Abstract
The flow of two-dimensional buoyant drops in a horizontal channel is studied by numerical simulations at finite Reynolds numbers. A linear shear flow is assumed inside the channel. The study is similar to that performed by Zhang and Campbell in granular flow regime (Zhang and Campbell in J Mech 237:541–568, 1992). The areal fraction is relatively large (0.72), and the flow is studied as a function of the bulk Reynolds number, a Reynolds number defined based on the acceleration due to gravity, and the capillary number. It is found that for a single drop motion the drop obtains an equilibrium position inside the channel. The equilibrium position is validated by comparing with other efforts. Results at a high areal fraction are compared to the work by Zhang and Campbell. The average velocity profile across the channel is relatively different compared to granular flow regime. The average fluctuation energy shows similar trends across the channel. The fluctuation energy is significantly lower on the average in the present study. The average normal stress (load) is also lower compared to granular flow regime. It is expected that this is due to the effect of interstitial fluid present in the present study.
Similar content being viewed by others
References
Vidyapati V., Subramaniam S.: Granular rheology and phase transition: DEM simulations and order-parameter based constitutive model. Chem. Eng. Sci. 72, 20–34 (2012)
Zhang Y., Campbell C.S.: The interface between fluid-like and solid-like behaviour in two-dimensional granular flows. J. Fluid Mech. 237, 541–568 (1992)
Liao C.-C., Hsiau S.-S., Li J.-S., Tai C.-H.: The influence of gravity on dynamic properties in sheared granular flows. Chem. Eng. Sci. 65, 2531–2540 (2010)
Campbell C.S.: Granular material flows—an overview. Powder Technol. 162, 208–229 (2006)
Halow J.S., Wills G.B.: Radial migration of spherical particles in couette systems. AIChE J. 16, 281–286 (1970)
Kowalewski T.A.: Concentration and velocity measurements in the flow of droplet suspensions through a tube. Exp. Fluids 2, 213–219 (1984)
Feng J., Hu H.H., Joseph D.D.: Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. J. Fluid Mech. 2, 271–301 (1994)
Li X., Zhou H., Pozrikidis C.: A numerical study of the shearing motion of emulsions and foams. J. Fluid Mech. 286, 379–404 (1995)
Loewenberg M., Hinch E.J.: Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech. 321, 395–419 (1996)
Zhu, M.: Direct numerical simulation of solid-liquid flow of Newtonian and viscoelastic fluids. Ph.D. thesis, University of Pennsylvania, Philadelphia (2000)
Mortazavi S., Tryggvason G.: A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop. J. Fluid Mech. 411, 325–350 (2000)
Feng Z.-G., Michaelides E.E.: Equilibrium position for a particle in a horizontal shear flow. Int. J. Multiph. Flow 29, 943–957 (2003)
Tao L., Xiyun L.: Numerical simulation of drop migration in channel flow under zero-gravity. Acta Mech. Sin. 20, 199–205 (2004)
Li X., Sarkar K.: Effects of inertia on the rheology of a dilute emulsion of drops in shear. J. Rheol. 49, 1377–1394 (2005)
Zhao X.: Drop breakup in dilute Newtonian emulsions in simple shear flow: new drop breakup mechanisms. J. Rheol. 51, 367–392 (2007)
Mortazavi S., Afshar Y., Abbaspour H.: Numerical simulation of two-dimensional drops suspended in simple shear flow at nonzero Reynolds numbers. J. Fluids Eng. 133, 031303 (2011)
Mortazavi S., Tafreshi M.M.: On the behavior of suspension of drops on an inclined surface. Phys. A Stat. Mech. Appl. 392, 58–71 (2013)
Amiri M., Mortazavi S.: Three-dimensional numerical simulation of sedimenting drops inside a vertical channel. Int. J. Multiph. Flow 56, 40–53 (2013)
Goodarzi S., Mortazavi S.: Numerical simulation of buoyant drops suspended in a shear flow: suspensions at low and moderate areal fractions. Fluid Dyn. Res. 45, 045502 (2013)
Unverdi S.O., Tryggvason G.: A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 25–37 (1992)
Unverdi S.O., Tryggvason G.: Computations of multi-fluid flows. Phys. D Nonlinear Phenom. 60, 70–83 (1992)
Adams J.C.: Mudpack: multigrid portable fortran software for the efficient solution of linear elliptic partial differential equations. Appl. Math. Comput. 34, 113–146 (1989)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Razavieh, A., Mortazavi, S. The interface between fluid-like and solid-like behavior for drops suspended in two-phase Couette flow. Acta Mech 226, 1105–1121 (2015). https://doi.org/10.1007/s00707-014-1241-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-014-1241-y