Through laboratory experiments of oil-in-water emulsification, we show that we can construct a high-shear-rate mixer (precession mixer) by using the precession of a cylindrical container without any mixing blades. For high-shear-rate mixing, a container with a larger diameter and its faster spin are preferable so that the wall velocity becomes large enough. Then, emulsification is most efficient when we set the Poincaré number Po=Ωp/Ωs, which is the ratio of the spin and precession rotation speeds, about 0.2–0.3. When Po is smaller than these values, shear rates in the mixer get much lower, though mixing in the bulk of the container is enhanced. On the other hand, when Po is larger, shear rates near the cylindrical wall get higher but mixing in the bulk drastically declines. Through our systematic parameter survey for efficient emulsification by the precession mixer, we have also discovered an experimental law describing the maximum shear rate in the mixer. Since we can use it to appropriately choose the driving conditions of the mixer according to the properties of the materials to be mixed, this experimental law gives useful information for the practical use of the mixer.

1.
H. P.
Greenspan
,
The Theory of Rotating Fluids
(
Cambridge University Press
,
1968
).
2.
P.
Meunier
, “
Geoinspired soft mixers
,”
J. Fluid Mech.
903
,
A15
(
2020
).
3.
D.
Watanabe
and
S.
Goto
, “
Simple bladeless mixer with liquid–gas interface
,”
Flow
2
,
E28
(
2022
).
4.
S.
Goto
,
M.
Shimizu
, and
G.
Kawahara
, “
Turbulent mixing in a precessing sphere
,”
Phys. Fluids
26
,
115106
(
2014
).
5.
S.
Goto
,
N.
Ishii
,
S.
Kida
, and
M.
Nishioka
, “
Turbulence generator using a precessing sphere
,”
Phys. Fluids
19
,
061705
(
2007
).
6.
S.
Goto
,
A.
Matsunaga
,
M.
Fujiwara
,
M.
Nishioka
,
S.
Kida
,
M.
Yamato
, and
S.
Tsuda
, “
Turbulence driven by precession in spherical and slightly elongated spheroidal cavities
,”
Phys. Fluids
26
,
055107
(
2014
).
7.
F. H.
Busse
, “
Steady fluid flow in a precessing spheroidal shell
,”
J. Fluid Mech.
33
,
739
751
(
1968
).
8.
R. R.
Kerswell
, “
On the inertial shear layer spawned by critical regions in oscillatory Ekman boundary layers
,”
J. Fluid Mech.
298
,
311
325
(
1995
).
9.
J.
Noir
,
D.
Jault
, and
P.
Cardin
, “
Numerical study of the motions within a slowly precessing sphere at low Ekman number
,”
J. Fluid Mech.
437
,
282
299
(
2001
).
10.
S.
Kida
, “
Steady flow in a rapidly rotating sphere with weak precession
,”
J. Fluid Mech.
680
,
150
193
(
2011
).
11.
S.
Kida
, “
Steady flow in a rapidly rotating spheroid with weak precession—Part 1
,”
Fluid Dyn. Res.
52
,
015513
(
2020
).
12.
S.
Kida
, “
Steady flow in a rapidly rotating spheroid with weak precession—Part 2
,”
Fluid Dyn. Res.
53
,
025501
(
2021
).
13.
R.
Manasseh
, “
Breakdown regimes of inertia waves in a precessing cylinder
,”
J. Fluid Mech.
243
,
261
296
(
1992
).
14.
A.
Tilgner
and
F. H.
Busse
, “
Fluid flows in precessing spherical shells
,”
J. Fluid Mech.
426
,
387
396
(
2001
).
15.
R.
Hollerbach
,
C.
Nore
,
P.
Marti
,
S.
Vantieghem
,
F.
Luddens
, and
J.
Léorat
, “
Parity-breaking flows in precessing spherical containers
,”
Phys. Rev. E
87
,
053020
(
2013
).
16.
Y.
Lin
,
P.
Marti
, and
J.
Noir
, “
Shear-driven parametric instability in a precessing sphere
,”
Phys. Fluids
27
,
046601
(
2015
).
17.
J.
Vormann
and
U.
Hansen
, “
Numerical simulations of bistable flows in precessing spheroidal shells
,”
Geophys. J. Int.
213
,
786
797
(
2018
).
18.
C.
Nobili
,
P.
Meunier
,
B.
Favier
, and
M.
Le Bars
, “
Hysteresis and instabilities in a spheroid in precession near the resonance with the tilt-over mode
,”
J. Fluid Mech.
909
,
A17
(
2021
).
19.
F.
Pizzi
,
A.
Giesecke
,
J.
Šimkanin
, and
F.
Stefani
, “
Prograde and retrograde precession of a fluid-filled cylinder
,”
New J. Phys.
23
,
123016
(
2021
).
20.
W. V. R.
Malkus
, “
Precession of the earth as the cause of geomagnetism
,”
Science
160
,
259
264
(
1968
).
21.
J.
Vanyo
,
P.
Wilde
,
P.
Cardin
, and
P.
Olson
, “
Experiments on precessing flows in the Earth's liquid core
,”
Geophys. J. Int.
121
,
136
142
(
1995
).
22.
P.
Meunier
,
C.
Eloy
,
R.
Lagrange
, and
F.
Nadal
, “
A rotating fluid cylinder subject to weak precession
,”
J. Fluid Mech.
599
,
405
440
(
2008
).
23.
M.
Le Bars
,
D.
Cébron
, and
P.
Le Gal
, “
Flows driven by libration, precession, and tides
,”
Ann. Rev. Fluid Mech.
47
,
163
193
(
2015
).
24.
D.
Cébron
,
R.
Laguerre
,
J.
Noir
, and
N.
Schaeffer
, “
Precessing spherical shells: Flows, dissipation, dynamo and the lunar core
,”
Geophys. J. Int.
219
,
S34
S57
(
2019
).
25.
K.
Komoda
and
S.
Goto
, “
Three-dimensional flow structures of turbulence in precessing spheroids
,”
Phys. Rev. Fluids
4
,
014603
(
2019
).
26.
K.
Matsuyama
,
K.
Mine
,
H.
Kubo
,
N.
Aoki
, and
K.
Mae
, “
Optimization methodology of operation of orifice-shaped micromixer based on micro-jet concept
,”
Chem. Eng. Sci.
65
,
5912
5920
(
2010
).
27.
S.
Kida
, “
Steady flow in a rotating sphere with strong precession
,”
Fluid Dyn. Res.
50
,
021401
(
2018
).
28.
F.
Pizzi
,
A.
Giesecke
, and
F.
Stefani
, “
Ekman boundary layers in a fluid filled precessing cylinder
,”
AIP Adv.
11
,
035023
(
2021
).
29.
S.
Middleman
, “
Drop size distributions produced by turbulent pipe flow of immiscible fluids through a static mixer
,”
Ind. Eng. Chem. Process Des. Dev.
13
,
78
83
(
1974
).
You do not currently have access to this content.