Sandip Ghosal

A dynamic localization model for large-eddy simulation of turbulent flows

In a previous paper, Germano, et al. (1991) proposed a method for computing coefficients of subgrid-scale eddy viscosity models as a function of space and time. This procedure has the distinct advantage of being self-calibrating and requires no a priori specification of model coefficients or the use of wall damping functions. However, the original formulation contained some mathematical inconsistencies that limited the utility of the model. In particular, the applicability of the model was restricted to flows that are statistically homogeneous in at least one direction. These inconsistencies and limitations are discussed and a new formulation that rectifies them is proposed. The new formulation leads to an integral equation whose solution yields the model coefficient as a function of position and time. The method can be applied to general inhomogeneous flows and does not suffer from the mathematical inconsistencies inherent in the previous formulation. The model has been tested in isotropic turbulence and in the flow over a backward-facing step.

On the representation of backscatter in dynamic localization models

The dynamic localization model is a recently developed method that allows one to compute rather than prescribe the unknown coefficients in a subgrid scale model as a function of position at each time‐step. A realistic subgrid scale model should describe both the direct and reverse (backscatter) energy transfers at the local level. A previously developed dynamic localization model accounted for backscatter by means of a (deterministic) eddy viscosity that could locally assume positive as well as negative values. Here this paper presents an alternative stochastic model of backscatter in the context of the dynamic procedure. A comparative discussion of the merits of stochastic versus deterministic modeling of backscatter is presented. These models are applied to a large eddy simulation of isotropic decaying and forced turbulence. Tests are also performed with versions of the model that do not account for backscatter. The results are compared to experiments and direct numerical simulation. It is shown that th...

Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge

Electro-osmotic flow is a convenient mechanism for transporting fluid in microfluidic devices. The flow is generated through the application of an external electric field that acts on the free charges that exist in a thin Debye layer at the channel walls. The charge on the wall is due to the particular chemistry of the solid–fluid interface and can vary along the channel either by design or because of various unavoidable inhomogeneities of the wall material or because of contamination of the wall by chemicals contained in the fluid stream. The channel cross-section could also vary in shape and area. The effect of such variability on the flow through microfluidic channels is of interest in the design of devices that use electro-osmotic flow. The problem of electro-osmotic flow in a straight microfluidic channel of arbitrary cross-sectional geometry and distribution of wall charge is solved in the lubrication approximation, which is justified when the characteristic length scales for axial variation of the wall charge and cross-section are both large compared to a characteristic width of the channel. It is thereby shown that the volume flux of fluid through such a microchannel is a linear function of the applied pressure drop and electric potential drop across it, the coefficients of which may be calculated explicitly in terms of the geometry and charge distribution on the wall. These coefficients characterize the ‘fluidic resistance’ of each segment of a microfluidic network in analogy to the electrical ‘resistance’ in a microelectronic circuit. A consequence of the axial variation in channel properties is the appearance of an induced pressure gradient and an associated secondary flow that leads to increased Taylor dispersion limiting the resolution of electrophoretic separations. The lubrication theory presented here offers a simple way of calculating the distortion of the flow profile in general geometries and could be useful in studies of dispersion induced by inhomogeneities in microfluidic channels.

Mathematical and physical constraints on large-eddy simulation of turbulence

Recent progress in the theoretical foundations of large-eddy simulation is reviewed. Most of the work reported is motivated by conceptual difficulties encountered in applying the large eddy simulation method to inhomogeneous complex geometry flows. Among the topics covered are the problem of the lack of commutation between filtering and derivative operators for inhomogeneous flows, the issues of enforcing symmetry and realizability conditions in subgrid modeling, and the problem of unacceptably high numerical errors in large eddy simulation implementations with finite difference methods

Effect of salt concentration on the electrophoretic speed of a polyelectrolyte through a nanopore

In a previous paper [S. Ghosal, Phys. Rev. E 74, 041901 (2006)] a hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through an axially symmetric slowly varying nanopore was presented in the limit of a vanishingly small Debye length. Here the case of a finite Debye layer thickness is considered while restricting the pore geometry to that of a cylinder of length much larger than the diameter. Further, the possibility of a uniform surface charge on the walls of the nanopore is taken into account. It is thereby shown that the calculated transit times are consistent with recent measurements in silicon nanopores.

Effects of heat release in laminar diffusion flames lifted on round jets

Laminar diffusion flames lifted on round jets are simulated using high order accurate numerical schemes. The results are examined in the light of analytical approximations of lift-off heights. A large variety of flame base topologies are observed when the fuel jet velocity is varied. Edge-flames, or triple-flames, progressively evolve into weakly varying partially premixed fronts, before blow-out occurs. The flame base is located on the stoichiometric surface at the point where the flow velocity is of the order of the stoichiometric and planar premixed flame burning velocity. In the simulations, this stabilization point is positioned further upstream than predicted by a frozen flow mixing description of the jet, even when effects of heat release and strain rate are included in the approximation of the triple-flame speed that is used to predict the lift-off height. The numerical results therefore suggest that the well known flow deflection, induced by heat release, brings the flame much closer to the burner than expected. Heat release is found to have a much stronger effect in the round jet than in the previously studied planar mixing layer. In the axisymmetric problem, this is attributed to the intricate coupling between the flow deflection and the position of iso-mixture fraction surfaces relatively to iso-velocity surfaces. Heat release also makes the flame base more robust than predicted by cold flow theory and helps to sustain large velocities before reaching the blow-out condition. Results suggest that the prediction of lift-off height cannot be reached without carefully accounting for the effect of heat release on the flow upstream of the flame base.

Stability diagram for lift-off and blowout of a round jet laminar diffusion flame

Abstract An idealized model of a lifted flame above a round laminar jet is considered where diffusion rates of species and temperature are assumed equal but differential diffusion with respect to jet momentum is allowed. The combustion is described in terms of a global Arrhenius chemistry that is symmetric in fuel and oxidizer. Theoretical results on the propagation speeds of triple flames, and, the Landau–Squire solution for a nonreacting laminar round jet are combined to arrive at a transcendental equation for the lift-off height. For given chemistry, the stability behavior is controlled by a single Schmidt number, S, characterizing the differential diffusion between species (or temperature) and momentum and a parameter B, which is inversely proportional to the square root of the jet Reynolds number. Lift-off and blowout are characterized by a pair of critical curves in this two-dimensional parameter space the region between which corresponds to a stable lifted flame. A critical value of the Schmidt number exists above which the lift-off height increases continuously from zero on increasing the jet speed but below which the flame lifts off in a discontinuous manner through a subcritical bifurcation.

Electrokinetic-flow-induced viscous drag on a tethered DNA inside a nanopore.

Recent work has shown that the resistive force arising from viscous effects within the pore region could explain observed translocation times in certain experiments involving voltage-driven translocations of DNA through nanopores [Ghosal, Phys. Rev. E 71, 051904 (2006); Phys. Rev. Lett. 98, 238104 (2007)]. The electrokinetic flow inside the pore and the accompanying viscous effects also play a crucial role in the interpretation of experiments where the DNA is immobilized inside a nanopore [Keyser, Nat. Phys. 2, 473 (2006)]. In this paper the viscous force is explicitly calculated for a nanopore of cylindrical geometry. It is found that the reductions of the tether force due to viscous drag and due to charge reduction by Manning condensation are of similar size. The result is of importance in the interpretation of experimental data on tethered DNA.

Electrophoresis of a polyelectrolyte through a nanopore

A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nanopore is presented. It is assumed that the speed is determined by a balance of electrical and viscous forces arising from within the pore and that classical continuum electrostatics and hydrodynamics may be considered applicable. An explicit formula for the translocation speed as a function of the pore geometry and other physical parameters is obtained and is shown to be consistent with experimental measurements on DNA translocation through nanopores in silicon membranes. Experiments also show a weak dependence of the translocation speed on polymer length that is not accounted for by the present model. It is hypothesized that this is due to secondary effects that are neglected here.

The effect of wall interactions in capillary-zone electrophoresis

Capillary-zone electrophoresis (CZE) is an efficient separation method in analytical chemistry. It exploits the difference in electrophoretic migration speeds between charged molecular species in aqueous solution when an external electric field is applied to achieve separation. In most cases the electrophoretic migration of species is also accompanied by a bulk electro-osmotic flow in the capillary due to the presence of a zeta-potential at the capillary wall. Adsorption of charged species at the wall could modify this zeta-potential in a non-uniform manner. This induces axial pressure gradients, so that the flow is no longer uniform over the capillary cross-section. The resulting shear-induced dispersion of the sample is a serious cause of band broadening in CZE particularly for species such as proteins and peptides which adsorb strongly on capillary walls. The problem of the spatio-temporal evolution of the sample concentration is studied in the presence of such wall interactions