32 research outputs found
Effective zero-thickness model for a conductive membrane driven by an electric field
The behavior of a conductive membrane in a static (DC) electric field is
investigated theoretically. An effective zero-thickness model is constructed
based on a Robin-type boundary condition for the electric potential at the
membrane, originally developed for electrochemical systems. Within such a
framework, corrections to the elastic moduli of the membrane are obtained,
which arise from charge accumulation in the Debye layers due to capacitive
effects and electric currents through the membrane and can lead to an
undulation instability of the membrane. The fluid flow surrounding the membrane
is also calculated, which clarifies issues regarding these flows sharing many
similarities with flows produced by induced charge electro-osmosis (ICEO).
Non-equilibrium steady states of the membrane and of the fluid can be
effectively described by this method. It is both simpler, due to the zero
thickness approximation which is widely used in the literature on fluid
membranes, and more general than previous approaches. The predictions of this
model are compared to recent experiments on supported membranes in an electric
field.Comment: 14 pages, 5 figure
Frequency response in surface-potential driven electro-hydrodynamics
Using a Fourier approach we offer a general solution to calculations of slip
velocity within the circuit description of the electro-hydrodynamics in a
binary electrolyte confined by a plane surface with a modulated surface
potential. We consider the case with a spatially constant intrinsic surface
capacitance where the net flow rate is in general zero while harmonic rolls as
well as time-averaged vortex-like components may exist depending on the spatial
symmetry and extension of the surface potential. In general the system displays
a resonance behavior at a frequency corresponding to the inverse RC time of the
system. Different surface potentials share the common feature that the
resonance frequency is inversely proportional to the characteristic length
scale of the surface potential. For the asymptotic frequency dependence above
resonance we find a 1/omega^2 power law for surface potentials with either an
even or an odd symmetry. Below resonance we also find a power law omega^alpha
with alpha being positive and dependent of the properties of the surface
potential. Comparing a tanh potential and a sech potential we qualitatively
find the same slip velocity, but for the below-resonance frequency response the
two potentials display different power law asymptotics with alpha=1 and
alpha~2, respectively.Comment: 4 pages including 1 figure. Accepted for PR
AC electrokinetic phenomena over semiconductive surfaces: effective electric boundary conditions and their applications
Electrokinetic boundary conditions are derived for AC electrokinetic (ACEK)
phenomena over leaky dielectric (i.e., semiconducting) surfaces. Such boundary
conditions correlate the electric potentials across the
semiconductor-electrolyte interface (consisting of the electric double layer
(EDL) inside the electrolyte solutions and the space charge layer (SCL) inside
the semiconductors) under AC electric fields with arbitrary wave forms. The
present electrokinetic boundary conditions allow for evaluation of induced zeta
potential contributed by both bond charges (due to electric polarization) and
free charges (due to electric conduction) from the leaky dielectric materials.
Subsequently, we demonstrate the applications of these boundary conditions in
analyzing the ACEK phenomena around a semiconducting cylinder. It is concluded
that the flow circulations exist around the semiconducting cylinder and are
shown to be stronger under an AC field with lower frequency and around a
cylinder with higher conductivity.Comment: 29 pages, 4 figure
Strongly nonlinear dynamics of electrolytes in large ac voltages
We study the response of a model micro-electrochemical cell to a large ac
voltage of frequency comparable to the inverse cell relaxation time. To bring
out the basic physics, we consider the simplest possible model of a symmetric
binary electrolyte confined between parallel-plate blocking electrodes,
ignoring any transverse instability or fluid flow. We analyze the resulting
one-dimensional problem by matched asymptotic expansions in the limit of thin
double layers and extend previous work into the strongly nonlinear regime,
which is characterized by two novel features - significant salt depletion in
the electrolyte near the electrodes and, at very large voltage, the breakdown
of the quasi-equilibrium structure of the double layers. The former leads to
the prediction of "ac capacitive desalination", since there is a time-averaged
transfer of salt from the bulk to the double layers, via oscillating diffusion
layers. The latter is associated with transient diffusion limitation, which
drives the formation and collapse of space-charge layers, even in the absence
of any net Faradaic current through the cell. We also predict that steric
effects of finite ion sizes (going beyond dilute solution theory) act to
suppress the strongly nonlinear regime in the limit of concentrated
electrolytes, ionic liquids and molten salts. Beyond the model problem, our
reduced equations for thin double layers, based on uniformly valid matched
asymptotic expansions, provide a useful mathematical framework to describe
additional nonlinear responses to large ac voltages, such as Faradaic
reactions, electro-osmotic instabilities, and induced-charge electrokinetic
phenomena.Comment: 30 pages, 17 eps-figures, RevTe
Nonlinear electrochemical relaxation around conductors
We analyze the simplest problem of electrochemical relaxation in more than
one dimension - the response of an uncharged, ideally polarizable metallic
sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric
field. In order to go beyond the circuit approximation for thin double layers,
our analysis is based on the Poisson-Nernst-Planck (PNP) equations of dilute
solution theory. Unlike most previous studies, however, we focus on the
nonlinear regime, where the applied voltage across the conductor is larger than
the thermal voltage. In such strong electric fields, the classical model
predicts that the double layer adsorbs enough ions to produce bulk
concentration gradients and surface conduction. Our analysis begins with a
general derivation of surface conservation laws in the thin double-layer limit,
which provide effective boundary conditions on the quasi-neutral bulk. We solve
the resulting nonlinear partial differential equations numerically for strong
fields and also perform a time-dependent asymptotic analysis for weaker fields,
where bulk diffusion and surface conduction arise as first-order corrections.
We also derive various dimensionless parameters comparing surface to bulk
transport processes, which generalize the Bikerman-Dukhin number. Our results
have basic relevance for double-layer charging dynamics and nonlinear
electrokinetics in the ubiquitous PNP approximation.Comment: 25 pages, 17 figures, 4 table
Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane
We discuss the electrostatic contribution to the elastic moduli of a cell or
artificial membrane placed in an electrolyte and driven by a DC electric field.
The field drives ion currents across the membrane, through specific channels,
pumps or natural pores. In steady state, charges accumulate in the Debye layers
close to the membrane, modifying the membrane elastic moduli. We first study a
model of a membrane of zero thickness, later generalizing this treatment to
allow for a finite thickness and finite dielectric constant. Our results
clarify and extend the results presented in [D. Lacoste, M. Cosentino
Lagomarsino, and J. F. Joanny, Europhys. Lett., {\bf 77}, 18006 (2007)], by
providing a physical explanation for a destabilizing term proportional to
\kps^3 in the fluctuation spectrum, which we relate to a nonlinear ()
electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent
studies of ICEO have focused on electrodes and polarizable particles, where an
applied bulk field is perturbed by capacitive charging of the double layer and
drives flow along the field axis toward surface protrusions; in contrast, we
predict "reverse" ICEO flows around driven membranes, due to curvature-induced
tangential fields within a non-equilibrium double layer, which hydrodynamically
enhance protrusions. We also consider the effect of incorporating the dynamics
of a spatially dependent concentration field for the ion channels.Comment: 22 pages, 10 figures. Under review for EPJ
Diffuse-Charge Dynamics in Electrochemical Systems
The response of a model micro-electrochemical system to a time-dependent
applied voltage is analyzed. The article begins with a fresh historical review
including electrochemistry, colloidal science, and microfluidics. The model
problem consists of a symmetric binary electrolyte between parallel-plate,
blocking electrodes which suddenly apply a voltage. Compact Stern layers on the
electrodes are also taken into account. The Nernst-Planck-Poisson equations are
first linearized and solved by Laplace transforms for small voltages, and
numerical solutions are obtained for large voltages. The ``weakly nonlinear''
limit of thin double layers is then analyzed by matched asymptotic expansions
in the small parameter , where is the
screening length and the electrode separation. At leading order, the system
initially behaves like an RC circuit with a response time of
(not ), where is the ionic diffusivity, but nonlinearity
violates this common picture and introduce multiple time scales. The charging
process slows down, and neutral-salt adsorption by the diffuse part of the
double layer couples to bulk diffusion at the time scale, . In the
``strongly nonlinear'' regime (controlled by a dimensionless parameter
resembling the Dukhin number), this effect produces bulk concentration
gradients, and, at very large voltages, transient space charge. The article
concludes with an overview of more general situations involving surface
conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference
Nonlinear electrophoresis of dielectric and metal spheres in a nematic liquid crystal
Electrophoresis is a motion of charged dispersed particles relative to a
fluid in a uniform electric field. The effect is widely used to separate
macromolecules, to assemble colloidal structures, to transport particles in
nano- and micro-fluidic devices and displays. Typically, the fluid is isotropic
(for example, water) and the electrophoretic velocity is linearly proportional
to the electric field. In linear electrophoresis, only a direct current (DC)
field can drive the particles. An alternate current (AC) field is more
desirable because it allows one to overcome problems such as electrolysis and
absence of steady flows. Here we show that when the electrophoresis is
performed in a nematic fluid, the effect becomes strongly non-linear with a
velocity component that is quadratic in the applied voltage and has a direction
that generally differs from the direction of linear velocity. The new
phenomenon is caused by distortions of the LC orientation around the particle
that break the fore-aft (or left-right) symmetry. The effect allows one to
transport both charged and neutral particles, even when the particles
themselves are perfectly symmetric (spherical), thus enabling new approaches in
display technologies, colloidal assembly, separation, microfluidic and
micromotor applications.Comment: 15 pages, 4 figure