Theoretical Analysis of Liquid–Ice Interaction in the Unsaturated Environment with Application to the Problem of Homogeneous Mixing

The process of ice–liquid water interaction in the unsaturated environment is explored both analytically and with the help of a numerical simulation. Ice–liquid water interaction via the condensation–evaporation mechanism is considered in relation to the problem of homogeneous mixing in an unmovable air volume. The process is separated into three stages: the homogenization stage, during which the rapid alignment of thermodynamic and microphysical parameters in the mixing volume takes place; the glaciation stage, during which the liquid droplets evaporate; and the ice stage, which leads to attaining a thermodynamic equilibrium. Depending on the initial temperature, humidity, and mixing ratios of liquid water and of ice water, the third stage may result in two outcomes: existence of ice particles under zero supersaturation with respect to ice or a complete disappearance of ice particles. Three characteristic times are associated with the microphysical stages: the phase relaxation time associated with droplets, the glaciation time determined by the Wegener–Bergeron–Findeisen process, and the phase relaxation time associated with ice. Since the duration of the second and third microphysical stages may be of the same order as the homogenization time or even longer, the homogeneous mixing scenario is more probable in mixed-phase clouds than in liquid clouds. It is shown that mixing of a mixed-phase cloud with a dry environment accelerates cloud glaciation, leading to a decrease in the glaciation time by more than 2 times. The conditions of fast ice particles’ disappearance due to sublimation are analyzed as well.

Influence of Microphysical Variability on Stochastic Condensation in a Turbulent Laboratory Cloud

Diffusional growth of droplets by stochastic condensation and a resulting broadening of the size distribution has been considered as a mechanism for bridging the cloud droplet growth gap between condensation and collision–coalescence. Recent studies have shown that supersaturation fluctuations can lead to a broadening of the droplet size distribution at the condensational stage of droplet growth. However, most studies using stochastic models assume the phase relaxation time of a cloud parcel to be constant. In this paper, two questions are asked: how variability in droplet number concentration and radius influence the phase relaxation time and what effect it has on the droplet size distributions. To answer these questions, steady-state cloud conditions are created in the laboratory and digital inline holography is used to directly observe the variations in local number concentration and droplet size distribution and, thereby, the integral radius. Stochastic equations are also extended to account for fluctuations in integral radius and obtain new terms that are compared with the laboratory observations. It is found that the variability in integral radius is primarily driven by variations in the droplet number concentration and not the droplet radius. This variability does not contribute significantly to the mean droplet growth rate but does contribute significantly to the rate of increase of the size distribution width.

Theoretical analysis of mixing in liquid clouds – Part 3: Inhomogeneous mixing

An idealized diffusion–evaporation model of time-dependent mixing between a cloud volume and a droplet-free volume is analyzed. The initial droplet size distribution (DSD) in the cloud volume is assumed to be monodisperse. It is shown that evolution of the microphysical variables and the final equilibrium state are unambiguously determined by two non-dimensional parameters. The first one is the potential evaporation parameter R, proportional to the ratio of the saturation deficit to the liquid water content in the cloud volume, that determines whether the equilibrium state is reached at 100 % relative humidity, or is characterized by a complete evaporation of cloud droplets. The second parameter Da is the Damkölher number equal to the ratio of the characteristic mixing time to the phase relaxation time. Parameters R and Da determine the type of mixing.The results are analyzed within a wide range of values of R and Da. It is shown that there is no pure homogeneous mixing, since the first mixing stage is always inhomogeneous. The mixing type can change during the mixing process. Any mixing type leads to formation of a tail of small droplets in DSD and, therefore, to DSD broadening that depends on Da. At large Da, the final DSD dispersion can be as large as 0.2. The total duration of mixing varies from several to 100 phase relaxation time periods, depending on R and Da.The definitions of homogeneous and inhomogeneous types of mixing are reconsidered and clarified, enabling a more precise delimitation between them. The paper also compares the results obtained with those based on the classic mixing concepts. >

Influence of Interfacial Exchange Interaction on the Two-Phase Relaxation Time of Superparamagnetic Nanoparticles

Within the frame of two-phase superparamagnetic nanoparticles the effect of magnetic and geometric properties of superparamagnetic nanoparicles on the time of their magnetic relaxation has been defined. With increasing of volume the time of relaxation grows rapidly. Metastability conditions of magnetic states have been developed. Growth of exchange constant magnitude of interphase interaction results in increasing of relaxation time regardless of exchange constant sign.

TRANSPORT ANOMALIES AND MARGINAL FERMI-LIQUID EFFECTS AT A QUANTUM CRITICAL POINT

The behaviour of the conductivity and the density of states, as well as the phase relaxation time, of disordered itinerant electrons across a quantum ferromagnetic transition is discussed. It is shown that critical fluctuations lead to anomalies in the temperature and energy dependence of the conductivity and the tunnelling density of states, respectively, that are stronger than the usual weak-localisation anomalies in a disordered Fermi liquid. This can be used as an experimental probe of the quantum critical behaviour. The energy dependence of the phase relaxation time at criticality is shown to be that of a marginal Fermi liquid.