arXiv subjects

J. Ravi Prakash

Publications and source records attributed to J. Ravi Prakash.

At least 37 records · Page 2Linked to original sources

arXiv2019

Uniaxial extensional viscosity of semidilute DNA solutions

The extensional rheology of polymeric liquids has been extensively examined through experiments and theoretical predictions. However, a systematic study of the extensional rheology of polymer solutions in the semidilute regime, in terms of examining the effects of concentration and molecular weight, has not been carried out so far. Prior studies of the shear rheology of semidilute polymer solutions have demonstrated that their behaviour is distinctively different from that observed in the dilute and concentrated regimes. This difference in behaviour is anticipated to be even more pronounced in extensional flows. In this work, the extensional rheology of linear, double-stranded DNA molecules, spanning an order of magnitude of molecular weights (25 to 289 kilobasepairs) and concentrations (0.03 to 0.3 mg/ml), has been investigated. DNA solutions are now used routinely as model polymeric systems due to their near-perfect monodispersity. Measurements have been carried out with a filament stretching rheometer since it is the most reliable method for obtaining an estimate of the elongational stress growth of a polymer solution. Transient and steady-state uniaxial extensional viscosities of DNA dissolved in a solvent under excess salt conditions, with a high concentration of sucrose in order to achieve a sufficiently high solvent viscosity, have been determined in the semidilute regime at room temperature. The dependence of the steady state uniaxial extensional viscosity on molecular weight, concentration and extension rate is measured with a view to determining if data collapse can be observed with an appropriate choice of variables. Steady state shear viscosity measurements suggest that sucrose-DNA interactions might play a role in determining the observed rheological behaviour of semidilute DNA solutions with sucrose as a component in the solvent.

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arXiv2019

Universality of the collapse transition of sticky polymers

The universality of the swelling of the radius of gyration of a homopolymer relative to its value in the $θ$ state, independent of polymer-solvent chemistry, in the crossover regime between $θ$ and athermal solvent conditions, is well known. Here we study, by Brownian dynamics, a polymer model where a subset of monomers is labelled as "stickers". The mutual interaction of the stickers is more attractive than those of the other ("backbone") monomers, and has the additional important characteristic of "functionality" $φ$, i.e., the maximum number of stickers that can locally bind to a given sticker. A saturated bond formed in this manner remains bound until it breaks due to thermal fluctuations, a requirement which can be viewed as an additional Boolean degree of freedom that describes the bonding. This, in turn, makes the question of the order of the collapse transition a non-trivial one. Nevertheless, for the parameters that we have studied (in particular, $φ=1$), we find a standard second-order $θ$ collapse, using a renormalised solvent quality parameter that takes into account the increased average attraction due to the presence of stickers. We examine the swelling of the radius of gyration of such a sticky polymer relative to its value in the altered $θ$ state, using a novel potential to model the various excluded volume interactions that occur between the monomers on the chain. We find that the swelling of such sticky polymers is identical to the universal swelling of homopolymers in the thermal crossover regime. Additionally, for our model, the Kuhn segment length under $θ$ conditions is found to be the same for chains with and without stickers.

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arXiv2019

Universal dynamics of dilute and semidilute solutions of flexible linear polymers

Experimental observations and computer simulations have recently revealed universal aspects of polymer solution behaviour that were previously unknown. This progress has been made possible due to developments in experimental methodologies and simulation techniques, and the formulation of scaling arguments that have identified the proper scaling variables with which to achieve data collapse, both for equilibrium and nonequilibrium properties. In this review, these advances in our understanding of universal polymer solution behaviour are discussed, along with a brief overview of prior experimental observations and theoretical predictions in order to provide a context for the discussion. Properties for which the existence of universality is still unclear, and those for which it has not yet been verified theoretically are highlighted, and theoretical predictions of universal behaviour that require experimental validation are pointed out.

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arXiv2018

Rheological consequences of wet and dry friction in a dumbbell model with hydrodynamic interactions and internal viscosity

The effect of fluctuating internal viscosity and hydrodynamic interactions on a range of rheological properties of dilute polymer solutions is examined using a finitely extensible dumbbell model for a polymer. Brownian dynamics simulations are used to compute both transient and steady state viscometric functions in shear flow. The results enable a careful differentiation of the influence, on rheological properties, of solvent-mediated friction from that of a dissipative mechanism that is independent of solvent viscosity. In particular, hydrodynamic interactions have a significant influence on the magnitude of the stress jump at the inception of shear flow, and on the transient viscometric functions, but a negligible effect on the steady state viscometric functions at high shear rates. Zero-shear rate viscometric functions of free-draining dumbbells remain essentially independent of the internal viscosity parameter, as predicted by the Gaussian approximation, but the inclusion of hydrodynamic interactions induces a dependence on both the hydrodynamic interaction and the internal viscosity parameter. Large values of the internal viscosity parameter lead to linear viscoelastic predictions that mimic the behavior of rigid dumbbell solutions. On the other hand, steady-shear viscometric functions at high shear rates differ in general from those for rigid dumbbells, depending crucially on the finite extensibility of the dumbbell spring.

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arXiv2018

Shear thinning in dilute and semidilute solutions of polystyrene and DNA

The viscosity of dilute and semidilute unentangled DNA solutions, in steady simple shear flow, has been measured across a range of temperatures and concentrations. For polystyrene solutions, measurements of viscosity have been carried out in the semidilute unentangled regime, while results of prior experimental measurements in the dilute regime have been used for the purpose of data analysis, and for comparison with the behaviour of DNA solutions. Interpretation of the shear rate dependence of viscosity in terms of suitably defined non-dimensional variables, is shown to lead to master plots, independent of temperature and concentration, in each of the two concentration regimes. In the case of semidilute unentangled solutions, defining the Weissenberg number in terms of a concentration dependent large scale relaxation time is found not to lead to data collapse across different concentrations. On the other hand, the use of an alternative relaxation time, with the concentration dependence of a single correlation blob, suggests the existence of universal shear thinning behaviour at large shear rates.

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arXiv2016

Direct observation of DNA dynamics in semi-dilute solutions in extensional flow

The dynamic behavior of semi-dilute polymer solutions is governed by an interplay between solvent quality, concentration, molecular weight, and flow type. Semi-dilute solutions are characterized by large fluctuations in concentration, wherein polymer coils interpenetrate but may not be topologically entangled at equilibrium. In non-equilibrium flows, it is generally thought that polymer chains can self-entangle in semi-dilute solutions, thereby leading to entanglements in solutions that are nominally unentangled at equilibrium. Despite recent progress, we still lack a complete molecular-level understanding of these dynamics. In this work, we use single molecule techniques to study the dynamics of semi-dilute solutions of DNA in planar extensional flow, including polymer relaxation from high stretch, transient stretching dynamics in step-strain experiments, and steady-state stretching in flow. Our results are consistent with a power-law scaling of the longest polymer relaxation time in semi-dilute solutions, revealing an effective excluded volume exponent $ν$ = 0.56. We further studied the non-equilibrium stretching dynamics in extensional flow, with results showing a decrease in transient polymer stretch at moderate Weissenberg number and a milder coil-to-stretch transition in semi-dilute solutions compared to dilute solutions. Interestingly, a unique set of molecular conformations during the transient stretching process for single polymers in semi-dilute solutions is observed, which suggests transient stretching pathways for polymer chains in semi-dilute solutions are qualitatively different than dilute solutions due to intermolecular interactions. Taken together, this work provides a molecular framework for understanding the non-equilibrium stretching dynamics of semi-dilute solutions in strong flows.

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arXiv2016

Parameter-free prediction of DNA dynamics in planar extensional flow of semidilute solutions

The dynamics of individual DNA molecules in semidilute solutions undergoing planar extensional flow is simulated using a multi-particle Brownian dynamics algorithm, which incorporates hydrodynamic and excluded volume interactions in the context of a coarse-grained bead-spring chain model for DNA. The successive fine-graining protocol [1, 2], in which simulation data acquired for bead-spring chains with increasing values of the number of beads $N_b$, is extrapolated to the number of Kuhn steps $N_\text{K}$ in DNA (while keeping key physical parameters invariant), is used to obtain parameter-free predictions for a range of Weissenberg numbers and Hencky strain units. A systematic comparison of simulation predictions is carried out with the experimental observations of [3], who have recently used single molecule techniques to investigate the dynamics of dilute and semidilute solutions of $λ$-phage DNA in planar extensional flow. In particular, they examine the response of individual chains to step-strain deformation followed by cessation of flow, thereby capturing both chain stretch and relaxation in a single experiment. The successive fine-graining technique is shown to lead to quantitatively accurate predictions of the experimental observations in the stretching and relaxation phases. Additionally, the transient chain stretch following a step strain deformation is shown to be much smaller in semidilute solutions than in dilute solutions, in agreement with experimental observations.

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arXiv2016

Equilibrium binding energies from fluctuation theorems and force spectroscopy simulations

Brownian dynamics simulations are used to study the detachment of a particle from a substrate. Although the model is simple and generic, we attempt to map its energy, length and time scales onto a specific experimental system, namely a bead that is weakly bound to a cell and then removed by an optical tweezer. The external driving force arises from the combined optical tweezer and substrate potentials, and thermal fluctuations are taken into account by a Brownian force. The Jarzynski equality and Crooks' fluctuation theorem are applied to obtain the equilibrium free energy difference between the final and initial states. To this end, we sample non--equilibrium work trajectories for various tweezer pulling rates. We argue that this methodology should also be feasible experimentally for the envisioned system. Furthermore, we outline how the measurement of a whole free energy profile would allow the experimentalist to retrieve the unknown substrate potential by means of a suitable deconvolution. The influence of the pulling rate on the accuracy of the results is investigated, and umbrella sampling is used to obtain the equilibrium probability of particle escape for a variety of trap potentials.

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arXiv2016

Effect of stretching-induced changes in hydrodynamic screening on coil-stretch hysteresis of unentangled polymer solutions

Extensional rheometry and Brownian Dynamics simulations of flexible polymer solutions confirm predictions based on blob concepts that coil--stretch hysteresis in extensional flows increases with concentration, reaching a maximum at the critical overlap concentration $c^\ast$ before progressively vanishing in the semidilute regime. These observations demonstrate that chain stretching strengthens intermolecular hydrodynamic screening in dilute solutions, but weakens it in semidilute solutions. Flow can thus strongly modify the concentration dependence of viscoelastic properties of polymer solutions.

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arXiv2015

Size, shape and diffusivity of a single Debye-Hückel polyelectrolyte chain in solution

Brownian dynamics simulations of a coarse-grained bead-spring chain model, with Debye-Hückel electrostatic interactions between the beads, are used to determine the root-mean-square end-to-end vector, the radius of gyration, and various shape functions (defined in terms of eigenvalues of the radius of gyration tensor) of a weakly-charged polyelectrolyte chain in solution, in the limit of low polymer concentration. The long-time diffusivity is calculated from the mean square displacement of the centre of mass of the chain, with hydrodynamic interactions taken into account through the incorporation of the Rotne-Prager-Yamakawa tensor. Simulation results are interpreted in the light of the OSFKK blob scaling theory (R. Everaers, A. Milchev, and V. Yamakov, Eur. Phys. J. E 8, 3 (2002)) which predicts that all solution properties are determined by just two scaling variables--the number of electrostatic blobs $X$, and the reduced Debye screening length, $Y$. We identify three broad regimes, the ideal chain regime at small values of $Y$, the blob-pole regime at large values of $Y$, and the crossover regime at intermediate values of $Y$, within which the mean size, shape, and diffusivity exhibit characteristic behaviours. In particular, when simulation results are recast in terms of blob scaling variables, universal behaviour independent of the choice of bead-spring chain parameters, and the number of blobs $X$, is observed in the ideal chain regime and in much of the crossover regime, while the existence of logarithmic corrections to scaling in the blob-pole regime leads to non-universal behaviour.

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arXiv2015

Viscoelastic fluid flow in a 2D channel bounded above by a deformable finite thickness elastic wall

The steady flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens model for blood) in a two-dimensional channel, partly bound by a deformable, finite thickness neo-Hookean solid, is computed. The limiting Weissenberg number beyond which computations fail to converge is found to increase with increasing dimensionless solid elasticity parameter Γ, following the trend Owens > FENE- P > Oldroyd-B. The highly shear thinning nature of Owens model leads to the elastic solid always collapsing into the channel, for the wide range of values of Γ considered here. In the case of the FENE-P and Oldroyd-B models, however, the fluid-solid interface can be either within the channel, or bulge outwards, depending on the value of Γ. This behaviour differs considerably from predictions of earlier models that treat the deformable solid as a zero-thickness membrane, in which case the membrane always lies within the channel. The capacity of the solid wall to support both pressure and shear stress, in contrast to the zero-thickness membrane that only responds to pressure, is responsible for the observed difference. Compar- ison of the stress and velocity fields in the channel for the three viscoelastic fluids, with the predictions for a Newtonian fluid, reveals that shear thinning rather than elasticity is the key source of the observed differences in behaviour.

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arXiv2015

Significance of thermal fluctuations and hydrodynamic interactions in receptor-ligand mediated adhesive dynamics of a spherical particle in wall bound shear flow

The dynamics of adhesion of a spherical micro-particle to a ligand-coated wall, in shear flow, is studied using a Langevin equation that accounts for thermal fluctuations, hydrodynamic interactions and adhesive interactions. Contrary to the conventional assumption that thermal fluctuations play a negligible role at high P$\acute{e}$clet numbers, we find that for particles with low surface densities of receptors, rotational diffusion caused by fluctuations about the flow and gradient directions aids in bond formation, leading to significantly greater adhesion on average, compared to simulations where thermal fluctuations are completely ignored. The role of wall hydrodynamic interactions on the steady state motion of a particle, when the particle is close to the wall, has also been explored. At high P$\acute{e}$clet numbers, the shear induced force that arises due to the stresslet part of the Stokes dipole, plays a dominant role, reducing the particle velocity significantly, and affecting the states of motion of the particle. The coupling between the translational and rotational degrees of freedom of the particle, brought about by the presence of hydrodynamic interactions, is found to have no influence on the binding dynamics. On the other hand, the drag coefficient, which depends on the distance of the particle from the wall, plays a crucial role at low rates of bond formation. A significant difference in the effect of both the shear force and the position dependent drag force, on the states of motion of the particle, is observed when the P$\acute{e}$let number is small.

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arXiv2014

The viscosity radius in dilute polymer solutions: Universal behaviour from DNA rheology and Brownian dynamics simulations

The swelling of the viscosity radius, $α_η$, and the universal viscosity ratio, $U_{ηR}$, have been determined experimentally for linear DNA molecules in dilute solutions with excess salt, and numerically by Brownian dynamics simulations, as a function of the solvent quality. In the latter instance, asymptotic parameter free predictions have been obtained by extrapolating simulation data for finite chains to the long chain limit. Experiments and simulations show a universal crossover for $α_η$ and $U_{ηR}$ from $θ$ to good solvents in line with earlier observations on synthetic polymer-solvent systems. The significant difference between the swelling of the dynamic viscosity radius from the observed swelling of the static radius of gyration, is shown to arise from the presence of hydrodynamic interactions in the non-draining limit. Simulated values of $α_η$ and $U_{ηR}$ are in good agreement with experimental measurements in synthetic polymer solutions reported previously, and with the measurements in linear DNA solutions reported here.

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arXiv2014

Brownian dynamics simulations of planar mixed flows of polymer solutions at finite concentrations

Periodic boundary conditions for planar mixed flows are implemented in the context of a multi-chain Brownian dynamics simulation algorithm. The effect of shear rate $\dotγ$, and extension rate $\dotε$, on the size of polymer chains, $\left $, and on the polymer contribution to viscosity, $η$, is examined for solutions of FENE dumbbells at finite concentrations, with excluded volume interactions between the beads taken into account. The influence of the mixedness parameter, $χ$, and flow strength, $\dotΓ$, on $\left $ and $η$, is also examined, where $χ\rightarrow 0$ corresponds to pure shear flow, and $χ\rightarrow 1$ corresponds to pure extensional flow. It is shown that there exists a critical value, $χ_\text{c}$, such that the flow is shear dominated for $χ< χ_\text{c}$, and extension dominated for $χ> χ_\text{c}$.

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arXiv2013

Universal solvent quality crossover of the zero shear rate viscosity of semidilute DNA solutions

The scaling behaviour of the zero shear rate viscosity of semidilute unentangled DNA solutions, in the double crossover regime driven by temperature and concentration, is mapped out by systematic experiments. The viscosity is shown to have a power law dependence on the scaled concentration $c/c^*$, with an effective exponent that depends on the solvent quality parameter $z$. The determination of the form of this universal crossover scaling function requires the estimation of the $θ$ temperature of dilute DNA solutions in the presence of excess salt, and the determination of the solvent quality parameter at any given molecular weight and temperature. The $θ$ temperature is determined to be $T_θ\approx 15^\circ$ C using static light scattering, and the solvent quality parameter has been determined by dynamic light scattering.

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arXiv2012

Dynamic crossover scaling in polymer solutions

The crossover region in the phase diagram of polymer solutions, in the regime above the overlap concentration, is explored by Brownian Dynamics simulations, to map out the universal crossover scaling functions for the gyration radius and the single-chain diffusion constant. Scaling considerations, our simulation results, and recently reported data on the polymer contribution to the viscosity obtained from rheological measurements on DNA systems, support the assumption that there are simple relations between these functions, such that they can be inferred from one another.

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arXiv2012

Optimisation of a Brownian dynamics algorithm for semidilute polymer solutions

Simulating the static and dynamic properties of semidilute polymer solutions with Brownian dynamics (BD) requires the computation of a large system of polymer chains coupled to one another through excluded-volume and hydrodynamic interactions. In the presence of periodic boundary conditions, long-ranged hydrodynamic interactions are frequently summed with the Ewald summation technique. By performing detailed simulations that shed light on the influence of several tuning parameters involved both in the Ewald summation method, and in the efficient treatment of Brownian forces, we develop a BD algorithm in which the computational cost scales as O(N^{1.8}), where N is the number of monomers in the simulation box. We show that Beenakker's original implementation of the Ewald sum, which is only valid for systems without bead overlap, can be modified so that θ-solutions can be simulated by switching off excluded-volume interactions. A comparison of the predictions of the radius of gyration, the end-to-end vector, and the self-diffusion coefficient by BD, at a range of concentrations, with the hybrid Lattice Boltzmann/Molecular Dynamics (LB/MD) method shows excellent agreement between the two methods. In contrast to the situation for dilute solutions, the LB/MD method is shown to be significantly more computationally efficient than the current implementation of BD for simulating semidilute solutions. We argue however that further optimisations should be possible.

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arXiv2012

Fluid-Structure Interaction in Deformable Microchannels

A microfluidic device is constructed from PDMS with a single channel having a short section that is a thin flexible membrane, in order to investigate the complex fluid-structure interaction that arises between a flowing fluid and a deformable wall. Experimental measurements of membrane deformation and pressure drop are compared with predictions of two-dimensional and three-dimensional computational models which numerically solve the equations governing the elasticity of the membrane coupled with the equations of motion for the fluid. It is shown that the two-dimensional model, which assumes a finite thickness elastic beam that is infinitely wide, approximates reasonably well the three-dimensional model, and is in excellent agreement with experimental observations of the profile of the membrane, when the width of the membrane is beyond a critical thickness, determined to be roughly twice the length of the membrane.

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