Micro-PIV study on the influence of viscosity on the dynamics of droplet impact onto a thin film

Abstract

This work presents a systematic experimental study of droplet impact onto a wet substrate. Four different silicone oils are used, covering a range of Reynolds number between 116<Re<1106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$116< \ ext{Re} <1106$$\\end{document} at two different initial wall film heights. The objective is to characterize the temporal and radial evolution of the velocity field within the crown crater by means of micro-PIV. Our findings show that the velocity field has the structure of an axisymmetric stagnation point flow with decaying strength a(t). The latter exhibits an exponential decay and can be explained in terms of the exponential decay of the pressure force exerted by the impacting droplet onto the wall film. In this context, the commonly accepted functional dependence a(t)∝t-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a(t) \\propto t^{-1}$$\\end{document} represents only the first-order Taylor approximation of the exponential decay and has therefore only a limited temporal validity. The analysis also corroborates the existence of an inertial regime concerning the velocity field for Re>270\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{Re}} > 270$$\\end{document}. This is not observed at lower Re numbers due to the increased pressure losses caused by the extensional (normal) strain during the radial spreading of the lamella. To validate these findings a holistic approach is chosen, which combines numerical results, analytical solutions and experimental data from literature. In particular, by using the continuity equation, it is shown that the experimental decay of the wall film height can be reconstructed from the velocity measurements. Consilience of results from different approaches provides a robust validation of the micro-PIV data obtained in this work.Graphical abstract