Coupled Systems Mechanics, Vol. 7, No. 4 (2018) 407-420 DOI: https://doi.org/10.12989/csm.2018.7.4.407 407 Copyright © 2018 Techno-Press, Ltd. http://www.techno-press.org/?journal=csm&subpage=8 ISSN: 2234-2184 (Print), 2234-2192 (Online) Hydrodynamic coupling distance between a falling sphere and downstream wall Cheng-Chuan Lin * , Hung-Tien Huang a and Fu-Ling Yang b Department of Mechanical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan (R.O.C.) (Received January 29, 2018, Revised January 30, 2018, Accepted January 31, 2018) Abstract. In solid-liquid two phase flow, the knowledge of how descending solid particles affected by the presence of downstream wall is important. This work studies at what interstitial distance the velocity of a vertically descending sphere is affected by a downstream wall as a consequence of wall-modified hydrodynamic forces through a validated dynamic model. This interstitial distance-the hydrodynamic coupling distance δc-is found to decay monotonically with the approach Stokes number St which compares the particle inertia to viscous drag characterized by the quasi-steady Stokes’ drag. The scaling relation δc- St-1 decays monotonically as literature below the value of St equal to 10. However, the faster diminishing rate is found above the threshold value from St =10-40. Furthermore, an empirical relation of δc-St shows dependence on the drop height which clearly indicates the non-negligible effect of unsteady hydrodynamic force components, namely the added mass force and the history force. Finally, we attempt a fitting relation which embedded the particle acceleration effect in the dependence of fitting constants on the diameter-scaled drop height. Keywords: hydrodynamic coupling; Stokes number; wall effect; added mass force; history force 1. Introduction Particle-laden solid-liquid two-phase flows appear in a wide range of industrial applications (fluidized bed, slurry transport, pharmaceutical process, suspension filtering) and natural events (debris flows, sedimentation, soil liquefaction). Though we have established fair knowledge to describe the motion of a continuum fluid and its transport phenomenon, the addition of a second phase in discrete form brings new mechanisms for bulk momentum and energy transport. For example, when particles possess sufficient inertia to move relative to local fluid motion, they can interact with local flow structure and even come into contact, collide and rebound to redistribute bulk momentum and energy. Hence, the dynamic process at the constituent size level shall characterize the microscopic mechanisms for bulk macroscopic transport process. Extensive works Corresponding author, Ph.D. Student, E-mail: f00522316@ntu.edu.tw a M.Sc., E-mail: r03522123@ntu.edu.tw b Professor, E-mail: fulingyang@ntu.edu.tw