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Research Papers: Multiphase Flows

Applying Contact Angle to a Two-Dimensional Multiphase Smoothed Particle Hydrodynamics Model

[+] Author and Article Information
Amirsaman Farrokhpanah

Centre for Advanced Coating Technologies,
Mechanical and Industrial
Engineering Department,
University of Toronto,
Toronto, Ontario M5S 3G8, Canada
e-mail: farrokh@mie.utoronto.ca

Babak Samareh

Simulent Inc.,
Toronto, Ontario M5T 1P9, Canada

Javad Mostaghimi

Fellow ASME
Professor
Centre for Advanced Coating Technologies,
Mechanical and Industrial
Engineering Department,
University of Toronto,
Toronto, Ontario M5S 3G8, Canada

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 18, 2014; final manuscript received October 16, 2014; published online January 13, 2015. Assoc. Editor: John Abraham.

J. Fluids Eng 137(4), 041303 (Apr 01, 2015) (10 pages) Paper No: FE-14-1458; doi: 10.1115/1.4028877 History: Received August 18, 2014; Revised October 16, 2014; Online January 13, 2015

Equilibrium contact angle of liquid drops over horizontal surfaces has been modeled using smoothed particle hydrodynamics (SPH). The model is capable of accurate implementation of contact angles to stationary and moving contact lines. In this scheme, the desired value for stationary or dynamic contact angle is used to correct the profile near the triple point. This is achieved by correcting the surface normals near the contact line and also interpolating the drop profile into the boundaries. Simulations show that a close match to the chosen contact angle values can be achieved for both stationary and moving contact lines. This technique has proven to reduce the amount of nonphysical shear stresses near the triple point and to enhance the convergence characteristics of the solver.

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References

Figures

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Fig. 1

Contact angle deviations from 90 deg for a half circle drop left to reach equilibrium using three surface tension coefficients of αlg= αsg= αsl= 1.0

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Fig. 2

Contact angle deviations from 90 deg for a half circle drop left to reach its equilibrium using one surface tension coefficient of αlg= 1.0 along with unit normal and ∇C correction

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Fig. 3

Variations of average shear rate along the solid boundary, starting from the center of the liquid drop (“0” on the x axis above) to the boundary wall on the right (“1” on the x axis above), using three surface tension coefficients of αlg= αsg= αsl= 1.0.

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Fig. 4

Variations of average shear rate along the solid boundary, starting from the center of the liquid drop (0 on the x axis above) to the boundary wall on the right (1 on the x axis above), using one surface tension coefficient of αlg= 1.0 along with unit normal and ∇C correction.

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Fig. 5

Maximum deviation of unit normal vectors near the interface and away from the triple point. The solid line shows the case with three surface coefficients while the dashed line is related to the case of one surface tension coefficient with correction methods.

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Fig. 6

Contact angle deviations from 60 deg when a no slip boundary condition is imposed. The dashed line shows the case with three surface tension coefficients of αlg= αsg= 1.0 and αsl= 0.5. The solid line shows results for the case with αlg= 1.0 and normal and ∇C corrections.

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Fig. 7

Variations of average shear rate at equilibrium (averaged near time = 4.4) along the solid boundary with a no slip boundary condition; starting from the center of the liquid drop (0 on the x axis above) to the boundary wall on the right (1 on the x axis above). The dashed line shows the case with three surface tension coefficients of αlg= αsg= 1.0 and αsl= 0.5. The solid line is showing results for the case with αlg= 1.0 and normal and ∇C corrections.

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Fig. 8

Spread factor of the drop (instantaneous diameter of drop divided by initial drop diameter). The line filled with unfilled triangles is showing results for the case with αlg= 1.0 and normal and ∇C corrections where free slip condition is imposed on the boundary. The line with unfilled circles is also related to the same case with the difference of having a no slip boundary condition. The dashed line demonstrates results of the three phase case with αlg= αsg= 1.0 and αsl= 0 where a free slip boundary condition is imposed. The solid line is also related to the same case with the difference of having a no slip boundary condition.

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Fig. 9

Variations of average shear rate at initial stages of drop's evolution (averaged near time = 0.25) along the solid boundary with a no slip boundary condition; starting from the center of the liquid drop (0 on the x axis above) to the boundary wall on the right (1 on the x axis above). The dashed line shows the case with three surface tension coefficients of αlg= αsg= 1.0 and αsl= 0.5. The solid line is showing results for the case with αlg= 1.0 and normal and ∇C corrections.

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Fig. 10

Droplet impact on a solid surface, comparing SPH (•) and VOF (—) methods (shown in mm)

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Fig. 11

Nondimensional diameter (D/D0) of spreading drops during simulations of impact versus nondimensional time (4μt/ρD02) for various constant contact angles

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Fig. 12

Impacted drops shown at their maximum expanded diameter for various constant contact angles imposed during impact

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Fig. 13

2D analytical solution for maximum nondimensional spread diameter for various constant contact angles [36]

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Fig. 14

Spreading factor of a glycerin droplet versus dimensionless time, comparing (•) experimental results of Ref. [15] against (—) the calculated values

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Fig. 15

Apparent dynamic contact angle of a glycerin droplet versus dimensionless time, comparing (•) experimental results of Ref. [13] against (—) the calculated values

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Fig. 16

Variations of average shear rate at equilibrium (averaged near time = 4.4) along the solid boundary with a no slip boundary condition; starting from the center of the liquid drop (0 on the x axis above) to the boundary wall on the right (1 on the x axis above). The solid line shows the case with the resolution of 0.5/105. The long dashed line is related to the resolution of 0.5/85. The dashed line shows results of the 0.5/65 case while the round dotted line shows the 0.5/45 case. In all cases, αlg= 1.0 and normal and ∇C corrections are used.

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Fig. 17

Total kinetic energy of all particles located inside the quarter of drop, using surface tension coefficient of αlg= 1.0 along with unit normal and ∇C corrections. Round dotted, dashed, long dashed, and solid lines represent cases with resolutions of 0.5/105, 0.5/85, 0.5/65, and 0.5/45, respectively.

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Fig. 18

Spread factor of the drop (instantaneous diameter of drop divided by initial drop diameter) for the case with αlg= 1.0 and normal and ∇C corrections. Round dotted, dashed, long dashed, and solid lines represent cases with resolutions of 0.5/105, 0.5/85, 0.5/65, and 0.5/45, respectively.

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Fig. 19

Contact angle deviations from 60 deg with a no slip boundary condition for various resolutions. Round dotted, dashed, long dashed, and solid lines represent cases with resolutions of 0.5/105, 0.5/85, 0.5/65, and 0.5/45, respectively.

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