On the variety of traveling fronts in one-variable multistable reaction-diffusion systems

The still-open problem of the variety of asymptotic solutions to one-variable, one-dimensional infinite multistable reaction-diffusion systems is solved. We show that in such systems, besides monotonic traveling fronts, nonmonotonic traveling fronts can exist for appropriate initial conditions. The dependence of numbers of various types of traveling fronts on the number of stable stationary states also is given. Examples of traveling fronts for the chemical model describing two enzymatic (catalytic) reactions inhibited by an excess of their reactant is presented.     

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)].     

Nonlinear traveling wave mechanisms of fast solid-phase cryochemical reactions

Theoretical and experimental investigations of the traveling wave mechanisms of fast solid-phase cryochemical reactions carried out over a period of three decades are summarized. Applications of the concepts of “non-Arrhenius combustion” and “gasless detonation” to studies of cosmochemical processes near 0 K, explosive-like decays of metastable phases in solid-state physics, and new ideas about the nature of earthquakes are considered.     

Influence of particle-particle interactions and particles rotational motion in traveling wave dielectrophoresis

Traveling wave dielectrophoresis provides an interesting method for the controlled movement of microsized particles in suspended mixtures, and as such is a promising tool in microfluidic technology. In this case, the electrostatic force acting on the particles has two components: one due to the spatially varying magnitude of the electric field and the other due to the spatially varying phase. The actual movement of the particle is determined by the combined effect of these two forces and corresponding torques, the viscous drag exerted by the fluid on the particle, and the electrostatic and hydrodynamic particle-particle interactions. This paper presents the first numerical simulations of the motion of particles subjected to all previous forces and torques. Our technique is based on a finite-element scheme in which the particles are moved using a direct simulation scheme respecting the fundamental equations of motion for both the fluid and the solid particles. The fluid-particle motion is resolved by the method of distributed Lagrange multipliers and the electrostatic forces are computed using the point-dipole approximation. Our simulations show that the particle behavior strongly depends on the mismatch of the dielectric properties between the particles and the fluid, and that the particle-particle interaction force as well as particles rotation speeds play crucial roles in the various regimes.     

Microscopic simulations of supersonic and subsonic exothermic chemical wave fronts and transition to detonation

We perform microscopic simulations using the direct simulation Monte Carlo approach to an exothermic chemical wave front of Fisher-Kolmogorov, Petrovsky, Piskunov-type in a one-dimensional gaseous medium. The results confirm the existence of a transition from a weak detonation or deflagration to a Chapman-Jouguet detonation wave, that we already investigated at the macroscopic scale [G. Dumazer et al., Phys. Rev. E 78, 016309 (2008)]. In the domain of weak detonation or deflagration, the discrepancy between the propagation speeds deduced from the simulations and the macroscopic balance equations of hydrodynamics is explained by two microscopic effects, the discretization of the variables, known as cutoff effect, and the departure from local equilibrium. Remarkably, the propagation speed of a Chapman-Jouguet detonation wave is not sensitive to these perturbations of microscopic origin.     

Evaluating the variation of ion energy under different parameter settings in traveling wave ion mobility mass spectrometry

Ion mobility mass spectrometry (IM-MS) can be used to differentiate and identify isobaric ions. To improve IM-MS resolution, the second generation of traveling wave ion mobility (TWIM) technology was launched. There were reports showing ions were heated up by TWIM. With higher ion energy, it could alter the conformation of larger ions or MS/MS experiments. To monitor the energy exchange relating to the TWIM process, the combined use of thermometer ions with unique molecular structure and theoretical calculations to determine the effective temperature of ions had been explored. In this report, the use of a simple experimental approach to estimate the variation on the ion energy that result from changing a TWIM parameter setting is demonstrated. The approach aims to achieve the same percentage of ion dissociation in a collision cell, which is part of the original instrument and located at the exit of TWIM cell. Similar to the traditional MS/MS experiments, the same level of ion dissociation could be achieved by adjusting the electrical potential that was applied to the collision cell. The higher the ion energy after the TWIM separation, the lower the electrical potential was required to achieve the same level of ion dissociation. Together with the information on the number of electrical charge in the selected ion, the difference in the required electrical potentials could be converted into electron volt of ion energy that resulted from changing the TWIM parameter setting. The results showed ion energy could be changed 1–9 eV when the parameter of TWIM was adjusted.     

High-velocity (detonation-like) traveling wave regime of cryocopolymerization of acetaldehyde with hydrogen cyanide

The effect of initiation conditions on the self-sustained-wave regime of copolymerization of acetaldehyde with hydrogen cyanide has been studied. The local brittle failure in the bottom of the sample makes it possible to implement the high-velocity (detonation-like) traveling wave regime of copolymerization. The velocity of propagation of the reaction wave front achieves 1870 mm/s at an irradiation dose of 55 kGy. However, the copolymer formed in the course of preliminary irradiation at 77 K changes the properties of the solid matrix of the reagents and, at high irradiation doses, the high-velocity traveling wave regime of copolymerization degenerates. The velocity of propagation of the copolymerization wave decreases, and, at an irradiation dose of 200 kGy, it is as low as 50 mm/s. The same velocity of propagation is observed when the reaction is initiated by the brittle failure in the top of the sample.     

The influence of drift gas composition on the separation mechanism in traveling wave ion mobility spectrometry: insight from electrodynamic simulations

The influence of three different drift gases (helium, nitrogen, and argon) on the separation mechanism in traveling wave ion mobility spectrometry is explored through ion trajectory simulations which include considerations for ion diffusion based on kinetic theory and the electrodynamic traveling wave potential. The model developed for this work is an accurate depiction of a second-generation commercial traveling wave instrument. Three ion systems (cocaine, MDMA, and amphetamine) whose reduced mobility values have previously been measured in different drift gases are represented in the simulation model. The simulation results presented here provide a fundamental understanding of the separation mechanism in traveling wave, which is characterized by three regions of ion motion: (1) ions surfing on a single wave, (2) ions exhibiting intermittent roll-over onto subsequent waves, and (3) ions experiencing a steady state roll-over which repeats every few wave cycles. These regions of ion motion are accessed through changes in the gas pressure, wave amplitude, and wave velocity. Resolving power values extracted from simulated arrival times suggest that momentum transfer in helium gas is generally insufficient to access regions (2) and (3) where ion mobility separations occur. Ion mobility separations by traveling wave are predicted to be effectual for both nitrogen and argon, with slightly lower resolving power values observed for argon as a result of band-broadening due to collisional scattering. For the simulation conditions studied here, the resolving power in traveling wave plateaus between regions (2) and (3), with further increases in wave velocity contributing only minor improvements in separations.     

Structural analysis of prion proteins by means of drift cell and traveling wave ion mobility mass spectrometry

The prion protein (PrP) is implicitly involved in the pathogenesis of transmissible spongiform encephalopathies (TSEs). The conversion of normal cellular PrP (PrP^C), a protein that is predominantly α-helical, to a β-sheet-rich isoform (PrP^Sc), which has a propensity to aggregate, is the key molecular event in prion diseases. During its short life span, PrP can experience two different pH environments; a mildly acidic environment, whilst cycling within the cell, and a neutral pH when it is glycosyl phosphatidylinositol (GPI)-anchored to the cell membrane. Ion mobility (IM) combined with mass spectrometry has been employed to differentiate between two conformational isoforms of recombinant Syrian hamster prion protein (SHaPrP). The recombinant proteins studied were α-helical SHaPrP(90-231) and β-sheet-rich SHaPrP(90-231) at pH 5.5 and pH 7.0. The recombinant proteins have the same nominal mass-to-charge ratio (m/z) but differ in their secondary and tertiary structures. A comparison of traveling-wave (T-Wave) ion mobility and drift cell ion mobility (DCIM) mass spectrometry estimated and absolute cross-sections showed an excellent agreement between the two techniques. The use of T-Wave ion mobility as a shape-selective separation technique enabled differentiation between the estimated cross-sections and arrival time distributions (ATDs) of α-helical SHaPrP(90-231) and β-sheet-rich SHaPrP(90-231) at pH 5.5. No differences in cross-section or ATD profiles were observed between the protein isoforms at pH 7.0. The findings have potential implications for a new ante-mortem screening assay, in bodily fluids, for prion misfolding diseases such as TSEs.     

Separation of isomeric disaccharides by traveling wave ion mobility mass spectrometry using CO2 as drift gas

The use of CO₂ as a massive and polarizable drift gas is shown to greatly improve peak‐to‐peak resolution (R_p‐p), as compared with N₂, for the separation of disaccharides in a Synapt G2 traveling wave ion mobility cell. Near or baseline R_p‐p was achieved for three pairs of sodiated molecules of disaccharide isomers, that is, cellobiose and sucrose (R_p‐p = 0.76), maltose and sucrose (R_p‐p = 1.04), and maltose and lactose (R_p‐p = 0.74). Ion mobility mass spectrometry using CO₂ as the drift gas offers therefore an attractive alternative for fast and efficient separation of isomeric disaccharides. Copyright © 2012 John Wiley & Sons, Ltd.     

Tracking protein electrodenaturation fronts in the electrochemical treatment of tumors

Electrochemical reactions in the electrochemical treatment of tumors (EChT) induce extreme pH changes and, consequently, protein electrodenaturation fronts intimately related to tumor destruction. Here we introduce a new in vitro EChT collagen–macronutrient gel (CMG) model to study protein electrodenaturation fronts as a mean of assessing EChT effectiveness. Our CMG model shows that from an initial uniform condition two electrodenaturation fronts evolve expanding towards each other until collision. Moreover, electrodenaturation front tracking reveals that the front grows under a diffusion-controlled regime. Based on this evidence it is possible, in principle, to predict the time needed for tumor destruction without compromising healthy tissue. These results are consistent with those previously obtained with in vivo and in vitro EChT modeling. In contrast to previous simpler in vitro models, our CMG model represents a better structural and chemical approximation to a real tissue thus providing a better tool for validation of new in silico EChT models aimed at a more accurate prediction of tissue destruction level.     

Formation of multimeric steroid metal adducts and implications for isomer mixture separation by traveling wave ion mobility spectrometry

Steroid analysis is essential to the fields of medicine and forensics, but such analyses can present some complex analytical challenges. While chromatographic methods require long acquisition times and often provide incomplete separation, ion mobility spectrometry (IMS) as coupled to mass spectrometry (MS) has demonstrated significant promise for the separation of steroids, particularly in concert with metal adduction and multimerization. In this study, traveling wave ion mobility spectrometry (TWIMS) was employed to separate multimer steroid metal adducts of isomers in mixtures. The results show the ability to separate steroid isomers with a decrease in resolution compared with single component standards because of the formation of heteromultimers. Additionally, ion‐neutral collision cross sections (CCS) of the species studied were measured in the mixtures and compared with CCSs obtained in single component standards. Good agreement between these values suggests that the CCS may aid in identification of unknowns. Furthermore, a complex mixture composed of five sets of steroid isomers were analyzed, and distinct features for each steroid component were identified. This study further demonstrated the potential of TWIMS‐MS methods for the rapid and isomer‐specific study of steroids in biological samples for use either in tandem with or without chromatographic separation.     

The evolution of steep fronts in non-fickian polymer-penetrant systems

We adapt a recently proposed model for non-Fickian diffusion of penetrants into polymers and use it to study a drug-delivery problem. The model modified Fick's diffusion equation by the addition of stress-induced flux. A stress evolution equation incorporating aspects of the Maxwell and Kelvin-Voigt viscoelastic stress models completes the model. The relaxation time in the polymer is taken as a function of the penetrant concentration. The system is studied under the assumption that the diffusivity is large. Singular perturbation techniques are used to show that the concentration and stress evolve diffusively for small time, but exhibit steep fronts in a narrow region within the domain for larger time. These predictions are verified numerically for specified parameter values. Finally, the equations are studied in the steady state and are found to predict the evolution of shocks.     

Identification and separation of saxitoxins using hydrophilic interaction liquid chromatography coupled to traveling wave ion mobility‐mass spectrometry

The aim of this work was to develop a reliable and efficient analytical method to characterise and differentiate saxitoxin analogues (STX), including sulphated (gonyautoxins, GTX) and non‐sulphated analogues. For this purpose, hydrophilic interaction liquid chromatography (HILIC) was used to separate sulphated analogues. We also resorted to ion mobility spectrometry to differentiate the STX analogues because this technique adds a new dimension of separation based on ion gas phase conformation. Positive and negative ionisation modes were used for gonyautoxins while positive ionisation mode was used for non‐sulphated analogues. Subsequently, the coupling of these three complementary techniques, HILIC‐IM‐MS, permitted the separation and identification of STX analogues; isomer differentiation was achieved in HILIC dimension while non‐sulphated analogues were separated in the IM‐MS dimension. Additional structural characteristics concerning the conformation of STXs could be obtained using IM‐MS measurements. Thus, the collision cross sections (CCS) of STXs are reported for the first time in the positive ionisation mode. These experimental CCSs correlated well with the calculated CCS values using the trajectory method. Copyright © 2015 John Wiley & Sons, Ltd.     

Electroosmosis-modulated bio-flow of nanofluid through a rectangular peristaltic pump induced by complex traveling wave with zeta potential and heat source

Electrokineticmicroperistaltic pumps are important biomechanical devices that help in targeted drugging of sick body parts. This article is focused on mathematical modeling and analysis of some important aspect of such flows in a rectangular duct with wall properties. Effects of zeta potential, heat source, and deby length are also studied. Carbon nanotubes (CNTs) in the Newtonian base fluid are assumed as drugging material. A comparison of single-walled CNTs and multiwalled CNTs is also presented. It is considered that the walls are flexible and encapsulating the region with limited permeability. The defined flow problem is modeled and analyzed analytically for the transport of CNT–water nanofluid. It is accepted that the flow is steady, nonturbulent, and propagating waves do have a considerably longer wavelength when compared to amplitude. The conditions and assumptions lead to a model of coupled partial differential equations of order two. The exact results using the eigenfunction expansion method are procured and shown accordingly. The predictions about the behavior of important parameters are displayed for single-walled CNT and multiwalled CNT—water nanofluidic behavior—using figures. The impact of sundry parametersis are analyzed. The application of the current study involved a transporting/targeted drug delivery system using peristaltic micropumps and magnetic fields in pharmacological engineering.