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Based on the classical nucleation theory, the effect of viscosity on bubble nucleation in water-saturated magma has been studied. A comparison with experimental data proves that viscosity has a pronounced effect on the rate of homogeneous nucleation in magma.The volcanic-eruption pattern is largely determined by nucleation and growth of gas bubbles dissolved in magma, which are predominantly formed by H 2 O and CO 2 [1]. Magma-degassing dynamics depends on the number of bubbles formed; the latter can be predicted using theoretical dependences for the nucleation rate [2,3]. Yet, these dependences ignore the effect of magma viscosity, which is known to be quite appreciable [4].The objective of the present work was to predict the rate of homogeneous nucleation in water-saturated magma on the basis of the classical nucleation theory [5] with allowance for viscosity. For the case of pure-liquid boiling, the rate of homogeneous nucleation was calculated with allowance for viscosity and thermal conductivity by Kagan [6]. The method proposed in [6] was used in the present study; to facilitate the comparison, we use the same notation.Let us briefly recall the main postulates of the classical nucleation theory [5]. We assume that the nuclei of the new phase are macroscopic and their size distribution function f (t, r) can be found from the following equation of the Fokker-Planck type:Here A is the growth rate of the nuclei, B is the diffusivity in the size space, and J is the nucleation rate. To calculate the growth rate of supercritical nuclei, we use the solution of an appropriate continual (heat-conduction or diffusion) problem. In constructing the steady-state solution of Eq. (1), the boundary condition at r → 0 is f (r) = f 0 (r), where f 0 (r) is the size distribution function of nuclei given by the thermodynamic fluctuation theory.The boundary condition at r → ∞ is J = const. It follows from these conditions that [5]where r k is the critical-nucleus radius, σ is the surface tension at the interface between the phases, k is the Boltzmann constant, and T is the temperature in the medium. Following the above-described approach, Toramaru [2] derived the following expression for the degassing conditions of water-saturated magma:

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A numerical simulation of the process of unsteady outflow of steam (steam-water mixture) from a volume under high pressure into a closed region with rigid boundaries is carried out. The calculations used a thermodynamically equilibrium homogeneous model of a vapor-liquid medium. At small and large (up to 0.15 s) times, spatial distributions of pressure, mass vapor content, density and temperature were obtained and analyzed.