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Hydrodynamic forces on randomly formed marine aggregates

Eunji Yoo, Shilpa Khatri, and François Blanchette*

  • Department of Applied Mathematics, University of California, Merced, 5200 N. Lake Road, Merced, California 95343, USA

  • *fblanchette@ucmerced.edu

Phys. Rev. Fluids 5, 044305 – Published 23 April, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.044305

Abstract

We study numerically the fluid forces acting on aggregates formed by a collation of cubic particles as a model of marine aggregates in the ocean. The flow around the aggregates and the resulting stresses on the surface of the aggregates are computed in the limit of zero Reynolds number using a boundary integral method, resulting in an accurate evaluation of the flow around fractal objects. We compare a single- and double-layer integral method to compute the velocity, and we determine that the single-layer approach is more suitable to capturing the flow around aggregates. We then characterize the drag of translation flows, the torque of rotational flows, and the straining force of extensional flows acting on aggregates as a function of their size and mode of formation. We determine that the force and torque are best characterized using the gyration radius of the aggregates, and the straining force is better characterized by the maximal radius.

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References (53)

  1. S. Honjo, T. Eglinton, C. Taylor, K. Ulmer, S. Sievert, A. Bracher, C. German, V. Edgcomb, R. Francois, M. Iglesias-Rodríguez, B. Van Mooy, and D. Rapeta, Understanding the role of the biological pump in the global carbon cycle: An imperative for ocean science, Oceanography 27, 10 (2014).
  2. T. Kiørboe, Colonization of marine snow aggregates by invertebrate zooplankton: Abundance, scaling, and possible role, Limnol. Oceanogr. 45, 479 (2000).
  3. T. Kiørboe, H.-P. Grossart, H. Ploug, and K. Tang, Mechanisms and rates of bacterial colonization of sinking aggregates, Appl. Environ. Microbiol. 68, 3996 (2002).
  4. A. Alldredge and C. Gotschalk, In situ settling behavior of marine snow, Limnol. Oceanogr. 33, 339 (1988).
  5. A. Burd and G. Jackson, Particle aggregation, Ann. Rev. Marine Sci. 1, 65 (2009).
  6. G. Jackson and A. Burd, Aggregation in the marine environment, Environ. Sci. Technol. 32, 2805 (1998).
  7. G. Jackson, Simulation of bacterial attraction and adhesion to falling particles in an aquatic environment, Limnol. Oceanogr. 34, 514 (1989).
  8. G. Jackson, A model of the formation of marine algal flocs by physical coagulation processes, Deep-Sea Res. 37, 1197 (1990).
  9. S. MacIntyre, A. Alldredge, and C. Gotschalk, Accumulation of marines now at density discontinuities in the water column, Limnol. Oceanogr. 40, 449 (1995).
  10. A. Alldredge, T. Cowles, S. MacIntyre, J. Rines, P. Donaghay, C. Greenlaw, D. Holliday, M. Dekshenieks, J. Sullivan, and J. Zaneveld, Occurrence and mechanisms of formation of a dramatic thin layer of marine snow in a shallow Pacific fjord, Marine Ecol. Prog. Ser. 233, 1 (2002).
  11. J. C. Prairie, K. Ziervogel, C. Arnosti, R. Camassa, C. Falcon, S. Khatri, R. McLaughlin, B. White, and S. Yu, Delayed settling of marine snow at sharp density transitions driven by fluid entrainment and diffusion-limited retention, Marine Ecol. Prog. Ser. 487, 185 (2013).
  12. R. Camassa, S. Khatri, R. M. McLaughlin, J. C. Prairie, B. L. White, and S. Yu, Retention and entrainment effects: Experiments and theory for porous spheres settling in sharply stratified fluids, Phys. Fluids 25, 081701 (2013).
  13. M. Panah, F. Blanchette, and S. Khatri, Simulations of a porous particle settling in a density-stratified ambient fluid, Phys. Rev. Fluids 2, 114303 (2017).
  14. H. Rosenstock and C. Marquardt, Cluster formation in two-dimensional random walks: Application to photolysis of silver halides, Phys. Rev. B 22, 5797 (1980).
  15. T. A. Witten and L. M. Sander, Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon, Phys. Rev. Lett. 47, 1400 (1981).
  16. T. A. Witten and M. E. Cates, Tenuous structures from disorderly growth processes, Science 232, 1607 (1986).
  17. M. Kolb, Anisotropic diffusion limited aggregation: From self-similarity to self-affinity, Europhys. Lett. 4, 85 (1987).
  18. P. Wiltzius, Hydrodynamic Behavior of Fractal Aggregates, Phys. Rev. Lett. 58, 710 (1987).
  19. M. Takayasu and F. Galembeck, Determination of the equivalent radii and fractal dimension of polystyrene latex aggregates from sedimentation coefficients, J. Colloid Interface Sci. 202, 84 (1998).
  20. C. Johnson, X. Li, and B. Logan, Settling velocities of fractal aggregates, Environ. Sci. Technol. 30, 1911 (1996).
  21. P. Tang, J. Greenwood, and J. A. Raper, A model to describe the settling behavior of fractal aggregates, J. Colloid Interface Sci. 247, 210 (2002).
  22. Z. Chen, J. Deutch, and P. Meakin, Translational friction coefficient of diffusion limited aggregates, J. Chem. Phys. 80, 2982 (1984).
  23. J. Brady and G. Bossis, Stokesian dynamics, Annu. Rev. Fluid Mech. 20, 111 (1988).
  24. S. Rogak and R. Flagan, Stokes drag on self-similar clusters of spheres, J. Colloid Interface Sci. 134, 206 (1990).
  25. G. Bossis, A. Meunier, and J. Brady, Hydrodynamic stress on fractal aggregates of spheres, J. Chem. Phys. 94, 5064 (1991).
  26. C. Binder, M. Hartig, and W. Peukert, Structural dependent drag force and orientation prediction for small fractal aggregates, J. Colloid Interface Sci. 331, 243 (2009).
  27. J. Zhang and Q. Zhang, Direct simulation of drag force on fractal flocs during settling, J. Coastal Res. 73, 753 (2015).
  28. A. Gastaldi and M. Vanni, The distribution of stresses in rigid fractal-like aggregates in a uniform flow field, J. Colloid Interface Sci. 357, 18 (2011).
  29. M. Vanni, Accurate modeling of flow induced stresses in rigid colloidal aggregates, Comput. Phys. Commun. 192, 70 (2015).
  30. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, England, 1992).
  31. C. Pozrikidis, Interfacial dynamics for Stokes Flow, J. Comput. Phys. 169, 250 (2001).
  32. A. Z. Zinchenko and R. H. Davis, A boundary-integral study of a drop squeezing through interparticle constrictions, J. Fluid Mech. 564, 227 (2006).
  33. Y. Bao, A. Donev, B. E. Griffith, D. M. McQueen, and C. S. Peskin, An immersed boundary method with divergence-free velocity interpolation and force spreading, J. Comput. Phys. 347, 183 (2017).
  34. Y. Bao, M. Rachh, E. E. Keaveny, L. Greengard, and A. Donev, A fluctuating boundary integral method for Brownian suspensions, J. Comput. Phys. 374, 1094 (2018).
  35. R. Cortez, The method of regularized Stokeslets, SIAM J. Sci. Comput. 23, 1204 (2001).
  36. K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind (Cambridge University Press, Cambridge, England, 1997).
  37. L. Delves and J. Mohamed, Computational Methods for Integral Equations (Cambridge University Press, Cambridge, England, 1985).
  38. C. Chan, A. Beris, and S. Advani, Second-order boundary element method calculations of hydrodynamic interactions between particles in close proximity, Int. J. Numer. Methods Fluids 14, 1063 (1992).
  39. D. Smith, A nearest-neighbour discretisation of the regularized stokeslet boundary integral equation, J. Comput. Phys. 358, 88 (2018).
  40. H. Power and G. Miranda, Second kind integral equation formulation of Stokes' flows past a particle of arbitrary shape, SIAM J. Appl. Math. 47, 689 (1987).
  41. M. Ingber and A. Mammoli, A comparison of integral formulations for the analysis of low Reynolds number flows, Eng. Anal. Bound. Elem. 23, 307 (1999).
  42. L. Gmachowski, Calculation of the fractal dimension of aggregates, Colloids Surf. A 211, 197 (2002).
  43. M. Eggersdorfer, D. Kadau, H. Herrmann, and S. Pratsinis, Multiparticle sintering dynamics: From fractal-like aggregates to compact structures, Langmuir 27, 6358 (2011).
  44. B. Logan and D. Wilkinson, Fractal geometry of marine snow and other biological aggregates, Limnol. Oceanogr. 35, 130 (1990).
  45. B. Kaye, A Random Walk Through Fractal Dimensions, 2nd ed. (Wiley-VCH, Weinheim, Germany, 1994).
  46. I. Stakgold, Boundary Value Problems of Mathematical Physics: Vol. 2, Classics in Applied Mathematics (SIAM, Philadelphia, 2000).
  47. G. K. Youngren and A. Acrivos, Stokes flow past a particle of arbitrary shape: A numerical method of solution, J. Fluid Mech. 69, 377 (1975).
  48. S. Gurel, S. G. Ward, and R. L. Whitmore, Studies of the viscosity and sedimentation of suspensions: Part 3. The sedimentation of isometric and compact particles, Br. J. Appl. Phys. 6, 83 (1955).
  49. D. Johnson, D. Leith, and P. Reist, Drag on non-spherical, orthotropic aerosol particles, J. Aerosol Sci. 18, 87 (1987).
  50. J. McNown and J. Malaika, Effects of particle shape on settling velocity at low Reynolds numbers, Eos, Trans. Am. Geophys. Union 31, 74 (1950).
  51. L. Delves, Numerical Solution of Integral Equations (Clarendon, Oxford, England, 1974).
  52. S. Karrila and S. Kim, Integral equations of the second kind for Stokes flow: Direct solution for physical variables and removal of inherent accuracy limitations, Chem. Eng. Commun. 82, 123 (1989).
  53. E. Guazzelli, J. Morris, and S. Pic, A Physical Introduction to Suspension Dynamics (Cambridge University Press, Cambridge, England, 2012).

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