Journal of Modern Physics, 2011, 2, 1115-1119
doi:10.4236/jmp.2011.210138 Published Online October 2011 (http://www.SciRP.org/journal/jmp)
Copyright © 2011 SciRes. JMP
Electromotive Force Generation with Hydrogen Release by
Salt Water Flow under a Transverse Magnetic Field
Roberto De Luca
Dipartimento di Matematica e Informatica (DMI), Università degli Studi di Salerno, Fisciano, Italy
E-mail: rdeluca@unisa.it
Received January 7, 2011; revised May 6, 2011; accepted June 10, 2011
Abstract
By considering an electrolyte solution in motion in a duct under a transverse magnetic field, we notice that a
so called Faraday voltage arises because of the Lorentz force acting on anions and cations in the fluid. When
salt water is considered, hydrogen production takes place at one of the electrodes if an electric current, gen-
erated by Faraday voltage, flows in an external circuit. The maximum amount of hydrogen production rate is
calculated by basic electrochemical concepts.
Keywords: Renewable Energies, Hydrogen Production, Faraday Voltage
1. Introduction
Aqueous ionic solutions and conducting metals show
some similarities in their electrical transport properties.
One of the simplest phenomenological laws of classical
electrodynamics is Ohm’s law of conduction [1], namely
J E (1)
where J is the current density flowing under the effect
of the electric field E , and is the electrical conductiv-
ity of the material. A similar relation can be found in
electrolyte solutions. In the latter case, the partial con-
ductivities can be expressed in terms of the mobility
P
of cations and
N
of anions, so that:
, , P N N P
e
N
(2)
where
N
is the volume density of both types of ions
and e is the electron charge. Mobility, on its turn, is de-
fined as the proportionality constant linking the ions ve-
locity
, P N
and the electric field v E , according to the
following:
, , PN PN
v E . We recall that the total con-
ductivity is given by
N P
.
It is well known that Lorentz force acts on charged
particles moving in the presence of a magnetic field. Let
us then consider anions and cations in an electrolyte so-
lution flowing in a duct with velocity
, E PN
v v v ,
where
, P N
is the velocity of the particles measured
with respect to a reference frame moving with the aque-
ous solution. In the presence of a constant magnetic field
v
0
B , these ions are subject to a Lorentz force given by:
, PN
Ze
0
F v B (3)
where the plus and minus signs refer to cations and ani-
ons, respectively, both assumed to have ionic charge Ze
in absolute value (Z thus being their valence). Because of
Lorentz force, a voltage difference
0
f , known in the
literature as Faraday voltage [2,3], appears between the
electrodes A and B of Figure 1. This voltage, similarly
to what observed in the Hall’s effect in metals [1], can be
expressed as the product
0 A
, when the electrolyte
flows in a circular pipe of diameter D. Notice that in the
present work boldface letters and corresponding plain
text letters are used for vectors and their amplitudes, re-
spectively. Geselowitz [4] has shown that this result is
valid for any velocity profile, provided the flow is axially
symmetric. It can also be shown that this result is valid,
in particular, for a thin rectangular wire [5].
BvD
In the present work we propose an electromotive force
(e.m.f.) generator consisting of a rectangular pipe with
two lateral conducting plates enclosing salt water in mo-
tion under a magnetic field orthogonal to the flow veloc-
ity vector (see Figure 1). A similar system has already
been proposed by Yamaguchi et al. [6] for a non-poison
electro-conductive polymer and its mixture with mag-
netic fluid. We here also notice that, taking salt water
solution as the electrolyte flowing in the rectangular pipe,
hydrogen gas is formed at one of the two electrodes of
the e.m.f. generator proposed. In the present work we
calculate a general expression for the rate of production
of hydrogen gas as a function of the flux rate of salt wa-