An Analytical and Experimental Study on Dynamics of Newtonian Falling Drops in Inertia Regime with Low Reynolds Numbers

Document Type : Research Article

Authors

1 Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

2 8Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

Two phases flows particularly motion of droplets into a second fluid have a variety of application in different industries including oil and gas industry, medicine and pharmaceutical, extraction of metals, power plants as well as heat exchangers. In this paper, dynamic of a Newtonian drop falling into a laminar regime is studied. A fluid with viscosity of 340 cP is used in order to produce an inertia flow. In experimental section, de-ionized water and glycerin solutions with volume concentrations of 21:79 and 17:83 are used for drop phase. By increasing the volume of drop that leads to rising the inertia force, the drop shape is changed from sphere and a dimple at the rear end of the drop has appeared. Inertial forces, surface tension, and hydrodynamic tension play a significant role in drop shape. Increasing the drop volume causes expanding the dimple consequently drag force is enhanced and terminal velocity of drop is decreased as well. According to the experimental observations, variation of viscosity ratio does not have a profound effect on drop deformation. Moreover, increasing the Reynolds number leads to reduction of pressure coefficient. It is shown that the experimental observations have an appropriate agreement with analytical results.

Keywords

Main Subjects

References

[1]  J. Choi, Y.-J. Kim, S. Lee, S.U. Son, H.S. Ko, V.D. Nguyen, D. Byun, Drop-on-demand printing of conductive ink by electrostatic field induced inkjet head, Applied Physics Letters, 93(19) (2008) 193508.
[2]  C. Hanson, Recent advances in liquid-liquid extraction, Elsevier, 2013.
[3]  K.W. Binder, A.J. Allen, J.J. Yoo, A. Atala, Drop-ondemand inkjet bioprinting: a primer, Gene Therapy and Regulation, 6(01) (2011) 33-49.
[4]  S. Karimnejad, A.A. Delouei, M. Nazari, M. Shahmardan, M. Rashidi, S. Wongwises, Immersed boundary—thermal lattice Boltzmann method for the moving simulation of non-isothermal elliptical particles, Journal of Thermal Analysis and Calorimetry,   1-15.
[5]  O. Breslouer, Rayleigh-Plateau Instability: Falling Jet, Project Report, (2010) pp. 1-10.
[6]  J. Hadamard, Mouvement permanent lent d’une sphère liquid et visqueuse dans un liquide visqueux, CR Hebd. Seances Acad. Sci. Paris, 152 (1911) 1735- 1738. (in French)
[7]  W. Rybczynski, Uber die fortschreitende Bewegung einer flussigen Kugel in einem zahen Medium, Bull. Acad. Sci. Cracovie A, 1 (1911) 40-46. (in German)
[8]  T. Taylor, A. Acrivos, On the deformation and drag of a falling viscous drop at low Reynolds number, Journal of Fluid Mechanics, 18(3) (1964) 466-476.
[9]  M. Aminzadeh, Z. A. Maleki, H. Afshin, B. Firoozabadi, Experimental Investigation on Rising of a Sequence of Drops in a Viscous Fluid, 1(12) (2011) 39-46.
[10]  A. Emamian, M. Norouzi, M. Davoodi, An analytical investigation on shape of a falling viscose drop at low Reynolds number, Modares Mechanical Engineering, 7(2) (2017) 251-262. (in Persian)
[11]   M.C. Sostarecz, A. Belmonte, Motion and shape of a viscoelastic drop falling through a viscous fluid, Journal of Fluid Mechanics, 497 (2003) 235-252.
[12]    N. Aggarwal, K. Sarkar, Deformation and breakup of a viscoelastic drop in a Newtonian matrix under steady shear, Journal of Fluid Mechanics, 584 (2007) 1-21.
[13]  M. Aminzadeh, A. Maleki, B. Firoozabadi, H. Afshin, On the motion of Newtonian and non-Newtonian liquid drops, Scientia Iranica, 19(5) (2012) 12651278.
[14]  S. Mukherjee, K. Sarkar, Viscoelastic drop falling through a viscous medium, Physics of Fluids, 23(1) (2011) 013101.
[15]  I. Smagin, M. Pathak, O.M. Lavrenteva, A. Nir, Motion and shape of an axisymmetric viscoplastic drop slowly falling through a viscous fluid, Rheologica Acta, 50(4) (2011) 361-374.
[16]  B. Vamerzani, M. Norouzi, B. Firoozabadi, Analytical solution for creeping motion of a viscoelastic drop falling through a Newtonian fluid, Korea-Australia Rheology Journal, 26(1) (2014) 91-104.
[17] O.M. Lavrenteva, Y. Holenberg, A. Nir, Motion of viscous drops in tubes filled with yield stress fluid, Chemical Engineering Science, 64(22) (2009) 47724786.
[18] A. Potapov, R. Spivak, O.M. Lavrenteva, A. Nir, Motion and deformation of drops in Bingham fluid, Industrial & engineering chemistry research, 45(21) (2006) 6985-6995.
[19] J.P. Singh, M.M. Denn, Interacting two-dimensional bubbles and droplets in a yield-stress fluid, Physics of Fluids, 20(4) (2008) 040901.
[20]  A. Acharya, R. Mashelkar, J. Ulbrecht, Mechanics of bubble motion and deformation in non-Newtonian media, Chemical Engineering Science, 32(8) (1977) 863-872.
[21]   A. Acharya, R. Mashelkar, J. Ulbrecht, Mechanics of bubble motion and deformation in non-Newtonian media, Chemical Engineering Science, 32(8) (1987) 863-872.
[22]  M. Coutanceau, M. Hajjam, Viscoelastic effect on the behaviour of an air bubble rising axially in a tube, in:  Mechanics and Physics of Bubbles in Liquids, Springer, 1982, pp. 199-207.
[23]  Y. Liu, T. Liao, D. Joseph, A two-dimensional cusp at the trailing edge of an air bubble rising in a viscoelastic liquid, Journal of Fluid Mechanics, 304 (1995) 321342.
[24]  E. Zana, L. Leal, The dynamics and dissolution of gas bubbles in a viscoelastic fluid, International Journal of Multiphase Flow, 4(3) (1978) 237-262.
[25] M. Norouzi, A. Emamian, M. Davoodi, An analytical and experimental study on dynamics of a circulating Boger drop translating through Newtonian fluids at inertia regime, Journal of Non-Newtonian Fluid Mechanics, 267 (2019) 1-13.
[26] M. Norouzi, H. Abdolnezhad, S. Mandani, An experimental investigation on inertia motion and deformation of Boger drops falling through Newtonian media, Meccanica, 54(3) (2019) 473-490.
[27] M. Norouzi, M. Davoodi, O.A. Bég, A.A. Joneidi, Analysis of the effect of normal stress differences on heat transfer in creeping viscoelastic Dean flow, International Journal of Thermal Sciences, 69 (2013) 61-69.
[28]  M.G. Wagner, J.C. Slattery, Slow flow of a non‐newtonian fluid past a droplet, AIChE Journal, 17(5) (1971) 1198-1207.
[29]  L.E. Payne, W.H. Pell, The Stokes flow problem for a class of axially symmetric bodies, Journal of Fluid Mechanics, 7(4) (1960) 529-549.
[30]  M.-J. Ni, S. Komori, N.B. Morley, Direct simulation of falling droplet in a closed channel, International Journal of Heat and Mass Transfer, 49(1-2) (2006) 366-376.
[31] L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics Vol. 6 Fluid Mechanies, Pergamon Press, 1959.
[32]  F.M. White, I. Corfield, Viscous fluid flow, McGrawHill New York, 2006.
[33]  R. Wanchoo, S.K. Sharma, R. Gupta, Shape of a Newtonian liquid drop moving through an immiscible quiescent non-Newtonian liquid, Chemical Engineering and Processing: Process Intensification, 42(5) (2003) 387-393.
[34]  C.K. Batchelor, G. Batchelor, An introduction to fluid dynamics, Cambridge university press, 2000.
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 11
February 2021
Pages 3033-3044

Files

Share

How to cite

Statistics