arXiv subjects

Sandip Ghosal

Publications and source records attributed to Sandip Ghosal.

25 records · Page 2Linked to original sources

arXiv2012

A nonlinear equation for ionic diffusion in a strong binary electrolyte

The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description consists of a diffusion equation for each species augmented by transport due to a self consistent electrostatic field determined by the Poisson equation. This mathematical framework also describes other important problems in physics such as electron and hole diffusion across semi-conductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here we derive a more general theory by exploiting the ratio of Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear integro-differential equation which replaces the classical linear equation for ambipolar diffusion but reduces to it in the appropriate limit. Through numerical integration of the full set of equations it is shown that this nonlinear equation provides a better approximation to the exact solution than the linear equation it replaces.

physics.chem-ph↗

arXiv2012

Does buckling instability of the pseudopodium limit how well an amoeba can climb?

The maximum force that a crawling cell can exert on a substrate is a quantity of interest in cell biomechanics. One way of quantifying this force is to allow the cell to crawl against a measurable and adjustable restraining force until the cell is no longer able to move in a direction opposite to the applied force. Fukui et al.[1] reported on an experiment where amoeboid cells were imaged while they crawled against an artificial gravity field created by a centrifuge. An unexpected observation was that the net applied force on the amoeba did not seem to be the primary factor that limited its ability to climb. Instead, it appeared that the amoeba stalled when it was no longer able to support a pseudopodium against the applied gravity field. The high g-load bend the pseudopodium thereby preventing its attachment to the target point directly ahead of the cell. In this paper we further refine this idea by identifying the bending of the pseudopodium with the onset of elastic instability of a beam under its own weight. It is shown that the principal features of the experiment may be understood through this model and an estimate for the limiting g-load in reasonable accord with the experimental measurements is recovered.

q-bio.CB↗

arXiv2012

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 [Ghosal, S. Phys. Rev. E. vol. 71, 051904 (2006) and Phys. Rev. Lett. vol. 98, 238104 (2007)] observed translocation times in certain experiments involving voltage driven translocations of DNA through nanopores. 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[U. Keyser, et al., Nature Physics vol. 2, 473 (2006)]. In this paper the viscous force is explicitly calculated for a nanopore of cylindrical geometry. It is found that the reduction 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.

physics.bio-ph↗

arXiv2012

Nonlinear waves in capillary electrophoresis

Electrophoretic separation of a mixture of chemical species is a fundamental technique of great usefulness in biology, health care and forensics. In capillary electrophoresis the sample migrates in a microcapillary in the presence of a background electrolyte. When the ionic concentration of the sample is sufficiently high, the signal is known to exhibit features reminiscent of nonlinear waves including sharp concentration `shocks'.In this paper we consider a simplified model consisting of a single sample ion and a background electrolyte consisting of a single co-ion and a counterion in the absence of any processes that might change the ionization states of the constituents. If the ionic diffusivities are assumed to be the same for all constituents the concentration of sample ion is shown to obey a one dimensional advection diffusion equation with a concentration dependent advection velocity.If the analyte concentration is sufficiently low in a suitable non-dimensional sense, Burgers' equation is recovered, and thus, the time dependent problem is exactly solvable with arbitrary initial conditions. In the case of small diffusivity either a leading edge or trailing edge shock is formed depending on the electrophoretic mobility of the sample ion relative to the background ions. Analytical formulas are presented for the shape, width and migration velocity of the sample peak and it is shown that axial dispersion at long times may be characterized by an effective diffusivity that is exactly calculated. These results are consistent with known observations from physical and numerical simulation experiments.

q-bio.QM↗

arXiv2012

Electromigration dispersion in Capillary Electrophoresis

In a previous paper (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, vol. 72, pg. 2047) it was shown that the evolution of the solute concentration in capillary electrophoresis is described by a nonlinear wave equation that reduced to Burger's equation if the nonlinearity was weak. It was assumed that only strong electrolytes (fully dissociated) were present. In the present paper it is shown that the same governing equation also describes the situation where the electrolytic buffer consists of a single weak acid (or base). A simple approximate formula is derived for the dimensionless peak variance which is shown to agree well with published experimental data.

physics.bio-ph↗

arXiv2007

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.

physics.chem-ph↗

arXiv2006

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.

physics.chem-ph↗