paul, Mark R.; Huang, Zhi-Feng (American Physical Society, 2020-09-10)
    Rotating spiral patterns in Rayleigh-Bénard convection are known to induce azimuthal flows, which raises the question of how different neighboring spirals interact with each other in spiral chaos and the role of hydrodynamics in this regime. Far from the core, we show that spiral rotations lead to an azimuthal body force that is irrotational and of magnitude proportional to the topological index of the spiral and its angular frequency. The force, although irrotational, cannot be included in the pressure field as it would lead to a nonphysical multivalued pressure. We calculate the asymptotic dependence of the resulting flow and show that it leads to a logarithmic dependence of the azimuthal velocity on distance r away from the spiral core in the limit of negligible damping coefficient. This solution dampens to approximately 1/r when accounting for no-slip boundary conditions for the convection cell's plate. This flow component can provide additional hydrodynamic interactions among spirals including those observed in spiral defect chaos. We show that the analytic prediction for the azimuthal velocity agrees with numerical results obtained from both two-dimensional generalized Swift-Hohenberg and three-dimensional Boussinesq models and find that the velocity field is affected by the size and charges of neighboring spirals. Numerically, we identify a correlation between the appearance of spiral defect chaos and the balancing between the mean-flow advection and the diffusive dynamics related to roll unwinding.
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    Velocity and geometry of propagating fronts in complex convective flow fields
    Mukherjee, Saikat; Paul, Mark R. (American Physical Society, 2019-01-22)
    We numerically study the propagation of reacting fronts through three-dimensional flow fields composed of convection rolls that include time-independent cellular flow, spatiotemporally chaotic flow, and weakly turbulent flow. We quantify the asymptotic front velocity and determine its scaling with system parameters including the local angle of the convection rolls relative to the direction of front propagation. For cellular flow fields, the orientation of the convection rolls has a significant effect upon the front velocity and the front geometry remains relatively smooth. However, for chaotic and weakly turbulent flow fields, the front velocity depends upon the geometric complexity of the wrinkled front interface and does not depend significantly upon the local orientation of the convection rolls. Using the box counting dimension we find that the front interface is fractal for chaotic and weakly turbulent flows with a dimension that increases with flow complexity.