The equations of motion of a bubble, expanding adiabatically through an incompressible viscous fluid, are deduced when the centre of the bubble moves in a vertical plane in the presence of gravitational acceleration, ...The equations of motion of a bubble, expanding adiabatically through an incompressible viscous fluid, are deduced when the centre of the bubble moves in a vertical plane in the presence of gravitational acceleration, acting vertically downwards. The non-linear equations of motion obtained are solved numerically for different values of the various parameters of the problem. The path traced by the centre of the bubble and velocity of the centre, the change of radius R with time, and the influence of the buoyancy force, which is experienced by the expanding bubble for different values of the gravitational acceleration on these quantities, are investigated. The radius R（t） of the bubble is found to vary periodically with time when the acceleration due to gravity is small. But when the acceleration due to gravity increases, this periodicity in the value of R（t） with t is lost. The influence of viscosity in determining the periodicity of the bubble motion is also investigated.展开更多
文摘The equations of motion of a bubble, expanding adiabatically through an incompressible viscous fluid, are deduced when the centre of the bubble moves in a vertical plane in the presence of gravitational acceleration, acting vertically downwards. The non-linear equations of motion obtained are solved numerically for different values of the various parameters of the problem. The path traced by the centre of the bubble and velocity of the centre, the change of radius R with time, and the influence of the buoyancy force, which is experienced by the expanding bubble for different values of the gravitational acceleration on these quantities, are investigated. The radius R（t） of the bubble is found to vary periodically with time when the acceleration due to gravity is small. But when the acceleration due to gravity increases, this periodicity in the value of R（t） with t is lost. The influence of viscosity in determining the periodicity of the bubble motion is also investigated.
