Nazish Hoda

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow with hydrodynamic interaction

The adsorption of single polyelectrolyte molecules in shear flow is studied using Brownian dynamics simulations with hydrodynamic interaction (HI). Simulations are performed with bead-rod and bead-spring chains, and electrostatic interactions are incorporated through a screened Coulombic potential with excluded volume accounted for by the repulsive part of a Lennard-Jones potential. A correction to the Rotne-Prager-Yamakawa tensor is derived that accounts for the presence of a planar wall. The simulations show that migration away from an uncharged wall, which is due to bead-wall HI, is enhanced by increases in the strength of flow and intrachain electrostatic repulsion, consistent with kinetic theory predictions. When the wall and polyelectrolyte are oppositely charged, chain behavior depends on the strength of electrostatic screening. For strong screening, chains get depleted from a region close to the wall and the thickness of this depletion layer scales as N(1/3)Wi(2/3) at high Wi, where N is the chain length and Wi is the Weissenberg number. At intermediate screening, bead-wall electrostatic attraction competes with bead-wall HI, and it is found that there is a critical Weissenberg number for desorption which scales as N(-1/2)kappa(-3)(l(B)|sigmaq|)(3/2), where kappa is the inverse screening length, l(B) is the Bjerrum length, sigma is the surface charge density, and q is the bead charge. When the screening is weak, adsorbed chains are observed to align in the vorticity direction at low shear rates due to the effects of repulsive intramolecular interactions. At higher shear rates, the chains align in the flow direction. The simulation method and results of this work are expected to be useful for a number of applications in biophysics and materials science in which polyelectrolyte adsorption plays a key role.

Energy amplification in channel flows of viscoelastic fluids

Energy amplification in channel flows of Oldroyd-B fluids is studied from an input-output point of view by analysing the ensemble-average energy density associated with the velocity field of the linearized governing equations. The inputs consist of spatially distributed and temporally varying body forces that are harmonic in the streamwise and spanwise directions and stochastic in the wall-normal direction and in time. Such inputs enable the use of powerful tools from linear systems theory that have recently been applied to analyse Newtonian fluid flows. It is found that the energy density increases with a decrease in viscosity ratio (ratio of solvent viscosity to total viscosity) and an increase in Reynolds number and elasticity number. In most of the cases, streamwise-constant perturbations are most amplified and the location of maximum energy density shifts to higher spanwise wavenumbers with an increase in Reynolds number and elasticity number and a decrease in viscosity ratio. For similar parameter values, the maximum in the energy density occurs at a higher spanwise wavenumber for Poiseuille flow, whereas the maximum energy density achieves larger maxima for Couette flow. At low Reynolds numbers, the energy density decreases monotonically when the elasticity number is sufficiently small, but shows a maximum when the elasticity number becomes sufficiently large, suggesting that elasticity can amplify disturbances even when inertial effects are weak.

Boundary integral simulations of liquid emptying from a model gravure cell

We perform boundary integral simulations to understand the removal of Newtonian liquids from a model gravure cell. Two different configurations are considered. In the first configuration, there is a free surface and an outlet boundary, and the liquid is driven out of a cavity by a combination of horizontal substrate motion and an imposed pressure gradient; a similar model was used by Powell et al. [Trans. IChemeE, Part C 78, 61 (2000)]. The percentage of liquid remaining in the cavity Vr is influenced by the capillary number Ca, cavity depth D, and contact angle θ. We found that Vr decreases with a decrease in Ca or D, consistent with prior studies, and for a shallow enough cavity, almost all of the liquid can be removed. Additionally, Vr decreases with an increase in θ. In the second configuration, there are two free surfaces, and the liquid is driven out of the cavity by moving the substrate both horizontally and vertically. Our simulations suggest that Vr decreases with an increase in the extensional v...

Orthogonal simulated annealing for multiobjective optimization

Abstract The paper proposes a new simulated annealing (SA) based multiobjective optimization algorithm, called orthogonal simulated annealing (OSA) algorithm in this work. The OSA algorithm incorporates an orthogonal experiment design (OED) with a simulated annealing based multiobjective algorithm aiming to provide an efficient multiobjective algorithm. OED involves several experiments based on an orthogonal table and a fractional factorial analysis to extract intelligently the best combination of decision vectors making the classical SA to explore search space effectively, to enhance convergence, and to improve quality of solutions in the Pareto set. These benefits have been tested by comparing the performance of OSA with one state-of-the-art multiobjective evolutionary algorithm (NSGA2) and one classical simulated annealing based multiobjective algorithm (CMOSA) considering multiobjective problems of varying degrees of complexity. The obtained Pareto sets by these three algorithms have been tested using standard methods like measure C, hypervolume comparison, etc. Simulation results show that the performance of and CPU time required by these algorithms are problem dependent, and with some problems, the OSA algorithm outperforms the other two algorithms. In particular, the comparison between OSA and CMOSA suggests that around 70% times OSA outperforms CMOSA and obtains a well diversified set of solutions. In addition, with some problems, OSA captures the Pareto fronts where CMOSA fails. Therefore, the development of OSA is noteworthy, and it provides an additional tool to solve multiobjective optimization problems.

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow: Effects of solvent quality and charge patterning

We probe the effects of solvent quality and charge patterning on polyelectrolyte adsorption in shear flow using Brownian dynamics simulations with hydrodynamic interaction (HI). The polyelectrolyte is modeled as a freely jointed bead-rod chain, and electrostatic and non-electrostatic interactions are accounted for by using screened Coulombic and Lennard-Jones potentials, respectively. In the absence of flow, the conformation of a polyelectrolyte molecule adsorbed onto a uniformly charged surface changes from flat to globular with an increase in bead-bead attraction (hydrophobicity), consistent with prior experimental observations. In the presence of flow, migration due to bead-wall HI and, as a consequence, desorption decrease with an increase in bead-bead attraction, implying that flow-induced desorption is more difficult under poor-solvent conditions. When bead-bead non-electrostatic attraction is strong, desorption can be enhanced by increasing bead-bead electrostatic repulsion. Analogous to the effect of bead-surface electrostatic attraction, an increase in the strength of bead-surface non-electrostatic attraction reduces desorption. We also study the effect of shear flow on the adsorption of a polyelectrolyte molecule onto surfaces decorated with periodic arrays of charged patches. An increase in patch periodicity increases desorption even when the effective surface charge density is kept the same. The results of this work suggest mechanisms for controlling the desorption of polyelectrolyte molecules in shear flows.

Frequency responses of streamwise-constant perturbations in channel flows of Oldroyd-B fluids

Non-modal amplification of disturbances in streamwise-constant channel flows of Oldroyd-B fluids is studied from an input-output point of view by analysing the responses of the velocity components to spatio-temporal body forces. These inputs into the governing equations are assumed to be harmonic in the spanwise direction and stochastic in the wall-normal direction and in time. An explicit Reynolds number (Re) scaling of frequency responses from different forcing to different velocity components is developed, showing the same Re dependence as in Newtonian fluids. It is found that some of the frequency response components peak at non-zero temporal frequencies. This is in contrast to Newtonian fluids, where peaks are always observed at zero frequency, suggesting that viscoelastic effects introduce additional time scales and promote development of flow patterns with smaller time constants than in Newtonian fluids. The temporal frequencies, corresponding to the peaks in the components of frequency response, decrease with an increase in viscosity ratio (ratio of solvent viscosity to total viscosity) and show maxima for non-zero elasticity number. Our analysis of the Reynolds-Orr equation demonstrates that the energy-exchange term involving the streamwise/wall-normal polymer stress component τ xy and the wall-normal gradient of the streamwise velocity ∂ y u becomes increasingly important relative to the Reynolds-stress term as the elasticity number increases and is thus the main driving force for amplification in flows with strong viscoelastic effects.

Kinetic theory of polyelectrolyte adsorption in shear flow

The effect of hydrodynamic interactions on the adsorption of a polyelectrolyte molecule onto a wall in shear flow is investigated using a bead-spring dumbbell model. Bead-bead and bead-wall electrostatic interactions are taken into account using screened Coulombic interactions, and the hydrodynamic interactions are incorporated using the approach proposed by Ma and Graham [Phys. Fluids 17, 083103 (2005)]. An analytical expression for the concentration profile of the polyelectrolyte is derived which predicts a competition between bead-wall hydrodynamic interactions and bead-wall electrostatic attraction. The behavior of the concentration profile is explored as a function of the Weissenberg number, surface (wall) charge density, charge on the beads, and screening length. The charge on the beads assists migration of the dumbbell away from an uncharged wall, whereas for an oppositely charged wall it increases the probability of finding the dumbbell close to the wall. In some cases, the concentration profile s...

Brownian dynamics simulations of single polymer chains with and without self-entanglements in theta and good solvents under imposed flow fields

The effects of self-entanglements (spring-spring uncrossability) and solvent quality on the static and dynamic properties of a polymer chain in shear and extensional flows are investigated using Brownian dynamics simulations. We model the polymer chain by a sequence of beads connected by finitely extensible non-linear elastic springs, and spring-spring uncrossability is enforced by applying a spring-spring repulsive potential together with an adaptive time-stepping. Our findings suggest that chain uncrossability has an insignificant effect on the dynamics of a polymer chain. Furthermore, we considered four different combinations of intramolecular interactions: (i) no interactions, (ii) repulsive spring-spring and attractive bead-bead interactions, (iii) only repulsive bead-bead interactions, and (iv) only repulsive spring-spring interactions. The first two cases model “theta” solvents, where the radius-of-gyration of a polymer chain, Rg∼N0.5, where N is the number of beads. For appropriately chosen parame...

On the Transient Analysis of a V-Shaped Microgrooved Heat Pipe

In this paper, we present a transient mathematical model for a V-shaped microgrooved heat pipe considering the temporal variations in the fluid flow, and heat and mass transfer, and utilizing a macroscopic approach. Unlike other heat pipe models, the shear stress at the liquid-vapor interface and the disjoining pressure have been used in the momentum balance equation of the model. The sensible heat used by the substrate is also taken into account using a pseudo-lump capacity model. The coupled nonlinear partial differential equations governing the transient fluid flow, heat and mass transfer have been solved numerically. The transient and steady-state profiles for the radius of curvature, liquid and vapor velocity, liquid pressure, and substrate temperature have been obtained. The mathematical model is capable of predicting the time required for the onset of dry out at the hot end, and for a micro heat pipe to reach steady state. The time required to reach steady state is independent of heat input, heat pipe inclination, groove angle, and Q ss profile. However, the time required for the onset of dry out at the hot end decreases with increasing heat input, inclination, and groove angle. The model predicted results have been successfully compared to the results from the literature. The general nature of this model and the associated study can be useful for many practical applications in the microscale heat exchange.

Theory of polyelectrolyte adsorption onto surfaces patterned with charge and topography

Mean-field theory is used to derive criteria for the adsorption of a weakly charged polyelectrolyte molecule from salt solution onto surfaces patterned with charge and topography. For flat surfaces patterned with periodic arrays of charged patches, the adsorbed layer thickness predicted using mean-field theory and that found by Brownian dynamics simulations are in quantitative agreement in the strong-adsorption regime, which corresponds to sufficiently small kappa or sufficiently large |sigma(eff)q|, where kappa is the inverse Debye screening length, sigma(eff) is an effective surface charge density, and q is the charge on each segment of the polyelectrolyte. Qualitative agreement is obtained in the weak-adsorption regime, and for the case where surfaces are patterned with both charge and topography. For uniformly charged, sinusoidally corrugated surfaces, the theory predicts that the critical temperature required for adsorption can be greater than or less than the corresponding value for a flat surface depending on the relative values of kappa and the corrugation wave number. If the surface charge is also allowed to vary sinusoidally, then adsorption is predicted to occur only when the topography crests have a surface charge opposite to that of the polyelectrolyte. Surfaces patterned with rectangular indentations having charged bottoms which are separated by flat charged plateaus are investigated as well. Adsorption is predicted to occur even when the net surface charge is zero, provided that the plateaus have a charge opposite to that of the polyelectrolyte. If the charge on the plateaus and polyelectrolyte is the same, adsorption may still occur if electrostatic attraction from the indentation bottoms is sufficiently strong.