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Research Papers: Fundamental Issues and Canonical Flows

On Importance of the Surface Charge Transport Equation in Numerical Simulation of Drop Deformation in a Direct Current Field

[+] Author and Article Information
Mohammadali Alidoost

Department of Mechanical Engineering,
Isfahan University of Technology,
Isfahan 8415683111, Iran
e-mail: alidoost.ma@gmail.com

Ahmad Reza Pishevar

Department of Mechanical Engineering,
Isfahan University of Technology,
Isfahan 8415683111, Iran
e-mail: apishe@cc.iut.ac.ir

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 3, 2017; final manuscript received May 10, 2018; published online June 13, 2018. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 140(12), 121201 (Jun 13, 2018) (16 pages) Paper No: FE-17-1516; doi: 10.1115/1.4040301 History: Received September 03, 2017; Revised May 10, 2018

In the present study, the deformation of a droplet is numerically modeled by considering the dynamic model for electric charge migration at the drop interface under the effect of a uniform electric field. The drop and its ambient are both considered behaving as leaky dielectric fluids. Solving the charge conservation equation at the interface, which is the most important part of this study, the effect of conduction and convection of charges on different deformation modes will be explored. In this work, the interface is followed by the level set method and the ghost fluid method (GFM) is used to model the jumps at the interface. Physical properties are also chosen in a way that solving the charge conservation equation becomes prominent. The small drop deformation is investigated qualitatively by changing various effective parameters. In cases, different patterns of charges and flows are observed indicating the importance of electric charges at the interface. It is also shown that the transient behavior of deformation parameter can be either a monotonic or a nonmonotonic approach toward the steady-state. Moreover, large drop deformations are studied in different ranges of capillary numbers. It will be shown that for the selected range of physical parameters, considering the dynamic model of electric charges strongly affects the oblate deformation. Nevertheless, for the prolate deformation, the results are approximately similar to those obtained from the static model.

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Figures

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Fig. 1

Illustration of the computational domain

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Fig. 2

Gradient discretization with the aid of the jump condition across the interface [25]

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Fig. 3

Changes in the dynamic response of electric charges at the apex (pole) of the droplet for the grid refinement study

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Fig. 4

Time evolution of surface electric charge density on the interface considering the effect of surface dilation: (a) first state and (b) final state at t = 9×10−5

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Fig. 5

Time evolution of electric charges on the interface considering the effect of surface convection: (a) first state and (b) final state at t = 10−4

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Fig. 6

Induced flow pattern and deformation of droplet caused by the electrical properties for μr=1 (A-E are the studied cases)

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Fig. 7

Drop deformation and induced flow pattern for case A with CaE=0.4, R=10−4m, and α=16

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Fig. 8

Electric charge distribution at the interface for case A with CaE=0.4, R=10−4m, and α=16

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Fig. 9

Distribution of surface charge and the tangential stresses on the interface of the drop: (a) RS > 1 and (b) RS < 1 [47]

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Fig. 10

Drop deformation and induced flow pattern for case B, CaE=0.4, R=10−4m, and α=16

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Fig. 11

Electric charge distribution at the interface for case B, CaE=0.4, R=10−4m, and α=16

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Fig. 12

Drop deformation and induced flow pattern for case C, CaE=0.4, R=10−4m, and α=16

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Fig. 13

Drop deformation and induced flow pattern for case D, CaE=0.4, R=10−4m, and α=16

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Fig. 14

Electric charge distribution at the interface for case C, CaE=0.4, R=10−4m, and α=16

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Fig. 15

Electric charge distribution at the interface for case D, CaE=0.4, R=10−4m, and α=16

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Fig. 16

Drop deformation and induced flow pattern for case E, CaE=0.4, R=10−4m, and α=16

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Fig. 17

Electric charge distribution at the interface for case E, CaE=0.4, R=10−4m, and α=16

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Fig. 18

Transient behavior of deformation parameter for leaky dielectric systems: (a) prolate droplet-case C and (b) oblate droplet-case B

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Fig. 19

Changes in deformation of droplet by increasing the capillary number for σr=10, εr=0.1, μr=1, and α=16

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Fig. 20

Evolution of distribution of charges for a prolate droplet for a system with CaE=0.3,σr=10, εr=0.1, μr=1, and α=16

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Fig. 21

Changes in deformation of droplet by increasing the capillary number for σr=0.1, εr=2, μr=1, and α=16

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Fig. 22

Velocity magnitude of droplet for a system with σr=0.1, εr=2, μr=1, and CaE=0.25 using (a) static model (α=0.016) and (b) dynamic model (α=16)

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Fig. 23

Evolution of distribution of charges for an oblate droplet for a system with CaE=0.3,σr=0.1, εr=2, μr=1, and α=16

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