Arkady B. Rovinsky

Convective instability induced by differential transport in the tubular packed-bed reactor

Abstract Convective (or spatial) instability, which manifests itself as the tuned amplification of perturbations in the course of their propagation along a non-isothermal packed-bed tubular reactor, is shown to occur in the exothermic standard reaction A → B + heat. The instability is caused by the interplay of the differential transport of heat and matter and of the activator-inhibitor kinetics inherent in non-isothermal, exothermic reactions (where heat plays the role of autocatalytic species or activator, and matter represents the inhibitor). The differential transport is caused by the inert reactor packing which acts as a thermal reservoir and slows down the diffusive and advective transport of heat relative to that of matter. This instability appears to be relevant to an earlier observation (Puszynski and Hlavacek, 1980, Chem. Engng Sci. 35 , 1769–1774) of sustained temperature oscillations in a packed-bed reactor at high Lewis number.

Patchiness and Enhancement of Productivity in Plankton Ecosystems due to the Differential Advection of Predator and Prey

The diffusive instability is considered as one important mechanism that accounts for the patchiness of ecosystems, e.g. the phytoplankton/zooplankton system. We show here that spatial differentiation of the plankton communities may occur alternatively through the differential flow instability. A differential flow (advection) between phyto-and zooplankton species arises naturally in the shear flow of a marine current due to the diurnal, differential vertical migration of the counteracting plankton species. Model calculations using an extension of Scheffers plankton model and literature values of the kinetic parameters predict a travelling wave pattern of biological activity on the spatial scale from a few kilometers to ca 100 km, depending on the parameter values, in agreement with the scales of observed structures. Most importantly we find that the productivity (the spatial average of biomass and production rate) of both predator and prey subpopulations may be enhanced in the patterned state by factors of the order of 2 and 20. The mechanism is discussed by which the productivity of both counteracting species may change (i.e. be enhanced) through the differential flow.

The Differential Flow Instabilities

Instabilities caused by the flow of matter have been known for a long time and their study constitutes a central task of hydrodynamics and its applications [1]. The driving force of these instabilities are the spatial gradients of the flow velocity field: when spatially separated elements are in relative motion, they exert destabilizing mechanical, electrical or electromagnetic forces on each other. The hydrodynamic system may be just a single species which is often simply referred to as ‘matter’ or ‘fluid’, regardless of its chemical nature. Perhaps the simplest example of a hydrodynamic instability is the Kelvin-Helmholtz instability of inviscid shear flow [1].

Differential flow instability of the exothermic standard reaction in a tubular cross-flow reactor

Abstract A differential-flow-induced instability, which generates travelling waves, may occur in the exothermic reaction A → B + heat in a packed bed tubular cross-flow reactor. It is caused by the differential flow (not to be confused with cross flow) between heat acting as autocatalyst and the reacting matter, at elevated Lewis numbers. The uncoupling of heat and matter transport releases the inherent tendency of the autocatalyst to grow. A stability analysis of the governing equations is presented. Simulations of the travelling wave patterns show that multiple solutions coexist and are asymptotically stable.

Absolute instability of a tubular packed-bed reactor with recycling

Abstract The stationary state of a non-isothermal tubular packed-bed reactor with partial recycling of the product flow or simply of the reaction heat, is shown to be absolutely unstable. This instability is closely related to the convective instability of a fixed-bed reactor without recycling [Yakhnin et al. , 1994, Chem. Engng Sci. (in press)] which manifests itself as the ability of the system to amplify perturbations in the course of their spatial propagation. Recycling causes these amplified perturbations to be reinjected, thereby keeping the reactor from settling into its stationary state. This results in self-sustained periodic waves that circulate through the reactor.

Control of activator-inhibitor systems by differential transport

Abstract When an activator-inhibitor system switches from a spatially uniform to a patterned state by a differential transport instability — the differential flow instability, or the diffusive or Turing instability — the values of variables, such as concentrations or reaction rates, including their averages, may drastically change. Analysis shows that such control of productivity by differential transport is a general property of nonlinear activator-inhibitor systems. By simulations and experiments using the Belousov-Zhabotinsky reaction, we show that average concentrations of the key species may be significantly enhanced when the reaction is run in the presence of a differential flow.

Dynamics of analog‐to‐frequency transduction by excitable systems: Sensory receptors

This paper analyzes the dynamics of analog‐to‐frequency transduction occurring in spatially extended excitable media with particular attention to sensory receptors. It is shown that spatially extended excitable media generate periodic traveling waves when forcing a dynamical variable by a constant stimulus at a boundary (i.e., by a Dirichlet boundary condition). However, the dynamical range of frequency ω(S) as a function of stimulus S is usually too narrow for sensory transducers, unless special physical conditions are met. The crucial property of an excitable medium that endows it with a wide transduction range in frequency is shown to be the nonlinear slowing down of the recovery variable in the vicinity of the steady state. This property is illustrated by computation for a series of models of the encoder region of sensory neurons possessing increasing physiological relevance.

Differential flow instability in the Ginzburg-Landau and Swift-Hohenberg approximations

Abstract The effects of a differential flow of the components of a reaction-diffusion system which is close to its stability boundary are described within the long wavelength approximation. In the vicinity of the Hopf bifurcation the systems evolution is governed by a complex Ginzburg-Landau equation modified by a purely imaginary convective term. If the system is near the zero real eigenvalue bifurcation, the governing equation is a modified Swift-Hohenberg equation. In both cases the homogeneous, stable reference steady state may be destabilized by the differential flow. In the Ginzburg-Landau equation, the destabilization occurs as long as the flow velocity exceeds some critical value v cr , which tends to zero as the system approaches the Hopf bifurcation. In the modified Swift-Hohenberg equation, the flow has either a destabilizing or stabilizing effect, depending on the sign of one of the system parameters. Destabilization occurs when the flow velocity exceeds some threshold; however in this case, the threshold remains finite even at the bifurcation point. In both Ginzburg-Landau and Swift-Hohenberg equations the differential flow instability produces traveling plane waves. The stability analysis shows that once a periodic plane wave is established, its spatial period remains unchanged over a finite range of the flow velocity and changes in discrete steps — the phenomenon of ‘wavenumber locking’. ‘Wavenumber locking’ is verified in numerical experiments with the Ginzburg-Landau equation. Near Hopf bifurcation, the Benjamin-Feir instability may occur. In this case irregular traveling waves are found, but a regular component of the wave pattern survives. Depending on a parameter, the differential flow either promotes or deters the Benjamin-Feir instability. As a result, the increasing flow may swithc the periodic wave pattern into a irregular state or, conversely, may stabilize the previously induced irregular pattern and produce periodic waves.

Analog-to-frequency transduction by nonlinear excitable media

Abstract Spatially extended excitable media may, through an appropriate constant force on the dynamical variables (boundary condition), be made to generate periodic travelling waves whose frequency encodes the constant external stimulus. It is shown that to operate as an analog-to-frequency converter over a wide dynamical frequency range, it is necessary that the systems recovery to its fixed point be nonlinearly slowed down.

Dynamics of analog-to-frequency transduction in sensory receptors

We analyze the analog-to-frequency transduction by sensory neurons in vivo. Spatially extended neural models are made to fire by applying the stimulus to the membrane potential at the boundary of the trigger zone. The membrane property that provides a broad dynamical range of frequency is a prolonged hyperpolarizing afterpotential. In support of this PDE model, we study the stimulus-dependent location of pulse-initiation in crayfish stretch receptors Ringham (1971).