Numerous natural systems depend on the sedimentation of passive particles in the presence of swimming microorganisms. Here, we investigate the dynamics of the sedimentation of spherical colloids at various E. coli concentrations within the dilute regime. Results show the appearance of two sedimentation fronts: a spherical particle front and the bacteria front. We find that the bacteria front behave diffusive at short times, whereas at long times it decays linearly. The sedimentation speed of passive particles decays at a constant speed and decreases as bacteria concentration () is increased. As is increased further, the sedimentation speed becomes independent of . The timescales of the bacteria front are associated with the particle settling speeds. Remarkably, all experiments collapse onto a single master line by using the bacteria front timescale. A phenomenological model is proposed that captures the sedimentation of passive particles in active fluids.
References
1.
M.
Schallenberg
and J.
Kalff
, “The ecology of sediment bacteria in lakes and comparisons with other aquatic ecosystems
,” Ecology
74
, 919
–934
(1993
).2.
L.
Zhang
, D.
Tu
, X.
Li
, W.
Lu
, and J.
Li
, “Impact of long-term industrial contamination on the bacterial communities in urban river sediments
,” BMC Microbiol.
20
, 254
(2020
).3.
A. A.
Roberto
, J. B.
Van Gray
, and L. G.
Leff
, “Sediment bacteria in an urban stream: Spatiotemporal patterns in community composition
,” Water Res.
134
, 353
–369
(2018
).4.
K. H.
Nealson
, “Sediment bacteria: Who's there, what are they doing, and what's new?
,” Annu. Rev. Earth Planet. Sci.
25
, 403
–434
(1997
).5.
G. J.
Herndl
and T.
Reinthaler
, “Microbial control of the dark end of the biological pump
,” Nat. Geosci.
6
, 718
–724
(2013
).6.
R. F.
Vaccaro
, M. P.
Briggs
, L.
Carey
, and B. H.
Ketchum
, “Viability of Escherichia coli in Sea Water
,” Am. J. Public Health
40
, 1257
–1266
(1950
).7.
P.
Tréguer
and P.
Pondaven
, “Global change: Silica control of carbon dioxide
,” Nature
406
, 358
(2000
).8.
J.
Sarmiento
and J.
Toggweiler
, “A new model for the role of the oceans in determining atmospheric
,” Nature
308
, 621
–624
(1984
).9.
T.
Kiørboe
, A Mechanistic Approach to Plankton Ecology
(Princeton University Press
, 2008
).10.
S.
Giorgi
, B. A. H.
Reitsma
, H. J. F.
van Fulpen
, R. W. P.
Berg
, and M.
Bechger
, “Primary sedimentation as a sustainability measure for newly built municipal wastewater treatment plants: Too expensive?
,” Water Sci. Technol.
78
, 1597
–1602
(2018
).11.
J. T.
Boock
, A. J. E.
Freedman
, G. A.
Tompsett
, S. K.
Muse
, A. J.
Allen
, L. A.
Jackson
, B.
Castro-Dominguez
, M. T.
Timko
, K. L. J.
Prather
, and J. R.
Thompson
, “Engineered microbial biofuel production and recovery under supercritical carbon dioxide
,” Nat. Commun.
10
, 587
(2019
).12.
J. A.
Vázquez
, A. I.
Durán
, A.
Menduíña
, and M.
Nogueira
, “Biotechnological valorization of food marine wastes: Microbial productions on peptones obtained from aquaculture by-products
,” Biomolecules
10
, 1184
(2020
).13.
J.
Hugenholtz
and E. J.
Smid
, “Nutraceutical production with food-grade microorganisms
,” Curr. Opin. Biotechnol.
13
, 497
–507
(2002
).14.
L.
Boutilier
, R.
Jamieson
, R.
Gordon
, C.
Lake
, and W.
Hart
, “Adsorption, sedimentation, and inactivation of E. coli within wastewater treatment wetlands
,” Water Res.
43
, 4370
–4380
(2009
).15.
G.
Batchelor
, “Sedimentation in a dilute dispersion of spheres
,” J. Fluid Mech.
52
, 245
–268
(1972
).16.
J. F.
Richardson
and W. N.
Zaki
, “Sedimentation and fluidisation: Part I
,” Trans. Inst. Chem. Engrs.
32
, 35
–53
(1954
).17.
W. B.
Russel
, W.
Russel
, D. A.
Saville
, and W. R.
Schowalter
, Colloidal Dispersions
(Cambridge University Press
, 1991
).18.
E.
Guazzelli
and J. F.
Morris
, A Physical Introduction to Suspension Dynamics
(Cambridge University Press
, 2011
), Vol. 45
.19.
E.
Guazzelli
and J.
Hinch
, “Fluctuations and instability in sedimentation
,” Annu. Rev. Fluid Mech.
43
, 97
–116
(2011
).20.
R.
Piazza
, “Settled and unsettled issues in particle settling
,” Rep. Prog. Phys.
77
, 056602
(2014
).21.
T. A.
Brzinski
and D. J.
Durian
, “Observation of two branches in the hindered settling function at low Reynolds number
,” Phys. Rev. Fluids
3
, 124303
(2018
).22.
J. F.
Brady
, “The sedimentation rate of disordered suspensions
,” Phys. Fluids
31
, 717
–727
(1988
).23.
R. H.
Davis
and A.
Acrivos
, “Sedimentation of noncolloidal particles at low Reynolds numbers
,” Annu. Rev. Fluid Mech.
17
, 91
–118
(1985
).24.
R.
Bürger
and W. L.
Wendland
, “Sedimentation and suspension flows: Historical perspective and some recent developments
,” J. Eng. Math.
41
, 101
–116
(2001
).25.
R.
Piazza
, S.
Buzzaccaro
, and E.
Secchi
, “The unbearable heaviness of colloids: Facts, surprises, and puzzles in sedimentation
,” J. Phys.: Condens. Matter
24
, 284109
(2012
).26.
J.
Palacci
, C.
Cottin-Bizonne
, C.
Ybert
, and L.
Bocquet
, “Sedimentation and effective temperature of active colloidal suspensions
,” Phys. Rev. Lett.
105
, 088304
(2010
).27.
S.
Hermann
and M.
Schmidt
, “Active ideal sedimentation: Exact two-dimensional steady states
,” Soft Matter
14
, 1614
–1621
(2018
).28.
J.
Singh
, A.
Patteson
, B.
Torres Maldonado
, P. K.
Purohit
, and P. E.
Arratia
, “Bacteria hinders particle sedimentation
,” Soft Matter
17
, 4151
–4160
(2021
).29.
F.
Ginot
, I.
Theurkauff
, D.
Levis
, C.
Ybert
, L.
Bocquet
, L.
Berthier
, and C.
Cottin-Bizonne
, “Nonequilibrium equation of state in suspensions of active colloids
,” Phys. Rev. X
5
, 011004
(2015
).30.
J.
Vachier
and M. G.
Mazza
, “Dynamics of sedimenting active Brownian particles
,” Eur. Phys. J. E
42
, 11
(2019
).31.
F.
Ginot
, A.
Solon
, Y.
Kafri
, C.
Ybert
, J.
Tailleur
, and C.
Cottin-Bizonne
, “Sedimentation of self-propelled Janus colloids: Polarization and pressure
,” New J. Phys.
20
, 115001
(2018
).32.
H. M.
López
, J.
Gachelin
, C.
Douarche
, H.
Auradou
, and E.
Clément
, “Turning bacteria suspensions into superfluids
,” Phys. Rev. Lett.
115
, 028301
(2015
).33.
J.
Gachelin
, G.
Miño
, H.
Berthet
, A.
Lindner
, A.
Rousselet
, and E.
Clément
, “Non-Newtonian viscosity of Escherichia Coli suspensions
,” Phys. Rev. Lett.
110
, 268103
(2013
).34.
X.-L.
Wu
and A.
Libchaber
, “Particle diffusion in a quasi-two-dimensional bacterial bath
,” Phys. Rev. Lett.
84
, 3017
–3020
(2000
).35.
D. T. N.
Chen
, A. W. C.
Lau
, L. A.
Hough
, M. F.
Islam
, M.
Goulian
, T. C.
Lubensky
, and A. G.
Yodh
, “Fluctuations and rheology in active bacterial suspensions
,” Phys. Rev. Lett.
99
, 148302
(2007
).36.
G.
Miño
, T. E.
Mallouk
, T.
Darnige
, M.
Hoyos
, J.
Dauchet
, J.
Dunstan
, R.
Soto
, Y.
Wang
, A.
Rousselet
, and E.
Clement
, “Enhanced diffusion due to active swimmers at a solid surface
,” Phys. Rev. Lett.
106
, 048102
(2011
).37.
A.
Jepson
, V. A.
Martinez
, J.
Schwarz-Linek
, A.
Morozov
, and W. C. K.
Poon
, “Enhanced diffusion of nonswimmers in a three-dimensional bath of motile bacteria
,” Phys. Rev. E
88
, 041002
(2013
).38.
A. E.
Patteson
, A.
Gopinath
, P. K.
Purohit
, and P. E.
Arratia
, “Particle diffusion in active fluids is non-monotonic in size
,” Soft Matter
12
, 2365
–2372
(2016
).39.
M. C.
Marchetti
, J. F.
Joanny
, S.
Ramaswamy
, T. B.
Liverpool
, J.
Prost
, M.
Rao
, and R. A.
Simha
, “Hydrodynamics of soft active matter
,” Rev. Mod. Phys.
85
, 1143
–1189
(2013
).40.
41.
S.
Ramaswamy
, “The mechanics and statistics of active matter
,” Annu. Rev. Condens. Matter Phys.
1
, 323
–345
(2010
).42.
R. W.
Nash
, R.
Adhikari
, J.
Tailleur
, and M. E.
Cates
, “Run-and-tumble particles with hydrodynamics: Sedimentation, trapping, and upstream swimming
,” Phys. Rev. Lett.
104
, 258101
(2010
).43.
J.
Tailleur
and M.
Cates
, “Statistical mechanics of interacting run-and-tumble bacteria
,” Phys. Rev. Lett.
100
, 218103
(2008
).44.
Z.
Wang
, H. Y.
Chen
, Y. J.
Sheng
, and H. K.
Tsao
, “Diffusion, sedimentation equilibrium, and harmonic trapping of run-and-tumble nanoswimmers
,” Soft Matter
10
, 3209
–3217
(2014
).45.
J.
Schwarz-Linek
, C.
Valeriani
, A.
Cacciuto
, M. E.
Cates
, D.
Marenduzzo
, A. N.
Morozov
, and W. C. K.
Poon
, “Phase separation and rotor self-assembly in active particle suspensions
,” Proc. Natl. Acad. Sci. U. S. A.
109
, 4052
–4057
(2012
).46.
R.
Jeanneret
, D. O.
Pushkin
, V.
Kantsler
, and M.
Polin
, “Entrainment dominates the interaction of microalgae with micron-sized objects
,” Nat. Commun.
7
, 12518
(2016
).47.
T. V.
Kasyap
, D. L.
Koch
, and M.
Wu
, “Hydrodynamic tracer diffusion in suspensions of swimming bacteria
,” Phys. Fluids
26
, 081901
(2014
).48.
S.
Kamdar
, S.
Shin
, P.
Leishangthem
, L. F.
Francis
, X.
Xu
, and X.
Cheng
, “The colloidal nature of complex fluids enhances bacterial motility
,” Nature
603
, 819
–823
(2022
).49.
R. K.
Iler
, The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry
(Wiley
, New York
, 1979
).50.
Q.
Chen
and Y. J.
Yuan
, “A review of polystyrene bead manipulation by dielectrophoresis
,” RSC Adv.
9
, 4963
–4981
(2019
).51.
J.
Cullum
and M.
Vicente
, “Cell growth and length distribution in Escherichia coli
,” J. Bacteriology
134
, 330
–337
(1978
).52.
C.
Douarche
, A.
Buguin
, H.
Salman
, and A.
Libchaber
, “E. coli and oxygen: A motility transition
,” Phys. Rev. Lett.
102
, 198101
(2009
).53.
J.
Schwarz-Linek
, J.
Arlt
, A.
Jepson
, A.
Dawson
, T.
Vissers
, D.
Miroli
, T.
Pilizota
, V. A.
Martinez
, and W. C.
Poon
, “Escherichia coli as a model active colloid: A practical introduction
,” Colloids Surf., B
137
, 2
–16
(2016
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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