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Lattice Boltzmann simulations of a single n-butanol drop rising in water
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Image of FIG. 1.
FIG. 1.

Simulation domain with boundary conditions: = 0 is the outflow boundary; = is the inflow boundary; all the rest side boundaries are the free-slip walls. The drop is kept in the middle of the simulation domain and has a spherical shape at = 0.

Image of FIG. 2.
FIG. 2.

Simulation domain slice ( = 0). Inertial (stationary) reference frame (-); non-inertial (moving) reference frame ( - ).

Image of FIG. 3.
FIG. 3.

The evolution of 2 mm drop rise velocity in time and terminal drop shape for different cases. ——Case 1 (TRT); ------case 2 (BGK).

Image of FIG. 4.
FIG. 4.

Domain size influence. The evolution of 2.0 mm drop rise velocity in time for different simulation domain widths. The length of the domain is 14 ; –·–·– ; —— ; ------ .

Image of FIG. 5.
FIG. 5.

Mesh resolution. Terminal drop velocity as a function of drop diameter in lattice units for 1.0 and 2.0 mm drops obtained.

Image of FIG. 6.
FIG. 6.

Time evolution of terminal rise velocity of 2.0 mm drop calculated in two test cases: ——stationary reference frame; ------moving reference frame.

Image of FIG. 7.
FIG. 7.

Streamlines with -component of velocity for 2.0 mm drop in two cases: moving reference frame and stationary reference frame. The white curve represents the interface.

Image of FIG. 8.
FIG. 8.

Simulated drop terminal velocities (*) of -butanol drops in water as a function of drop diameter compared to semi-empirical correlation proposed by Henschke (solid line), experiments (○), and simulations (▷) by Bertakis , simulations ( ) by Bäumler

Image of FIG. 9.
FIG. 9.

Simulated aspect ratio (*) as a function of Eötvös number Eo in comparison with Bäumler (the results of numerical simulation due to Ref. are denoted as ; the solid curve stands for the data fitting curve described by Eq. (44) ).

Image of FIG. 10.
FIG. 10.

Drop rise velocity as a function of time for different drop diameters; (a) 1.0 mm drop in spherical regime and 1.5, 2.48 mm drops in deformed regime; (b) 2.6 and 2.8 mm drops refer to transition between deformed and oscillating droplets; (c) 3.0 mm drop; (d) 3.48 mm drop; (e) 3.8 mm drop; (f) 4.0 mm drop is the largest simulated drop in the present study.

Image of FIG. 11.
FIG. 11.

Streamlines and drop shape for = 3.48 mm (upper row) and = 3.8 mm (bottom row) drops at different moments.

Image of FIG. 12.
FIG. 12.

The -butanol drop deformation of 4.0 mm diameter at different time steps.

Image of FIG. 13.
FIG. 13.

Comparison of simulated Reynolds numbers Re as a function of Eötvös number Eo for Morton number Mo = 1.23 × 10 to the graphical correlation by Clift

Image of FIG. 14.
FIG. 14.

Simulated Reynolds number Re versus Weber number We plotted with drop shapes in steady-state.

Image of FIG. 15.
FIG. 15.

Capillary number Ca versus Eötvös number Eo; (*) present simulations; ( ) the Ca number value plotted using the terminal velocity obtained with semi-empirical correlation proposed by Henschke.


Generic image for table
Table I.

Physical parameters of the -butanol/water binary system.

Generic image for table
Table II.

Drop diameter and corresponding Eötvös number Eo considered in the present simulations.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Lattice Boltzmann simulations of a single n-butanol drop rising in water