Inviscid bubble dynamics in a viscous fluid, moving with velocity $V$ far from the bubble, is considered. The Cauchy problem of recovering the bubble evolution from its initial shape is completely solved without surface tension. This dynamical system is well-posed (after a Tikhonov regularization) and possesses an extensive list of unsteady nonsingular closed-form solutions due to integrability. A new rational class of solutions is obtained and added to the logarithmic class found earlier [Phys. Rev. E 89, 061003(R) (2014)]. The only attractor of the system selects the observable bubble shape and velocity $U=2V$ from the continuum of possible solutions. The attractor is asymptotically stable. Numerical results essential for illustrating and understanding the most salient geometric aspects of the bubble dynamics are presented.

Close

PrevNext

View figure in article

• Bubble dynamics
• Hele-shaw flows
• Interfacial flows