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On the role of the history force for inertial particles in turbulence

Published online by Cambridge University Press:  09 October 2015

Anton Daitche
Anton Daitche*
Affiliation:
Institute for Theoretical Physics, Westfälische Wilhelms-Universität, 48149 Münster, Germany Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University of Oldenburg, 26129 Oldenburg, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The history force is one of the hydrodynamic forces that act on a particle moving through a fluid. It is an integral over the full time history of the particle’s motion and significantly complicates the equations of motion (accordingly it is often neglected). We present here a study of the influence of this force on particles moving in a turbulent flow, for a wide range of particle parameters. It is shown that the magnitude of the history force can be significant and that it can have a considerable effect on the particles’ slip velocity, acceleration, preferential concentration and collision rate. We also investigate the parameter dependence of the strength of these effects.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 782 , 10 November 2015 , pp. 567 - 593
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Copyright
© 2015 Cambridge University Press 

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References

van Aartrijk, M. & Clercx, H. J. H. 2009 Dispersion of heavy particles in stably stratified turbulence. Phys. Fluids 21 (3), 033304.CrossRefGoogle Scholar
van Aartrijk, M. & Clercx, H. J. H. 2010 Vertical dispersion of light inertial particles in stably stratified turbulence: the influence of the Basset force. Phys. Fluids 22 (1), 013301.Google Scholar
Abbad, M. & Souhar, M. 2004 Experimental investigation on the history force acting on oscillating fluid spheres at low Reynolds number. Phys. Fluids 16 (10), 3808–3817.Google Scholar
Armenio, V. & Fiorotto, V. 2001 The importance of forces acting on particles in turbulent flows. Phys. Fluids 13, 2437–2440.Google Scholar
Auton, T. R., Hunt, J. C. R. & Prud’Homme, M. 1988 The force exerted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241–257.Google Scholar
Babiano, A., Cartwright, J. H. E., Piro, O. & Provenzale, A. 2000 Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems. Phys. Rev. Lett. 84, 5764–5767.Google Scholar
Basset, A. B. 1888 A Treatise on Hydrodynamics: with Numerous Examples. Deighton, Bell and Co.Google Scholar
Bec, J., Celani, a., Cencini, M. & Musacchio, S. 2005 Clustering and collisions of heavy particles in random smooth flows. Phys. Fluids 17 (7), 073301.Google Scholar
Bergougnoux, L., Bouchet, G., Lopez, D. & Guazzelli, É. 2014 The motion of solid spherical particles falling in a cellular flow field at low Stokes number. Phys. Fluids 26 (9), 093302.Google Scholar
Boussinesq, V. J. 1885 Sur la résistance qu’oppose un liquide indéfini en repos. C. R. Acad. Sci. Paris 100, 935–937.Google Scholar
Calzavarini, E., Kerscher, M., Lohse, D. & Toschi, F. 2008 Dimensionality and morphology of particle and bubble clusters in turbulent flow. J. Fluid Mech. 607, 13–24.CrossRefGoogle Scholar
Calzavarini, E., Volk, R., Lévêque, E., Pinton, J. F. & Toschi, F. 2012 Impact of trailing wake drag on the statistical properties and dynamics of finite-sized particle in turbulence. Physica D 241 (3), 237–244.CrossRefGoogle Scholar
Candelier, F. 2008 Time-dependent force acting on a particle moving arbitrarily in a rotating flow, at small Reynolds and Taylor numbers. J. Fluid Mech. 608, 319–336.Google Scholar
Candelier, F., Angilella, J. R. & Souhar, M. 2004 On the effect of the Boussinesq–Basset force on the radial migration of a Stokes particle in a vortex. Phys. Fluids 16 (5), 1765–1776.CrossRefGoogle Scholar
Candelier, F., Mehaddi, R. & Vauquelin, O. 2014 The history force on a small particle in a linearly stratified fluid. J. Fluid Mech. 749, 184–200.CrossRefGoogle Scholar
Canuto, C., Hussaini, M., Quarteroni, A. & Zang, T. 1987 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Coimbra, C. F. M. & Kobayashi, M. H. 2002 On the viscous motion of a small particle in a rotating cylinder. J. Fluid Mech. 469, 257–286.CrossRefGoogle Scholar
Coimbra, C. F. M., L’Esperance, D., Lambert, R. A., Trolinger, J. D. & Rangel, R. H. 2004 An experimental study on stationary history effects in high-frequency Stokes flows. J. Fluid Mech. 504, 353–363.Google Scholar
Coimbra, C. F. M. & Rangel, R. H. 1998 General solution of the particle momentum equation in unsteady Stokes flows. J. Fluid Mech. 370, 53–72.CrossRefGoogle Scholar
Daitche, A. 2013 Advection of inertial particles in the presence of the history force: higher order numerical schemes. J. Comput. Phys. 254 (0), 93–106.CrossRefGoogle Scholar
Daitche, A. & Tél, T. 2011 Memory effects are relevant for chaotic advection of inertial particles. Phys. Rev. Lett. 107, 244501.CrossRefGoogle ScholarPubMed
Daitche, A. & Tél, T. 2014 Memory effects in chaotic advection of inertial particles. New J. Phys. 16 (7), 073008.CrossRefGoogle Scholar
Druzhinin, O. A. & Ostrovsky, L. A. 1994 The influence of Basset force on particle dynamics in two-dimensional flows. Physica D 76, 34–43.CrossRefGoogle Scholar
Farazmand, M. & Haller, G. 2015 The Maxey–Riley equation: existence, uniqueness and regularity of solutions. Nonlinear Anal. 22 (0), 98–106.CrossRefGoogle Scholar
Garbin, V., Dollet, B., Overvelde, M., Cojoc, D., Di Fabrizio, E., van Wijngaarden, L., Prosperetti, A., de Jong, N., Lohse, D. & Versluis, M. 2009 History force on coated microbubbles propelled by ultrasound. Phys. Fluids 21 (9), 092003.Google Scholar
Gatignol, R. 1983 The Faxén formulae for a rigid particle in an unsteady non-uniform Stokes flow. J. Mèc. Thèor. Appl. 1 (2), 143–160.Google Scholar
Grassberger, P. & Procaccia, I. 1983 Characterization of strange attractors. Phys. Rev. Lett. 50 (5), 346–349.Google Scholar
Guseva, K., Feudel, U. & Tél, T. 2013 Influence of the history force on inertial particle advection: gravitational effects and horizontal diffusion. Phys. Rev. E 88, 042909.Google Scholar
Hill, R. J. 2005 Geometric collision rates and trajectories of cloud droplets falling into a Burgers vortex. Phys. Fluids 17 (3), 037103.CrossRefGoogle Scholar
van Hinsberg, M. A. T., ten Thije Boonkkamp, J. H. M. & Clercx, H. J. H. 2011 An efficient, second order method for the approximation of the Basset history force. J. Comput. Phys. 230 (4), 1465–1478.Google Scholar
Hou, T. Y. & Li, R. 2007 Computing nearly singular solutions using pseudo-spectral methods. J. Comput. Phys. 226, 379–397.CrossRefGoogle Scholar
Langlois, G. P., Farazmand, M. & Haller, G. 2015 Asymptotic dynamics of inertial particles with memory. J. Nonlinear Sci.; doi:10.1007/s00332-015-9250-0.Google Scholar
L’Espérance, D., Coimbra, C. F. M., Trolinger, J. D. & Rangel, R. H. 2005 Experimental verification of fractional history effects on the viscous dynamics of small spherical particles. Exp. Fluids 38 (1), 112–116.CrossRefGoogle Scholar
Lim, E. A., Kobayashi, M. H. & Coimbra, C. F. M. 2014 Fractional dynamics of tethered particles in oscillatory Stokes flows. J. Fluid Mech. 746, 606–625.Google Scholar
Lovalenti, P. M. & Brady, J. F. 1993 The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256, 561–605.Google Scholar
Maxey, M. R. 1993 The equation of motion for a small rigid sphere in a nonuniform or unsteady flow. Trans. ASME J. Fluids Engng 166, 57–62.Google Scholar
Maxey, M. R., Chang, E. J. & Wang, L. P. 1996 Interactions of particles and microbubbles with turbulence. Exp. Therm. Fluid Sci. 12 (4), 417–425.Google Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
Mazzitelli, I. M., Lohse, D. & Toschi, F. 2003 On the relevance of the lift force in bubbly turbulence. J. Fluid Mech. 488, 283–313.Google Scholar
Mei, R. 1994 Flow due to an oscillating sphere and an expression for unsteady drag on the sphere at finite Reynolds number. J. Fluid Mech. 270, 133–174.CrossRefGoogle Scholar
Mei, R., Adrian, R. J. & Hanratty, T. J. 1991 Particle dispersion in isotropic turbulence under Stokes drag and Basset force with gravitational settling. J. Fluid Mech. 225, 481–495.Google Scholar
Michaelides, E. E. 1992 A novel way of computing the Basset term in unsteady multiphase flow computations. Phys. Fluids A 4, 1579–1582.Google Scholar
Mordant, N. & Pinton, J. F. 2000 Velocity measurement of a settling sphere. Eur. Phys. J. B 18 (2), 343–352.Google Scholar
Olivieri, S., Picano, F., Sardina, G., Iudicone, D. & Brandt, L. 2014 The effect of the Basset history force on particle clustering in homogeneous and isotropic turbulence. Phys. Fluids 26 (4), 041704.Google Scholar
Podlubny, I. 1998 Fractional Differential Equations, Mathematics in Science and Engineering, vol. 198. Academic.Google Scholar
Reeks, M. W. & McKee, S. 1984 The dispersive effects of Basset history forces on particle motion in a turbulent flow. Phys. Fluids 27 (7), 1573–1582.Google Scholar
Saffman, P. G. & Turner, J. S. 1956 On the collision of drops in turbulent clouds. J. Fluid Mech. 1 (01), 16–30.CrossRefGoogle Scholar
Sapsis, T. & Haller, G. 2008 Instabilities in the dynamics of neutrally buoyant particles. Phys. Fluids 20 (1), 017102.Google Scholar
Shu, C. W. & Osher, S. 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (2), 439–471.Google Scholar
Tatom, F. B. 1988 The Basset term as a semiderivative. Appl. Sci. Res. 45 (3), 283–285.Google Scholar
Toegel, R., Luther, S. & Lohse, D. 2006 Viscosity destabilizes sonoluminescing bubbles. Phys. Rev. Lett. 96, 114301.Google Scholar
Voßkuhle, M., Pumir, A., Lévêque, E. & Wilkinson, M. 2014 Prevalence of the sling effect for enhancing collision rates in turbulent suspensions. J. Fluid Mech. 749, 841–852.CrossRefGoogle Scholar
Wang, Q., Squires, K. D., Chen, M. & McLaughlin, J. B. 1997 On the role of the lift force in turbulence simulations of particle deposition. Int. J. Multiphase Flow 23 (4), 749–763.Google Scholar
Weinstein, J. A., Kassoy, D. R. & Bell, M. J. 2008 Experimental study of oscillatory motion of particles and bubbles with applications to Coriolis flow meters. Phys. Fluids 20 (10), 103306.CrossRefGoogle Scholar
Yannacopoulos, A. N., Rowlands, G. & King, G. P. 1997 Influence of particle inertia and Basset force on tracer dynamics: analytic results in the small-inertia limit. Phys. Rev. E 55 (4), 4148–4157.CrossRefGoogle Scholar