Coherent particulate structures by boundary interaction of small particles in confined periodic flows

Rapid demixing of small density-matched particles in the incompressible flow in a cylindrical thermocapillary liquid bridge by the mechanism of particle-boundary interaction is studied. The flow considered is an azimuthally traveling hydrothermal wave which is periodic in time and azimuth. The length scale of the particles relative to that of the liquid bridge ranges from 7×10−4 to 4×10−2. The mechanism of demixing is based on the finite size of a particle, which otherwise perfectly follows the flow, and a specular reflection of the particle from the free-surface bounding the domain. To enable long-time accurate predictions of particle trajectories we consider a model flow which reflects the characteristic features of the hydrothermal wave for which particle accumulation has been detected in experiments. We find that, depending on the size of the particles, the particle-free-surface interaction causes particle attraction to a closed spiral or to the surface of a closed spiral tube. Even in the absence of spiral accumulation patterns very small particles can be completely removed from certain regions of the domain. All structures found are time periodic, exactly as is the underlying flow. The particle-accumulation structures found and the dynamics of the demixing agree qualitatively with experimental data. In the specular reflection model employed, reflected particles are restricted to move on a stream surface which becomes increasingly fragmented as the particles repeatedly interact with the free-surface. Repeated particle-free-surface interactions finally lead to a complex geometry of the stream surface on which particles are restricted to move. The results obtained can explain the line-like and tubular particle accumulation and the characteristic particle-depletion zones observed in experiments.