Effects of viscosity ratio and three dimensional positioning on hydrodynamic interactions between two viscous drops in a shear flow at finite inertia

Singh, Rajesh Kumar; Sarkar, Kausik
October 2009
Physics of Fluids;Oct2009, Vol. 21 Issue 10, p103303
Academic Journal
Drops driven toward each other by shear at finite inertia follow two distinct types of trajectories. Type I trajectory is similar to the one in Stokes flow where drops slide past each other. However, at finite inertia, drops display a new type II trajectory, where they reverse their paths. Increasing viscosity ratio results in a transition from type II to type I trajectory. The transition is caused by decreased drop deformation and increased alignment with the flow at higher drop viscosity; both decrease the zone of reversed streamlines that accompanies a drop at finite inertia. The transition is delineated in a phase diagram of Reynolds number and viscosity ratio for different capillary numbers. The critical viscosity ratio, where a type II transitions into type I, increases with Reynolds number except at higher capillary numbers, where the critical viscosity ratio shows a slight nonmonotonic variation with Reynolds number. Also, it is nonmonotonic with capillary numbers in that for a fixed Reynolds number, the critical viscosity ratio first increases with increasing capillary number and then decreases. Similar to the Stokes regime, increased viscosity ratio leads to a decreased postcollision cross-stream separation effectively decreasing the shear induced diffusion. Higher viscosity ratio results in an increased separation between drops during encounter, which results in a smaller interaction time. With drops placed initially at different shear planes, drops come under the influence of the reversed flow zone around a single drop that broadens off the central shear plane. Consequently, the trajectory changes from type I to type II as the offset in the vorticity direction increases. The change depends on the initial offset in the shear direction as well. The final displacement in the shear direction varies linearly with the initial offset. The net relative displacement in the shear direction shows a gradual decrease with increasing offset. The net relative displacement in the vorticity direction with increasing offset first increases from a zero value when drops are placed at the same shear plane to a maximum and then decreases. For certain cases, it reaches a negative value.


Related Articles

  • Electroviscous effects in capillary filling of nanochannels. Mortensen, Niels Asger; Kristensen, Anders // Applied Physics Letters;2/11/2008, Vol. 92 Issue 6, p063110 

    We theoretically examine the widespread hypothesis of an electroviscous origin of the increase in apparent viscosity observed in recent experiments on capillary filling of nanochannels. Including Debye-layer corrections to the hydraulic resistance, we find that the apparent viscosity reaches a...

  • BIANCHI TYPE I UNIVERSE WITH VISCOUS FLUID. SAHA, BIJAN // Modern Physics Letters A;9/14/2005, Vol. 20 Issue 28, p2127 

    We study the evolution of a homogeneous, anisotropic Universe given by a Bianchi type-I cosmological model filled with viscous fluid, in the presence of a cosmological constant Λ. The role of viscous fluid and Λ term in the evolution the BI spacetime is studied. Though the viscosity...

  • Spectral modeling of rotating turbulent flows. Baerenzung, J.; Mininni, P. D.; Pouquet, A.; Politano, H.; Ponty, Y. // Physics of Fluids;Feb2010, Vol. 22 Issue 2, p025104 

    A subgrid-scale spectral model of rotating turbulent flows is tested against direct numerical simulations (DNSs). The case of Taylor–Green forcing is considered, a configuration that mimics the flow between two counter-rotating disks as often used in the laboratory. Computations are...

  • Mixing in a drop moving through a serpentine channel: A computational study. Muradoglu, Metin; Stone, Howard A. // Physics of Fluids;Jul2005, Vol. 17 Issue 7, p073305 

    The chaotic mixing in a drop moving through a winding channel is studied computationally in a two-dimensional setting. The molecular mixing is ignored and only the mixing due to the chaotic advection is considered. Passive tracer particles are used to visualize the mixing patterns and mixing is...

  • A model for the pressure dependence of viscosity in liquids. Kapoor, Kamal; Dass, Narsingh // Journal of Applied Physics;9/15/2005, Vol. 98 Issue 6, p066105 

    In the present paper, a model with two adjustable parameters is developed to study the viscosity of liquid as a function of pressure. The model so developed has been applied in 38 liquids. The computed results have been found to be in very good agreement with the experimental data in case of...

  • Local viscosity measurements using oscillating magnetic holes. Svåsand, Eldrid; Skjeltorp, Arne T.; Akselvoll, Jo\rgen; Helgesen, Geir // Journal of Applied Physics;3/1/2007, Vol. 101 Issue 5, p054910 

    Many complex fluids are only available in tiny quantities or used in confined regions. The task of measuring their rheological properties is then a challenge. Here we present a method showing how the viscosity of very small volumes of ferrofluid may be measured using immersed nonmagnetic...

  • Mathematical modeling of phase separation of a multiphase medium. Ibyatov, R.; Kholpanov, L.; Akhmadiev, F.; Fazylzyanov, R. // Theoretical Foundations of Chemical Engineering;Jul2006, Vol. 40 Issue 4, p339 

    The effect of phase separation and a moving deposit layer on the hydrodynamics of the flow of heterogeneous media over permeable surfaces is studied. Conservation equations of the mechanics of heterogeneous media are written in an orthogonal coordinate system with Lamé coefficients for a...

  • Interfacial phenomena in high temperature processes. Mills, K.; Hondros, E.; Li, Zushu // Journal of Materials Science;May2005, Vol. 40 Issue 9/10, p2403 

    Interfacial phenomena can have a major effect on high temperature processes; these are reviewed and examples given. Interfacial phenomena have been divided into the following categories (i) Marangoni flows, (ii) Wetting, (iii) Emulsions, (iv) Foams, and (v) Jets and surface waves. Examples and...

  • Viscous elongation of glass rods: Experiments, simulations, and analysis. Irisawa, T.; Cargill III, G. S.; Hwang, K. J.; Maniatty, A. M. // Journal of Applied Physics;Dec2010, Vol. 108 Issue 11, p113515 

    Viscous elongation of glass rods has been investigated to improve procedures for producing parabolic capillaries from straight capillaries for use as intensity concentrating x-ray optical elements. Experiments and simulations have been carried out pulling Corning 7740 borosilicate glass rods in...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics