A hybrid axisymmetric conservative phase-field lattice Boltzmann method is applied to investigate the influence of Marangoni number (Ma), density ratio (ρr), and radius ratio (Rr) on thermocapillary migration of a deformable hollow droplet with difference in variable fluid properties, where ρr (Rr) is the density (radius) ratio of the hollow part of the droplet. The isotherms show that heat transfer around the hollow droplet is changed from conduction to convection with the increase in Ma. However, the temperature gradient across the hollow droplet decreases with Ma, which induces a small magnitude of migration velocity. When ρr is increased, the isotherms are accumulated around the hollow droplet front with a large temperature gradient, which enhances the hollow droplet migration, while the migration velocity is decreased with the increase in Rr. It is observed that thermocapillary migration of the hollow droplet finally becomes a pure droplet with the influence of aforementioned parameters, and it experiences interface breaking and coalescing, which causes a large transient variation in migration velocity. The magnitude of this transient variation in migration velocity is not obviously affected by Ma but significantly affected by ρr and Rr. The measured evolution of d (the dimensionless distance between inner and outer fronts of the hollow droplet) demonstrates that ρr has a significant influence on the reduction rate of d in comparison with the influence of Ma and Rr. Similar influences on the relative migration velocity between the fluid of the hollow part inside the droplet and the sealed fluid of the droplet are observed.

In this study, we first define the logarithmic likelihood ratio as a measure between arbitrary generalized information sources and non-homogeneous Markov sources and then establish a class of generalized information sources for small deviation theorems, strong limit theorems, and the asymptotic equipartition property. The present outcomes generalize some existing results.