Interaction between two drops ascending in a linearly stratified fluid. (English) Zbl 1408.76237
Summary: Three-dimensional numerical simulations of the interaction between two drops rising in a thermally stable stratified fluid are presented. The governing equations are solved using a finite-volume/front-tracking method. The influence of stratification on the dynamics of two drops moving in line and side by side is studied. For the case of nearly spherical drops ascending side by side, drops remain in the horizontal alignment during the interaction; but the rate of separation, after their initial collision, decreases for stronger stratifications. We demonstrate that, in contrast to the case of a homogeneous fluid, two drops moving in tandem in a strongly stratified fluid retain their in-line configuration.
MSC:
| 76D50 | Stratification effects in viscous fluids |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
References:
| [1] | Srdic-Mitrovic, A. N.; Mohamed, N. A.; Fernando, H. J.S., Gravitational settling of particles through density interfaces, J. Fluid Mech., 381, 175-198, (1999) · Zbl 0939.76503 |
| [2] | Torres, C. R.; Ochoa, J.; Castillo, Jose E.; Hanazaki, H., Numerical simulation of flow past a sphere in vertical motion within a stratified fluid, J. Comput. Appl. Math., 103, 67-76, (1999) · Zbl 0977.76510 |
| [3] | Torres, C. R.; Hanazaki, H.; Ochoa, J.; Castillo, J.; Van Woert, M., Flow past a sphere moving vertically in a stratified diffusive fluid, J. Fluid Mech., 417, 211-236, (2000) · Zbl 0971.76023 |
| [4] | Higginson, R. C.; Dalziel, S. B.; Linden, P. F., The drag on a vertically moving grid of bars in a linearly stratified fluid, Exp. Fluids, 34, 678-686, (2003) |
| [5] | Yick, K. Y.; Torres, C. R.; Peacock, T.; Stocker, R., Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers, J. Fluid Mech., 632, 49-68, (2009) · Zbl 1183.76058 |
| [6] | Doostmohammadi, A.; Stocker, R.; Ardekani, A. M., Low-Reynolds-number swimming at pycnoclines, Proc. Natl. Acad. Sci., 109, 3856-3861, (2012) |
| [7] | Young, N. O.; Goldstein, J. S.; Block, M. J., The motion of bubbles in a vertical temperature gradient, J. Fluid Mech., 6, 350-356, (1959) · Zbl 0087.19902 |
| [8] | Zhang, L.; Subramanian, R. S.; Balasubramaniam, R., Motion of a drop in a vertical temperature gradient at small Marangoni number-the critical role of inertia, J. Fluid Mech., 448, 197-211, (2001) · Zbl 0997.76083 |
| [9] | Blanchette, F.; Shapiro, A. M., Drops settling in sharp stratification with and without Marangoni effects, Phys. Fluids, 24, (2012) |
| [10] | Bayareh, M.; Doostmohammadi, A.; Dabiri, S.; Ardekani, A. M., On the rising motion of a drop in stratified fluids, Phys. Fluids, 25, 103302, (2013) |
| [11] | Dabiri, S.; Doostmohammadi, A.; Bayareh, M.; Ardekani, A. M., Rising motion of a swarm of drops in a linearly stratified fluid, Int. J. Multiph. Flow, 69, 8-17, (2015) |
| [12] | Harper, J. F., On bubble rising in line at large Reynolds numbers, J. Fluid Mech., 41, 751-758, (1970) · Zbl 0211.29504 |
| [13] | Bunner, B.; Tryggvason, G., Effect of bubble deformation on the properties of bubbly flows, J. Fluid Mech., 495, 77-118, (2003) · Zbl 1085.76067 |
| [14] | Velez-Cordero, J. R.; Sámano, D.; Yue, P.; Feng, J. J.; Zenit, R., Hydrodynamic interaction between a pair of bubbles ascending in shear-thinning inelastic fluids, J. Non-Newton. Fluid Mech., 166, 118-132, (2011) · Zbl 1281.76045 |
| [15] | Liang, S. C.; Hong, T.; Fan, L. S., Effects of particle arrangements on the drag force of a particle in the intermediate flow regime, Int. J. Multiph. Flow, 22, 285-306, (1996) · Zbl 1135.76475 |
| [16] | Legendre, D.; Magnudet, J.; Mougin, G., Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid, J. Fluid Mech., 497, 133-166, (2003) · Zbl 1060.76026 |
| [17] | Hallez, Y.; Legendre, D., Interaction between two spherical bubbles rising in a viscous liquid, J. Fluid Mech., 673, 406-431, (2011) · Zbl 1225.76280 |
| [18] | Katz, J.; Meneveau, C., Wake-induced relative motion of bubbles rising in line, Int. J. Multiph. Flow, 22, 239-258, (1996) · Zbl 1135.76453 |
| [19] | Zhang, J.; Fan, L. S., On the rise velocity of an interactive bubble in liquids, Chem. Eng. J., 92, 169-176, (2003) |
| [20] | Yuan, H.; Prosperetti, A., On the in-line motion of two spherical bubbles in a viscous fluid, J. Fluid Mech., 278, 325-349, (1994) · Zbl 0819.76022 |
| [21] | Martin, W. W.; Chandler, G. M., The local measurements of size and velocity of bubbles rising in liquids, Appl. Sci. Res., 38, 239-246, (1982), http://link.springer.com/chapter/10.1007 |
| [22] | Ruzicka, M. C., On bubbles rising in line, Int. J. Multiph. Flow, 26, 1141-1181, (2000) · Zbl 1137.76730 |
| [23] | Ruzicka, M. C., Vertical stability of bubble chain: multiscale approach, Int. J. Multiph. Flow, 31, 1063-1096, (2005) · Zbl 1135.76535 |
| [24] | Tryggvason, G.; Bunner, B.; Esmaeeli, A.; Juric, D.; Al-Rawahi, N.; Tauber, W.; Han, J.; Nas, S.; Jan, Y.-J., A front tracking method for the computations of multiphase flow, J. Comput. Phys., 169, 708-759, (2001) · Zbl 1047.76574 |
| [25] | Dabiri, S.; Lu, J.; Tryggvason, G., Transition between regimes of a vertical channel bubbly up flow due to bubble deformability, Phys. Fluids, 25, 10, (2013), article no. 102110 |
| [26] | Gottlieb, S.; Shu, C., Total variation diminishing Runge-Kutta schemes, Math. Comput., 67, 221, 73-85, (1998) · Zbl 0897.65058 |
| [27] | Leonard, B. P., A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput. Methods Appl, M. 19, 59-98, (1979) · Zbl 0423.76070 |
| [28] | Schlichting, H., Boundary-layer theory, (1968), McGraw-Hill |
| [29] | Doostmohammadi, A.; Dabiri, S.; Ardekani, A. M., A numerical study of dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid, J. Fluid Mech., 750, 5-32, (2014) |
| [30] | Sanada, T.; Sato, A.; Shirota, M.; Watanabe, M., Motion and coalescence of a pair of bubbles rising side-by-side, Chem. Eng. Sci, 64, 2659-2671, (2009) |
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