Allen Hjelmfelt

Tests of thermodynamic theory of relative stability in one‐variable systems

Schlogl’s criterion for equistability of two stable stationary states of an inhomogeneous chemical kinetic system is valid only for single‐variable cases dependent along a single spatial coordinate. We test the thermodynamic theory, developed in the preceding article for multivariable systems, in one dimension by comparison with calculations based on the deterministic reaction‐diffusion equation for a cubic Schlogl model (single variable). This reaction‐diffusion system is equivalent to a coupled multivariable system. The prediction of the thermodynamic theory of equistability approaches Schlogl’s result as the length of the system increases. We also test the theory for an optically bistable (ZnSe) system which has been studied experimentally; in this system, temperature is the variable, and there is transport by thermal conduction. Again, we find that the prediction of the multivariable thermodynamic theory approaches the result from the deterministic kinetic equation as the length of the system increase...

Experiments on an oscillatory system close to equilibrium

A theoretical study of systems with multiple equilibrium states due to nonidealities predicts that such systems may show oscillations arbitrarily close to equilibrium and with arbitrarily small dissipation [X.‐L. Chu and J. Ross, J. Chem. Phys. 93, 1613 (1990)]. A crystal of V2O3 shows bistability in electrical resistance for a certain range of temperature. When the crystal is placed in an electric current clamp and in a bath at a temperature lower than that of the bistability region oscillations occur due to the difference in heating on each branch of the hysteresis loop. The period of oscillations increases as the electric current in the clamp is decreased. Within a range of conditions the experiment supports the theory.

Effects of periodic variations of reactant influxes on the combustion of methane in power production

Periodic variations are applied to the influxes of oxygen and methane entering a reaction vessel in which takes place a combustion reaction. We measure the temperature and chemical responses of the system as we change the forcing amplitudes, periods, and equivalence ratios. Using a simple model of a Carnot engine we calculate efficiency changes in an externally varied flux mode (VFM) of operation relative to the constant flux mode (CFM) of operation. We find increases and decreases in the average temperature, efficiency, and unburnt fuel concentrations in the VFM relative to the CFM. For certain constraints we find regions where the average temperature in the VFM is less than that of the CFM and there is an efficiency increase. We find other regions where the entire temperature response in the VFM is greater than that of the CFM and this also can lead to an efficiency increase which is due to changes in extent of combustion and heat losses. The effects of forcing amplitudes, periods, and equivalence ratio...

Theory and experiments on the effects of perturbations on nonlinear chemical systems: Generation of multiple attractors and efficiency

Periodic perturbations are applied to the input fluxes of reactants in a system which exhibits autonomous oscillations, the combustion of acetaldehyde (ACH) and oxygen, and a system which exhibits damped oscillations, the combustion of methane and oxygen. The ACH system is studied by experiments and numerical analysis and the methane system is studied by numerical analysis. The periodic perturbations are in the form of a two‐term Fourier series. Such perturbations may generate multiple attractors, which are either periodic or chaotic. We discuss two types of bistable responses: a new phase bistability, in which a subharmonic frequency is added to a sinusoidal perturbation at different phases relative to the periodic response; and jump phenomena, in which the resonant frequency of a nonlinear oscillator depends on the amplitude of the periodic perturbation. Both the ACH and the methane systems confirm the phase bistability. The additional complex behavior of bistability due to jump phenomena is seen only i...

On the mechanistic dependence of the affinity decay

In a series of articles M. Garfinkle has presented an empirical thermodynamic approach to chemical reactions from an initial nonequilibrium state to equilibrium in a closed isothermal system. He claims that (1) (essential points made by M. Garfinkle are numbered for reference later in the text) ‘‘a stoichiometric chemical reaction in a closed system traverses a unique natural path from reaction initiation to equilibrium. Along such a natural reaction path the time rate of change of the thermodynamic functions can be analytically described independently of phenomenological or mechanistic consideration’’ [M. Garfinkle, J. Phys. Chem. 93, 2158 (1989)]. We show these and other claims not to be correct; this approach has validity limited to: reaction mechanisms with essentially only one velocity (mechanisms with one rate‐determining step or mechanisms in a quasi‐stationary state); reactions occurring at times close to the initial time; and no products present at the initial time. Garfinkle’s method of plotting...

Optimization of kinetic and thermodynamic properties in irreversible open chemical and thermal engines

Periodic variations of an external parameter or constraint of open chemical systems have been shown to induce changes in time averaged kinetic and thermodynamic quantities. We examine the effects of the analytic form of the periodic variation on the time averaged quantities and find the maximum changes obtainable through periodic variations. A variational procedure is proposed, based on a Fourier expansion of the form of the periodic perturbation, the laws of thermodynamics, conservation of matter, and the kinetics. The efficiency of power production in a combustion system is examined with this method in a numerical example. A unique maximum in the efficiency is found, with the gains achievable for more complex functions exceeding those for a sinusoidal perturbation. We interpret the changes in efficiency in terms of the magnitude of the response of the system (resonance) and phase shifts between the periodic perturbations and the response of the system. We illustrate the mechanisms of efficiency changes ...

Resonant response of a driven chemical system: effects on efficiency

Periodic variations are applied to the influxes of oxygen and methane entering a reaction vessel in which takes place a combustion reaction and, in the absence of these variations, the system is in a stable focus. We measure the reaction of the system to these variations and find a resonant response, and changes of phase relations between the forcing and response of the system, near the autonomous frequency. We calculate the enthalpy content of the gases and using a simple model of a Carnot engine we study the power output of the system and find increases (∼7% in power) in these quantities near the autonomous frequency. The experimental results are compared to the predictions of a numerical model specific to our system and to the analytic solution of a linear set of differential equations with a stable focus. We find good agreement with both, but there is an aspect of the experimental results which requires additional hypotheses.

Measurements and calculations of oscillations and phase relations in the driven gas‐phase combustion of acetaldehyde

Oscillations in light emission and species concentrations, are measured as periodic perturbations are simultaneously applied to the input rates of acetaldehyde and oxygen in the gas‐phase combustion of acetaldehyde in a continuous‐flow stirred tank reactor for conditions where the autonomous reaction itself is oscillatory. The experimental results are compared with the predictions of a five‐variable thermokinetic model. We measure periodic responses in the fundamental entrainment band (ratio of frequency of perturbation to frequency of response equal to unity) for four different values of phase shift between the acetaldehyde and oxygen perturbation wave forms as we vary the frequency and amplitude of the external periodic perturbations. Outside of the entrainment bands we find quasiperiodic response. We determine the phases of the light emission and six species concentrations, as measured with a mass spectrometer, with respect to the periodic perturbation, the variation of these phases across the fundamen...

Stabilization of Unstable Spatial Structures in an Optically Bistable System

We stabilize the unstable steady state of a spatially inhomogeneous optically bistable ZnSe interference filter and measure the average intensity of the light transmitted and reflected by the filter. We also image the spatial structures which are the stable and unstable steady states by spatially resolving the transmitted light. We further measure relaxations from the unstable branch to the two stable branches. Relaxations to the low-temperature branch occur homogeneously while relaxations to the high-temperature branch occur by the propagation of a front. The results are in agreement with calculated predictions of a deterministic model of this system. A comparison is also made to nonlinear reaction-diffusion systems