Hydrodynamic and thermal interaction of two droplets migrating in an unbounded porous matrix
摘要
The axisymmetric thermocapillary migration and interaction of two spherical droplets embedded in an unbounded porous medium saturated with a viscous fluid are investigated analytically within the quasi-steady Stokes–diffusion limit. The droplets are subjected to a uniform temperature gradient applied along the line joining their centers, generating thermocapillary stresses that drive their motion through the surrounding Brinkman medium. The analysis accounts for coupled hydrodynamic and thermal interactions together with the effects of porous resistance, viscosity ratio, thermal conductivity ratio, droplet separation distance, and droplet size ratio. The flow and temperature fields are constructed using superposition techniques in spherical coordinates combined with a multipole collocation procedure to satisfy the interfacial boundary conditions. The results demonstrate that porous resistance significantly modifies the thermocapillary migration velocities and the strength of droplet interactions compared with clear-fluid systems. In addition, the migration characteristics are strongly influenced by the viscosity and thermal conductivity contrasts between the droplets and the surrounding medium, as well as by the droplet spacing. The present formulation extends previous studies on isolated droplets and clear-fluid thermocapillary transport to interacting multiphase systems in porous Brinkman media. The obtained solutions reduce to several limiting cases available in the literature, providing additional validation of the analysis.