A physical model of a one-dimensional flow of a viscous bubbly fluid in an intermediate regime between bubble formation and breakage is presented. The model takes into account multiple physical effects including gravity, viscosity, and surface tension, and is based on mechanics and thermal exchange that occurs at the boundary of a single bubble, coupled to the dynamics of the viscous fluid as a whole. The dimensionless versions of the resulting nonlinear model are obtained, and typical values of dimensionless parameters are estimated for typical magma flows in horizontal subaerial lava fields and vertical volcanic conduits. Exact solutions of the resulting system of nonlinear equations corresponding to equilibrium flows and traveling waves are analyzed. Generalized Su-Gardner-type perturbation analysis is employed to study approximate solutions of the model in the the long-wave ansatz. Simplified nonlinear partial differential equations (PDE) satisfied by the leading terms of the pertu 查看全文>>