Experimental study on coherent structures by small particles suspended in high aspect-ratio (Γ=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma =$$\\end{document} 2.5) thermocapillary liquid bridges of high Prandtl number

Abstract

In time-dependent traveling-wave convection, it has been confirmed that small particles of low Stokes number (St≪\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{St}\\ll$$\\end{document} 1) form three-dimensional closed structures known as the particle accumulation structures (PASs). We focus on coherent structures formed in high aspect-ratio thermocapillary liquid bridges (Γ=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma =$$\\end{document} 2.5), where oscillatory convection due to the so-called hydrothermal wave instability of mHTW=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{\ extrm{HTW}}=$$\\end{document} 1 stably emerges, and carry out experimental explorations into the volume ratio dependence of the emergence of coherent structures. Variation in the volume ratio induces the presence of coherent structures with different azimuthal wave numbers, that is, different spatial structures. Among the particles added to the liquid bridge, we perform spatio-temporal tracking of particles to quantify the correlation between the behavior of particles and the spatial structures of coherent structures with different rational wave numbers.