Viscous fingering in a horizontal flow through a porous medium induced by chemical reactions under isothermal and adiabatic conditions

In this work we analyze the viscous fingering instability induced by an autocatalytic chemical reaction in a liquid flowing horizontally through a porous medium. We have analyzed the behavior of the system for isothermal as well as adiabatic conditions. The kinetics of the reaction is chosen so that the rate depends on the concentration of only a single species. Since the reaction is autocatalytic the system admits a traveling wave solution. For endothermic reactions the concentration wave and temperature wave are mirror images, whereas for an exothermic reaction they are similar or parallel. The viscosity of the fluid is assumed to depend strongly on the concentration of the product and temperature of the medium. The dependence of viscosity on concentration (decrease with concentration) can destabilize the traveling wave resulting in the formation of viscous fingers. We have performed a linear stability analysis to determine the stability of the base traveling wave solution. The stability predictions have been confirmed by nonlinear simulations of the governing equations based on a finite difference scheme. We observe that including the temperature dependency of viscosity stabilizes the flow for an endothermic reaction, i.e., regions which exhibited viscous fingering now demonstrate stable displacement. For exothermic systems, however, the system exhibits less stable behavior under adiabatic conditions, i.e., it is destabilized by both concentration and temperature dependencies of viscosity.     

Numerical modeling of surface reaction kinetics in electrokinetically actuated microfluidic devices

We outline a comprehensive numerical procedure for modeling of species transport and surface reaction kinetics in electrokinetically actuated microfluidic devices of rectangular cross section. Our results confirm the findings of previous simplified approaches that a concentration wave is created for sufficiently long microreactors. An analytical solution, developed for the wave propagation speed, shows that, when normalizing with the fluid mean velocity, it becomes a function of three parameters comprising the channel aspect ratio, the relative adsorption capacity, and the kinetic equilibrium constant. Our studies also reveal that the reactor geometry idealized as a slit, instead of a rectangular shape, gives rise to the underestimation of the saturation time. The extent of this underestimation increases by increasing the Damkohler number or decreasing the dimensionless Debye–Hückel parameter. Moreover, increasing the values of the Damkohler number, the dimensionless Debye–Hückel parameter, the relative adsorption capacity, and the velocity scale ratio results in lower saturation times.     

Communication: a minimal model for the diffusion-relaxation backbone dynamics of proteins

We present a model for the local diffusion-relaxation dynamics of the C(α)-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ≥ 0. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the C(α)-atoms exceptionally well and reveals moreover a strong correlation between the residue's solvent-accessible surface and the fitted model parameters.     

Computing minimal entropy production trajectories: an approach to model reduction in chemical kinetics

Advanced experimental techniques in chemistry and physics provide increasing access to detailed deterministic mass action models for chemical reaction kinetics. Especially in complex technical or biochemical systems the huge amount of species and reaction pathways involved in a detailed modeling approach call for efficient methods of model reduction. These should be automatic and based on a firm mathematical analysis of the ordinary differential equations underlying the chemical kinetics in deterministic models. A main purpose of model reduction is to enable accurate numerical simulations of even high dimensional and spatially extended reaction systems. The latter include physical transport mechanisms and are modeled by partial differential equations. Their numerical solution for hundreds or thousands of species within a reasonable time will exceed computer capacities available now and in a foreseeable future. The central idea of model reduction is to replace the high dimensional dynamics by a low dimensional approximation with an appropriate degree of accuracy. Here I present a global approach to model reduction based on the concept of minimal entropy production and its numerical implementation. For given values of a single species concentration in a chemical system all other species concentrations are computed under the assumption that the system is as close as possible to its attractor, the thermodynamic equilibrium, in the sense that all modes of thermodynamic forces are maximally relaxed except the one, which drives the remaining system dynamics. This relaxation is expressed in terms of minimal entropy production for single reaction steps along phase space trajectories.     

Dual control cell reaction ensemble molecular dynamics: a method for simulations of reactions and adsorption in porous materials

We present a simulation tool to study fluid mixtures that are simultaneously chemically reacting and adsorbing in a porous material. The method is a combination of the reaction ensemble Monte Carlo method and the dual control volume grand canonical molecular dynamics technique. The method, termed the dual control cell reaction ensemble molecular dynamics method, allows for the calculation of both equilibrium and nonequilibrium transport properties in porous materials such as diffusion coefficients, permeability, and mass flux. Control cells, which are in direct physical contact with the porous solid, are used to maintain the desired reaction and flow conditions for the system. The simulation setup closely mimics an actual experimental system in which the thermodynamic and flow parameters are precisely controlled. We present an application of the method to the dry reforming of methane reaction within a nanoscale reactor model in the presence of a semipermeable membrane that was modeled as a porous material similar to silicalite. We studied the effects of the membrane structure and porosity on the reaction species permeability by considering three different membrane models. We also studied the effects of an imposed pressure gradient across the membrane on the mass flux of the reaction species. Conversion of syngas (H2/CO) increased significantly in all the nanoscale membrane reactor models considered. A brief discussion of further potential applications is also presented.     

No fragile-to-strong crossover in LiCl-H2O solution

Dynamics of water, especially in the temperature range of the "no man's land", remain a mystery. We present detailed study of dynamics in aqueous LiCl solution that is often considered as a model for bulk water. We employ broadband dielectric and light scattering spectroscopy in a broad frequency and temperature range. Our analysis reveals no sign of the fragile-to-strong crossover (FSC) neither in structural relaxation nor in translational motions. Our experimental results combined with a large selection of literature data lead to the clear conclusion-there is no FSC in dynamics of aqueous solutions at T ～ 200-230 K. Instead, our analysis reveals appearance of the so-called excess wing at the high frequency tail of the structural relaxation peak. We discuss the localized nature of the relaxation process that contributes to the excess wing.     

Dynamic Gradient Directed Molecular Transport and Concentration in Hydrogel Films

Materials which selectively transport molecules along defined paths offer new opportunities for concentrating, processing and sensing chemical and biological agents. Here, we present the use of traveling ionic waves to drive molecular transport and concentration of hydrophilic molecules entrained within a hydrogel. The traveling ionic wave is triggered by the spatially localized introduction of ions, which through a dissipative ion exchange process, converts quaternary ammonium groups in the hydrogel from hydrophilic to hydrophobic. Through a reaction–diffusion process, the hydrophobic region expands with a sharp transition at the leading edge; it is this sharp gradient in hydrophilicity that drives the transport of hydrophilic molecules dispersed within the film. The traveling wave moved up to 450 μm within 30 min, while the gradient length remained 20 μm over this time. As an example of the potential of molecular concentration using this approach, a 70‐fold concentration of a hydrophilic dye was demonstrated.     

Dynamics of an enzymatic substitution reaction in haloalkane dehalogenase

Reactive flux molecular dynamics simulations have been carried out using a combined QM/MM potential to study the dynamics of the nucleophilic substitution reaction of dichloroethane by a carboxylate group in haloalkane dehalogenase and in water. We found that protein dynamics accelerates the reaction rate by a factor of 2 over the uncatalyzed reaction. Compared to the thermodynamic effect in barrier reduction, protein dynamic contribution is relatively small. However, analyses of the friction kernel reveal that the origins of the reaction dynamics in water and in the enzyme are different. In aqueous solution, there is significant electrostatic solvation effect, which is reflected by the slow reorganization relaxation of the solvent. On the other hand, there is no strong electrostatic coupling in the enzyme and the major effect on reaction coordinate motion is intramolecular energy relaxation.     

Kinetics of metal ion binding by polysaccharide colloids

The dynamics of metal sorption by a gel-like polysaccharide is investigated by means of the electrochemical technique of stripping chronopotentiometry (SCP). The measured response reflects the diffusive flux properties of the metallic species in the dispersion. The colloidal ligand studied here is a functionalized carboxymethyldextran. Its complexation with Pb(II) reveals a time dependence that identifies strong differences in the dynamic nature of the successive metal complexes formed. Apparently, the formation of intramolecular bidentate complexes requires a slow conformational reorganization of the macromolecule that becomes the rate-limiting step in the complexation reaction. The relevant parameters for metal binding and release kinetics are computed and thus provide knowledge of the time-dependent stability and lability of metal polysaccharide complexes.     

Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: comparison between experiments, analytical calculations and numerical simulations

We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.     

ETD in a Traveling Wave Ion Guide at Tuned Z-Spray Ion Source Conditions Allows for Site-Specific Hydrogen/Deuterium Exchange Measurements

The recent application of electron transfer dissociation (ETD) to measure the hydrogen exchange of proteins in solution at single-residue resolution (HX-ETD) paves the way for mass spectrometry-based analyses of biomolecular structure at an unprecedented level of detail. The approach requires that activation of polypeptide ions prior to ETD is minimal so as to prevent undesirable gas-phase randomization of the deuterium label from solution (i.e., hydrogen scrambling). Here we explore the use of ETD in a traveling wave ion guide of a quadrupole-time-of-flight (Q-TOF) mass spectrometer with a “Z-spray” type ion source, to measure the deuterium content of individual residues in peptides. We systematically identify key parameters of the Z-spray ion source that contribute to collisional activation and define conditions that allow ETD experiments to be performed in the traveling wave ion guide without gas-phase hydrogen scrambling. We show that ETD and supplemental collisional activation in a subsequent traveling wave ion guide allows for improved extraction of residue-specific deuterium contents in peptides with low charge. Our results demonstrate the feasibility, and illustrate the advantages of performing HX-ETD experiments on a high-resolution Q-TOF instrument equipped with traveling wave ion guides. Determination of parameters of the Z-spray ion source that contribute to ion heating are similarly pertinent to a growing number of MS applications that also rely on an energetically gentle transfer of ions into the gas-phase, such as the analysis of biomolecular structure by native mass spectrometry in combination with gas-phase ion-ion/ion-neutral reactions or ion mobility spectrometry.     

Acoustic wave detection of chemical species electrokinetically transported within a capillary tube

For the first time, we report the acoustic wave detection of chemical species being transported in a capillary tube to a region where acoustic coupling occurs. The measured parameter was a change in phase, which was originally only attributed to a change in solution density as the analyte passed by the detection region. Accordingly, we report the detection of change in phase as various chemical species (e.g. Cy5 dye, Cy5-derivatized glycine and underivatized glycine) were introduced into and migrated along a capillary tube through electrokinetic processes. To improve detection sensitivity, we modified various experimental parameters, such as run buffer concentration, capillary wall thickness and transducer frequency. Although acoustic wave detection was feasible, the peak width and detection limit were inadequate as compared to conventional detection methods for HPLC or CE. Nevertheless, the effects of various physical and chemical relaxation processes on acoustic wave absorption were discussed, and this has shed some light on explaining some observations, which cannot be explained by density differences alone. Accordingly, the acoustic wave method is suggested to investigate these processes, as studied in ultrasonic relaxation spectroscopy, in a flow system.     

Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as square root Ra for Ra>5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)].     

Non-exponential non-Arrhenius relaxation in the course of CO rebinding to heme proteins

The dispersive transport model for relaxation of photolyzed heme proteins has been improved to take into account the coupling of the ligand-heme geminate recombination and the non-Gaussian diffusive dynamics of conformational changes in heme proteins. Contrary to the earlier deterministic version of the model, the present more rigorous formulation is based on the stochastic approach to the problem. This implies that the time evolution of protein conformations should be described in terms of the transient distribution which satisfies the Smoluchowski-type differential equation with a time-dependent diffusion coefficient. The obtained analytical solution of this equation enables us to relate main kinetic parameters of the geminate recombination and quantities characterizing the ligand-heme interaction. The derived expressions demonstrate that the reaction barrier shifts with time towards higher values following the near-stretched exponential behavior in agreement with experiment. Such a behavior is governed by the non-exponential non-Arrhenius conformational relaxation. The latter process can be identified by the characteristics “footprint” left on the experimental rebinding curve and is shown to be responsible for some kinetically different phases of the ligand-heme geminate recombination observed within distinct temperature ranges.     

Spectroscopic and photopolymerization studies of benzyl methacrylate/poly(benzyl methacrylate) two‐component system

The influence of the viscosity of a two‐component system on its molecular dynamics (on the basis of hypersonic wave velocity and attenuation coefficient) and photopolymerization kinetics was studied. The system investigated represented the solution of poly(benzyl methacrylate), PBzMA (MW = 70000) in its monomer, benzyl methacrylate (BzMA). The viscosity of the system was varied by adding various amounts of the polymer to the monomer (10–50 wt %). The molecular dynamics in the neat BzMA was studied by the proton Nuclear Magnetic Resonance (NMR) spin‐lattice relaxation time measurements and the wide‐line ¹H NMR spectroscopy in a wide range of temperature. Information on the local dynamics in liquid BzMA above its melting temperature was gained from the high‐resolution ¹H and ¹³C NMR spectra. The hypersonic wave velocity and the attenuation coefficient were investigated in the appropriate temperature range related to a viscoelastic relaxation process by the Brillouin light scattering method. The kinetic measurements have demonstrated that the photopolymerization rate rapidly increases and the monomer conversion decreases with increasing polymer‐to‐monomer ratio; this effect has been noted in the whole range of polymer concentration and reaction temperature studied. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1336–1348, 2010     

Transport Coefficients Of Ar—Kr Mixtures by Molecular Dynamics Computer Simulation

Abstract

Equilibrium molecular dynamics computer simulations have been used to determine the transport coefficients of model Ar—Kr mixtures, which are represented by Lennard-Jones pair potentials with Lorentz—Berthelot rules for the cross-species interactions. The component self-diffusion and mutual-diffusion coefficients are calculated from time correlation functions and mean square displacements. Time correlation functions are used to evaluate the shear and bulk viscosity, thermal conductivity and the thermal diffusion coefficient (Soret/Dufour coefficient). In the case of the thermal transport coefficients, the partial enthalpy of the two species is required at each state point to define the heat flux rigorously. We obtain this and the partial volume (and species resolved chemical potential) using particle-exchange (and particle insertion) techniques implemented in separate [NPT] simulations at the same state point.

The viscoelasticity of the fluids is characterised by the relaxation times for bulk and shear stress relaxation. The results are for dense liquids close to the triple point temperature and density. Agreement with experiment and previous simulation is particularly good for the density of the mixtures, the shear modulus, shear viscosity, shear stress relaxation time and thermal conductivity. As for the single component noble gas fluids (simulated and experiment) there is a significant qualitative difference in the temperature and, for mixtures, composition dependence of the bulk viscosity.