By means of a matched asymptotic expansions approach the electrophoretic velocity and zeta potential of a catalytic particle that uniformly releases ions have been investigated. Attention is focused on large, compared to diffuse layer, particles characterized by the surface potential Φs and Damköhler number Da. The latter represents the ratio of the surface reaction rate to the diffusive transfer one. For vanishing Da, we recover the classical Smoluchowski formula for the electrophoretic velocity, which states that the zeta potential of the particle is equal to Φs and that the migration direction is determined by its sign. For small values of Da we show that the migration velocity is controlled mostly by Φs and affected by an ion release only slightly. However, even small Da can induce the electrophoresis of electro-neutral particles that would be immobile if inert. For larger Da the direction of migration and the sign of zeta potential become independent of Φs and are solely determined by the difference in diffusivity of released cations and anions. Still, the surface potential affects the magnitude of the particle velocity.

1.
J. Th. G.
Overbeek
, “
Quantitative interpretation of the electrophoretic velocity of colloids
,”
Adv. Colloid Sci.
3
,
797
823
(
1950
).
2.
M.
von Smoluchowski
,
Handbuch der Electrizität und des Magnetism
(
Barth, J. A., Leipzig
,
1921
), Vol.
2
.
3.
J. N.
Israelachvili
,
Intermolecular and Surface Forces
, 3rd ed. (
Academic Press
,
2011
).
4.
T. M.
Squires
and
S. R.
Quake
, “
Microfluidics: Fluid physics at the nanoliter scale
,”
Rev. Mod. Phys.
77
,
977
1026
(
2005
).
5.
M. C.
Ruiz-Martinez
,
J.
Berka
,
A.
Belenkii
,
F.
Foret
,
A. W.
Miller
, and
B. L.
Karger
, “
DNA sequencing by capillary electrophoresis with replaceable linear polyacrylamide and laser-induced fluorescence detection
,”
Anal. Chem.
65
(
20
),
2851
2858
(
1993
).
6.
S. T.
Chen
,
C. M.
Proctor
, and
G. G.
Malliaras
, “
Materials and device considerations in electrophoretic drug delivery devices
,”
Sci. Rep.
10
,
7185
(
2020
).
7.
E.
Hückel
, “
Die Kataphorese der Kugel
,”
Physikalische Z.
25
,
204
210
(
1924
).
8.
D. C.
Henry
, “
The cataphoresis of suspended particles. Part I. The equation of cataphoresis
,”
Proc. R. Soc. Lond. Ser. A
133
(
821
),
106
129
(
1931
).
9.
O. I.
Vinogradova
and
E. F.
Silkina
, “
Electrophoresis of ions and electrolyte conductivity: From bulk to nanochannels
,”
J. Chem. Phys.
159
,
174707
(
2023
).
10.
R. W.
O'Brien
and
L. R.
White
, “
Electrophoretic mobility of a spherical colloidal particle
,”
J. Chem. Soc. Faraday Trans. 2
74
,
1607
1626
(
1978
).
11.
A. S.
Khair
and
T. M.
Squires
, “
The influence of hydrodynamic slip on the electrophoretic mobility of a spherical colloidal particle
,”
Phys. Fluids
21
,
042001
(
2009
).
12.
H.
Ohshima
, “
Electrokinetic phenomena in a dilute suspension of spherical solid colloidal particles with a hydrodynamically slipping surface in an aqueous electrolyte solution
,”
Adv. Colloid Interface Sci.
272
,
101996
(
2019
).
13.
O. I.
Vinogradova
,
E. F.
Silkina
, and
E. S.
Asmolov
, “
Slippery and mobile hydrophobic electrokinetics: From single walls to nanochannels
,”
Curr. Opin. Colloid Interface Sci.
68
,
101742
(
2023
).
14.
B.
Dünweg
,
V.
Lobaskin
,
K.
Seethalakshmy-Hariharan
, and
C.
Holm
, “
Colloidal electrophoresis: Scaling analysis, Green – Kubo relation, and numerical results
,”
J. Phys. Condens. Matter
20
(
40
),
404214
(
2008
).
15.
G.
Giupponi
and
I.
Pagonabarraga
, “
Colloid electrophoresis for strong and weak ion diffusivity
,”
Phys. Rev. Lett.
106
,
248304
(
2011
).
16.
A. S.
Khair
, “
Nonlinear electrophoresis of colloidal particles
,”
Curr. Opin. Colloid Interface Sci.
59
,
101587
(
2022
).
17.
T. V.
Nizkaya
,
E. S.
Asmolov
, and
O. I.
Vinogradova
, “
Theoretical modeling of catalytic self-propulsion
,”
Curr. Opin. Colloid Interface Sci.
62
,
101637
(
2022
).
18.
J. L.
Moran
and
J. D.
Posner
, “
Phoretic self-propulsion
,”
Annu. Rev. Fluid Mech.
49
,
511
540
(
2017
).
19.
Y.
Peng
,
P.
Xu
,
S.
Duan
,
J.
Liu
,
J. L.
Moran
, and
W.
Wang
, “
Generic rules for distinguishing autophoretic colloidal motors
,”
Angew. Chem.
134
(
12
),
e202116041
(
2022
).
20.
J. J.
McDermott
,
A.
Kar
,
M.
Daher
,
S.
Klara
,
G.
Wang
,
A.
Sen
, and
D.
Velegol
, “
Self-generated diffusioosmotic flows from calcium carbonate micropumps
,”
Langmuir
28
(
44
),
15491
15497
(
2012
).
21.
D.
Feldmann
,
P.
Arya
,
T. Y.
Molotilin
,
N.
Lomadze
,
A.
Kopyshev
,
O. I.
Vinogradova
, and
S. A.
Santer
, “
Extremely long-range light-driven repulsion of porous microparticles
,”
Langmuir
36
(
25
),
6994
7004
(
2020
).
22.
K. K.
Dey
,
X.
Zhao
,
B. M.
Tansi
,
W. J.
Méndez-Ortiz
,
U. M.
Córdova-Figueroa
,
R.
Golestanian
, and
A.
Sen
, “
Micromotors powered by enzyme catalysis
,”
Nano Lett.
15
(
12
),
8311
8315
(
2015
).
23.
X.
Ma
,
A. C.
Hortelao
,
T.
Patino
, and
S.
Sanchez
, “
Enzyme catalysis to power micro/nanomachines
,”
ACS Nano
10
(
10
),
9111
9122
(
2016
).
24.
T.
Patiño
,
X.
Arqué
,
R.
Mestre
,
L.
Palacios
, and
S.
Sánchez
, “
Fundamental aspects of enzyme-powered micro- and nanoswimmers
,”
Acc. Chem. Res.
51
(
11
),
2662
2671
(
2018
).
25.
E. S.
Asmolov
and
O. I.
Vinogradova
, “
Diffusiophoresis of ionic catalytic particles
,”
Phys. Fluids
36
(
9
),
092026
(
2024
).
26.
D. C.
Prieve
,
J. L.
Anderson
,
J. P.
Ebel
, and
M. E.
Lowell
, “
Motion of a particle generated by chemical gradients. Part 2. Electrolytes
,”
J. Fluid Mech.
148
,
247
269
(
1984
).
27.
D.
Velegol
,
A.
Garg
,
R.
Guha
,
A.
Kar
, and
M.
Kumar
, “
Origins of concentration gradients for diffusiophoresis
,”
Soft Matter
12
(
21
),
4686
4703
(
2016
).
28.
M.
De Corato
,
X.
Arqué
,
T.
Patino
,
M.
Arroyo
,
S.
Sánchez
, and
I.
Pagonabarraga
, “
Self-propulsion of active colloids via ion release: Theory and experiments
,”
Phys. Rev. Lett.
124
(
10
),
108001
(
2020
).
29.
U. M.
Córdova-Figueroa
and
J. F.
Brady
, “
Osmotic propulsion: The osmotic motor
,”
Phys. Rev. Lett.
100
(
15
),
158303
(
2008
).
30.
S.
Michelin
and
E.
Lauga
, “
Phoretic self-propulsion at finite Péclet numbers
,”
J. Fluid Mech.
747
,
572
604
(
2014
).
31.
A.
Nourhani
,
P. E.
Lammert
,
V. H.
Crespi
, and
A.
Borhan
, “
A general flux-based analysis for spherical electrocatalytic nanomotors
,”
Phys. Fluids
27
(
1
),
012001
(
2015
).
32.
E. S.
Asmolov
,
T. V.
Nizkaya
, and
O. I.
Vinogradova
, “
Self-diffusiophoresis of Janus particles that release ions
,”
Phys. Fluids
34
,
032011
(
2022
).
33.
Y.
Ibrahim
,
R.
Golestanian
, and
T. B.
Liverpool
, “
Multiple phoretic mechanisms in the self-propulsion of a Pt-insulator Janus swimmer
,”
J. Fluid Mech.
828
,
318
352
(
2017
).
34.
M.
Teubner
, “
The motion of charged colloidal particles in electric fields
,”
J. Chem. Phys.
76
(
11
),
5564
5573
(
1982
).
35.
H.
Masoud
and
H. A.
Stone
, “
The reciprocal theorem in fluid dynamics and transport phenomena
,”
J. Fluid Mech.
879
,
P1
(
2019
).
36.
J. L.
Anderson
, “
Colloid transport by interfacial forces
,”
Annu. Rev. Fluid Mech.
21
(
1
),
61
99
(
1989
).
You do not currently have access to this content.