- Rapid Communication
- Access by Xinjiang University
Droplet depinning in a wake
Phys. Rev. Fluids 2, 031601(R) – Published 8 March, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.031601
Abstract
Pinning and depinning of a windswept droplet on a surface is familiar yet deceptively complex for it depends on the interaction of the contact line with the microscopic features of the solid substrate. This physical picture is further compounded when wind of the Reynolds number greater than 100 blows over pinned drops, leading to the boundary layer separation and wake generation. In this Rapid Communication, we incorporate the well-developed ideas of the classical boundary layer to study partially wetting droplets in a wake created by a leader object. Depending on its distance from the leader, the droplet is observed to exhibit drafting, upstream motion, and splitting, due to the wake-induced hydrodynamic coupling that is analogous to drafting of moving bodies. We successfully rationalize the onset of the upstream motion regime using a reduced model that computes the droplet shape governed by the pressure field inside the wake.
Physics Subject Headings (PhySH)
Article Text
References (38)
- A. D. Becker, H. Masoud, J. W. Newbolt, M. Shelley, and L. Ristroph, Hydrodynamic schooling of flapping swimmers, Nat. Commun. 6, 8514 (2015).
- M. M. Zdravkovich, Review—Review of flow interference between two circular cylinders in various arrangements, J. Fluids Eng. 99, 618 (1977).
- J. C. Liao, D. N. Beal, G. V. Lauder, and M. S. Triantafyllou, Fish exploiting vortices decrease muscle activity, Science 302, 1566 (2003).
- D. N. Beal, F. S. Hover, M. S. Triantafyllou, J. C. Liao, and G. V. Lauder, Passive propulsion in vortex wakes, J. Fluid Mech. 549, 385 (2006).
- S. Jung, K. Mareck, M. Shelley, and J. Zhang, Dynamics of a Deformable Body in a Fast Flowing Soap Film, Phys. Rev. Lett. 97, 134502 (2006).
- L. Ristroph and J. Zhang, Anomalous Hydrodynamic Drafting of Interacting Flapping Flags, Phys. Rev. Lett. 101, 194502 (2008).
- P. G. de Gennes, Wetting: Statics and dynamics, Rev. Mod. Phys. 57, 827 (1985).
- D. Quéré, Wetting and roughness, Annu. Rev. Mater. Res. 38, 71 (2008).
- R. J. Kind, M. G. Potapczuk, A. Feo, C. Golia, and A. D. Shah, Experimental and computational simulation of in-flight icing phenomena, Prog. Aero. Sci. 34, 257 (1998).
- T. Cebeci and F. Kafyeke, Aircraft icing, Annu. Rev. Fluid Mech. 35, 11 (2003).
- I. Ghai, J. Wentz, R. E. DeVor, S. G. Kapoor, and J. Samuel, Droplet behavior on a rotating surface for atomization-based cutting fluid application in micromachining, J. Manuf. Sci. Eng. 132, 011017 (2010).
- S. G. Kandlikar and M. E. Steinke, Contact angles and interface behavior during rapid evaporation of liquid on a heated surface, Int. J. Heat Mass Transfer 45, 3771 (2002).
- E. B. Dussan V. and R. Tao-Ping Chow, On the ability of drops or bubbles to stick to non-horizontal surfaces of solids, J. Fluid Mech. 137, 1 (1983).
- E. B. Dussan V., On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. Part 2. Small drops or bubbles having contact angles of arbitrary size, J. Fluid Mech. 151, 1 (1985).
- P. Dimitrakopoulos, Deformation of a droplet adhering to a solid surface in shear flow: Onset of interfacial sliding, J. Fluid Mech. 580, 451 (2007).
- P. A. Durbin, On the wind force needed to dislodge a drop adhered to a surface, J. Fluid Mech. 196, 205 (1988).
- P. Dimitrakopoulos and J. J. L. Higdon, Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows, J. Fluid Mech. 336, 351 (1997).
- J. Bico, F. Besselievre, and M. Fermigier, Windswept droplets, in 58th Annual Meeting of the Division of Fluid Dynamics (American Physical Society, Chicago, IL, 2005).
- K. Njifenju, J. Bico, E. Andres, and M. Fermigier, Windswept droplets, in 62nd Annual Meeting of the APS Division of Fluid Dynamics (American Physical Society, Minneapolis, MN, 2009), Vol. 54.
- J. A. Schmucker, Ph.D. thesis, Experimental investigation of wind-forced drop stability, Texas A&M University, 2012.
- M. Acarlar and C. Smith, A study of hairpin vortices in a laminary boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance, J. Fluid Mech. 175, 1 (1987).
- M. S. Bloor, The transition to turbulence in the wake of a circular cylinder, J. Fluid Mech. 19, 290 (1964).
- J. H. Gerrard, The mechanics of the formation region of vortices behind bluff bodies, J. Fluid Mech. 25, 401 (1966).
- R. Sluder, L. Gris, and J. Katz, Aerodynamics of a generic optical turret, J. Aircraft 45, 1814 (2008).
- E. Savory and N. Toy, Hemispheres and hemisphere-cylinders in turbulent boundary layers, J. Wind Eng. Ind. Aerod. 23, 345 (1986).
- J. S. Wu and G. M. Faeth, Sphere wakes at moderate reynolds numbers in a turbulent environment, AIAA J. 32, 535 (1994).
- T. Maxworthy, Experiments on the flow around a sphere at high Reynolds numbers, J. Appl. Mech. 36, 598 (1969).
- F. M. Najjar and S. P. Vanka, Numerical study of a separated-reattaching flow, Theor. Comput. Fluid Dyn. 5, 291 (1993).
- F. Liang-Shih and K. Tsuchiya, Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions (Butterworth-Heinemann, Stoneham, MA, 1990).
- J. E. McDonald, The shape and aerodynamics of large raindrops, J. Meteorol. 11, 478 (1954).
- R. H. Magarvey and R. L. Bishop, Wakes in liquid-liquid systems, Phys. Fluids 4, 800 (1961).
- S. Nogueira, R. G. Sousa, A. M. F. R. Pinto, M. L. Riethmuller, and J. B. L. M. Campos, Simultaneous PIV and pulsed shadow technique in slug flow: A solution for optical problems, Exp. Fluids 35, 598 (2003).
- S. Nogueira, M. L. Riethmuller, J. B. L. M. Campos, and A. M. F. R. Pinto, Flow patterns in the wake of a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids: An experimental study, Chem. Eng. Sci. 61, 7199 (2006).
- J. Faramarzi and E. Logan, Reattachment length behind a single roughness element in turbulent pipe flow, J. Fluids Eng. 113, 712 (1991).
- H. Le, P. Moin, and J. Kim, Direct numerical simulation of turbulent flow over a backward-facing step, J. Fluid Mech. 330, 349 (1997).
- T. A. Johnson and V. C. Patel, Flow past a sphere up to a Reynolds number of 300, J. Fluid Mech. 378, 19 (1999).
- H. J. Kim and P. A. Durbin, Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation, Phys. Fluids 31, 3260 (1988).
- S. Lee, A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers, Comput. Fluids 29, 639 (2000).