A. V. Vinogradov

1/f noise and self-organized criticality in crisis regimes of heat and mass transfer

Abstract Thermal fluctuations under the transition from nucleate to film boiling of water on a wire heater and fluctuations of jet form during an outflow of superheated liquid from a pressure vessel were experimentally investigated. It has been found that power spectrum of the fluctuations has got a low frequency component corresponding to a 1/f law (flicker noise). The effect given is connected with the occurrence of nonequilibrium phase transitions in the systems: a crisis of heat transfer under the transition from nucleate to film boiling and a crisis of a flow in boiling-up of superheated liquid jet.

Self-organized criticality and 1/f-noise at interacting nonequilibrium phase transitions

Oscillatory combustion regimes were experimentally investigated under the conditions of ignitable liquid boiling-up before the reaction front. Fluctuations with a power spectral density inversely proportional to frequency (1/f-noise) were observed and the power-law character of distribution functions was found. The phenomena are connected with the intersection and interaction of nonequilibrium phase transitions. A mathematical model describing the initiation of 1/f fluctuations at the interaction of a subcritical phase transition and supercritical one in a space-distributed system was suggested.

Dynamics of transition processes and structure formation in critical heat-mass transfer regimes during liquid boiling and cavitation

The results of experimental studies concerning the development of critical phenomena and structure formation in the process of boiling in falling films and during liquid cavitation are given. In conditions of stepwise and periodic pulsed surges of a thermal load, the parameters of formed metastable regular structures and critical parameters of heat-releasing surface drying are shown to be determined by the dynamics of moving wetting boundaries in the process of system self-organization. In the case of high-intensity heat fluxes, decomposition of a falling film is determined by propagation regimes of self-maintaining boiling fronts with a complex shape of intermediate structures. The study of ultrasonic cavitation of water, glycerin, and vacuum oil shows that structures of interacting gas-vapor bubbles (having the form of fractal clusters) are formed near the emitter surface. Spatial structures are characterized by a low-frequency divergence of the power spectra and a scale-invariant function of the fluctuation distributions. The experimental results are in good qualitative agreement with the numerical simulations performed within the theory of 1/f fluctuations in the case of nonequilibrium phase transitions in a spatially distributed system.

Glass transition and crystallization of low-temperature amorphous condensates of the water-propane mixture

Interest in gas hydrates stems from the existence of vast reserves of hydrocarbons on the earth in the form of gas hydrates, prospects for using them as a fuel source, and the possibility of storage and transporta� tion of gas in the gas hydrate state. The known meth� ods of production of gas hydrates are based on rela� tively small deviations from the equilibrium condi� tions of gas dissolution. They require the use of high pressures in laboratory or manufacturing equipment. For example, the pressure corresponding to the for� mation conditions of methane hydrate at temperatures near 0°С amounts to tens of bars. In addition, forma� tion of the crystal hydrate requires dispersion of water, which is afforded by longterm and vigorous stirring of the water-gas mixture. In this work, we have proposed another approach implying that hydrates are formed under conditions far from thermodynamic equilibrium. The approach is based on lowtemperature molecularbeam deposi� tion in a vacuum onto a surface cooled by liquid nitro� gen. During this process, amorphous (glassy) layers of the water-gas mixture are initially formed, which are stabilized by high viscosity. Heating of the amorphous layers is accompanied by avalanchetype nucleation and growth of gas hydrate crystallization sites. This method requires neither high pressures nor stirring of the water-gas system. Its advantage is that it is univer� sal and can be used for producing various gas hydrates. This work deals with studying the glass transition and crystallization of amorphous condensates of the binary water-propane system obtained by lowtem� perature condensation to determine the conditions of crystal hydrate formation. Amorphous solid (glassy) layers of lowmolecular� weight substances can be obtained by molecularbeam deposition onto a cooled surface. At low temperatures, the amorphous state of these substances is stabilized by the high viscosity. Molecularbeam deposition onto a copper substrate cooled by liquid nitrogen affords amorphous layers of water and simple molecular com� pounds (1), as well as of aqueous solutions of organic liquids (2). Cooling rates under these conditions are as high as 10 5 -10 7 K/s. On heating, the condensates undergo glass transition (softening) and subsequent spontaneous crystallization. In the course of the latter, a decisive role for phase transformation is played by homogeneous nucleation. The crystallization of amorphous water-gas condensates can result in the formation of gas hydrates (3-5). Hydrate formation is facilitated by the low chemical affinity of the hydrate� forming substance, as well as by the size and shape of its molecules corresponding to the geometry of cavi� ties in the arising clathrate framework. Among such substances, there are light hydrocarbons of the meth� ane series. Experiments with lowtemperature con� densates of the water-methane mixture showed the possibility of producing massive samples of crystal hydrates with high gas content capable of sustained burning (5).

Low-frequency fluctuations with 1/fα power spectrum in transient modes of water boiling on a wire heater

The investigation of transient modes of water boiling on a wire heater reveals the presence of random vibrations with the frequency dependence of power spectra of S ∼ f−α, where the exponent α has values in the range 0.8 ≤ α < 2. Large-scale low-frequency fluctuations exhibiting the property of scale invariance, the duration of which is distributed by the power law P ∼ τ−β, are present in experimental realizations of random processes describing thermal fluctuations. The properties of such fluctuation processes are described using two nonlinear stochastic differential equations which describe the interaction between different phase transitions. Relations of dynamic scaling are determined between the critical exponents which define the frequency dependence of the power spectra of fluctuations α and of the distribution function of the amplitudes of extreme low-frequency fluctuations β. It is demonstrated that the critical exponents are related by the relation α + β = 2 both in the experiments and in the theoretical model of interacting phase transitions. The power spectra of fluctuations are determined in the experiments with greater simplicity and accuracy than the distribution function of extreme amplitudes. In the cases where only the spectral dependence of power spectra of fluctuations is known, the correlations between the exponents enable one to obtain information about the distribution of large-scale surges and estimate dangerous amplitudes.

Fluctuation dynamics and 1/f spectra characterizing the acoustic cavitation of liquids

The dynamics of acoustic cavitation in water and glycerin is studied experimentally. The power spectra and distribution functions of fluctuations are determined. In transient regimes, bubble structures in the form of fractal clusters are formed near the ultrasonic radiator. The power spectra have the form 1/f, and the distribution functions of local fluctuations differ from the Gaussian ones and exhibit the scale invariance property.

1/f noise in oscillatory modes of combustion

Fluctuation processes whose power spectrum varies inversely proportional to the frequency (flicker noise, or 1/f noise) are a subject of thorough investigations for many years. First discovered in electric circuits, 1/f noise is observed in systems of various nature (geophysical, astrophysical, biological, ecological, etc.). Presently, extensive data concerning the properties of the flicker noise in particular systems (see, e.g., reviews [1, 2]) are accumulating. For example, one of the most known studies involves a model according to which the 1/f noise is the consequence of the superposition of independent Lorentz sources having the relaxation-time distribution function g(τ) ~ τ–1 [1, 2]. Thermal models are also widely discussed in which the thermal conduction mechanisms [3] are considered to be responsible for the 1/f noise in solids. Explaining experimental manifestations of 1/f noise in particular physical systems can be problematic when using the current models; we run into problems in attempting to explain the origin of the 1/f noise in systems of different natures. In spite of long-standing efforts, no commonly accepted picture of this phenomenon has been available until now and the mechanisms leading to fluctuations obeying the 1/f spectrum are often unclear. Therefore, the problem of searching for new systems with flicker noise and of constructing new models for this phenomenon remains urgent.

Stability of low-frequency pulsations in a transient heat transfer regime upon phase transitions

Using the principle of maximum entropy, we investigate the stability of stochastic processes with the 1/f power spectrum in the system of two nonlinear stochastic differential equations when modeling pulsations in crisis and transient heat-mass transfer regimes with intensive phase transitions. An analysis of the stability of the resultant process, which appears upon the interaction of the stochastic process and the 1/f spectrum of external deterministic impact, is performed. Under the action of harmonic force, stable resultant processes are divided into two types depending on the amplitude of the harmonic force. We have experimentally studied the influence of harmonic impact on the stability of pulsations with the 1/f spectrum upon the crisis of water boiling on a heated wire. The results are in qualitative agreement with theoretical estimations.

Properties of gas hydrates formed by nonequilibrium condensation of molecular beams

Low-temperature crystallization of amorphous materials has been analyzed theoretically taking into account nonstationary nucleation. The kinetics of crystallization of amorphous water layers, formed by depositing molecular beams on a substrate cooled by liquid nitrogen, has been investigated by differential thermal analysis. The conditions of gas hydrate formation in low-temperature amorphous-ice layers saturated with carbon dioxide have been studied. The glass-transition and crystallization temperatures of the gas hydrates have been determined from the change in dielectric properties upon heating. Under the deep-metastability conditions, crystallization of water-gas layers leads to the formation of crystallohydrates. Gas molecules are captured by the avalanche-like nucleation of crystallization centers and, therefore, are not displaced by the moving crystal-melt interface. Gas-hydrate samples formed in nonequilibrium water-gas layers are convenient for studying their thermophysical properties.

The 1/f spectrum of acoustic cavitation

The fluctuations of a response signal during acoustic cavitation in water in an ultrasonic field were studied by photometry of the transmitted laser radiation. In a broad range of frequencies, the spectral density of photocurrent fluctuations exhibits the 1/f behavior and their amplitude distribution function has a bimodal character. Coarsening of the scale of the experimental time series makes the bimodal character more pronounced and reveals the scale invariance of fluctuations.