A Thermodynamically Consistent Phase-Field Model and an Entropy Stable Numerical Method for Simulating Two-Phase Flows with Thermocapillary Effects
arxiv(2024)
摘要
In this study, we have derived a thermodynamically consistent phase-field
model for two-phase flows with thermocapillary effects. This model accommodates
variations in physical properties such as density, viscosity, heat capacity,
and thermal conductivity between the two components. The model equations
encompass a Cahn-Hilliard equation with the volume fraction as the phase
variable, a Navier-Stokes equation, and a heat equation, and meanwhile
maintains mass conservation, energy conservation, and entropy increase
simultaneously. Given the highly coupled and nonlinear nature of the model
equations, we developed a semi-decoupled, mass-preserving, and entropy-stable
time-discrete numerical method. We conducted several numerical tests to
validate both our model and numerical method. Additionally, we have
investigated the merging process of two bubbles under non-isothermal conditions
and compared the results with those under isothermal conditions. Our findings
reveal that temperature gradients influence bubble morphology and lead to
earlier merging. Moreover, we have observed that the merging of bubbles slows
down with increasing heat Peclect number PeT when the initial temperature field
increases linearly along the channel, while bubbles merge faster with heat
Peclect number PeT when the initial temperature field decreases linearly along
the channel.
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