8 research outputs found
Numerical electrokinetics
A new lattice method is presented in order to efficiently solve the
electrokinetic equations, which describe the structure and dynamics of the
charge cloud and the flow field surrounding a single charged colloidal sphere,
or a fixed array of such objects. We focus on calculating the electrophoretic
mobility in the limit of small driving field, and systematically linearise the
equations with respect to the latter. This gives rise to several subproblems,
each of which is solved by a specialised numerical algorithm. For the total
problem we combine these solvers in an iterative procedure. Applying this
method, we study the effect of the screening mechanism (salt screening vs.
counterion screening) on the electrophoretic mobility, and find a weak
non-trivial dependence, as expected from scaling theory. Furthermore, we find
that the orientation of the charge cloud (i. e. its dipole moment) depends on
the value of the colloid charge, as a result of a competition between
electrostatic and hydrodynamic effects.Comment: accepted for publication in Journal of Physics Condensed Matter
(proceedings of the 2012 CODEF conference
Studying Flow Close to an Interface by Total Internal Reflection Fluorescence Cross Correlation Spectroscopy: Quantitative Data Analysis
Total Internal Reflection Fluorescence Cross Correlation Spectroscopy
(TIR-FCCS) has recently (S. Yordanov et al., Optics Express 17, 21149 (2009))
been established as an experimental method to probe hydrodynamic flows near
surfaces, on length scales of tens of nanometers. Its main advantage is that
fluorescence only occurs for tracer particles close to the surface, thus
resulting in high sensitivity. However, the measured correlation functions only
provide rather indirect information about the flow parameters of interest, such
as the shear rate and the slip length. In the present paper, we show how to
combine detailed and fairly realistic theoretical modeling of the phenomena by
Brownian Dynamics simulations with accurate measurements of the correlation
functions, in order to establish a quantitative method to retrieve the flow
properties from the experiments. Firstly, Brownian Dynamics is used to sample
highly accurate correlation functions for a fixed set of model parameters.
Secondly, these parameters are varied systematically by means of an
importance-sampling Monte Carlo procedure in order to fit the experiments. This
provides the optimum parameter values together with their statistical error
bars. The approach is well suited for massively parallel computers, which
allows us to do the data analysis within moderate computing times. The method
is applied to flow near a hydrophilic surface, where the slip length is
observed to be smaller than 10nm, and, within the limitations of the
experiments and the model, indistinguishable from zero.Comment: 18 pages, 12 figure
Unified Homogenization Theory for Magnetoinductive and Electromagnetic Waves in Split Ring Metamaterials
A unified homogenization procedure for split ring metamaterials taking into
account time and spatial dispersion is introduced. The procedure is based on
two coupled systems of equations. The first one comes from an approximation of
the metamaterial as a cubic arrangement of coupled LC circuits, giving the
relation between currents and local magnetic field. The second equation comes
from macroscopic Maxwell equations, and gives the relation between the
macroscopic magnetic field and the average magnetization of the metamaterial.
It is shown that electromagnetic and magnetoinductive waves propagating in the
metamaterial are obtained from this analysis. Therefore, the proposed time and
spatially dispersive permeability accounts for the characterization of the
complete spectrum of waves of the metamaterial. Finally, it is shown that the
proposed theory is in good quantitative and qualitative agreement with full
wave simulations.Comment: 4 pages, 3 figure
Computer simulation of electrokinetics in colloidal systems
The contribution gives a brief overview outlining how our theoretical understanding of the phenomenon of colloidal electrophoresis has improved over the decades. Particular emphasis is put on numerical calculations and computer simulation models, which have become more and more important as the level of description became more detailed and refined. Due to computational limitations, it has so far not been possible to study “perfect” models. Different complementary models have hence been developed, and their various strengths and deficiencies are briefly discussed. This is contrasted with the experimental situation, where there are still observations waiting for theoretical explanation. The contribution then outlines our recent development of a numerical method to solve the electrokinetic equations for a finite volume in three dimensions, and describes some new results that could be obtained by the approach
Dynamic and dielectric response of charged colloids in electrolyte solutions to external electric fields
Computer simulations are used to investigate the response of a charged
colloid and its surrounding microion cloud to an external electric field. Both
static fields (DC) and alternating fields (AC) are considered. A mesoscopic
simulation method is implemented to account in full for hydrodynamic and
electrostatic interactions. The response of the system can be characterized by
two quantities: the mobility and the polarizability. Due to the interplay of
the electrostatic attraction and hydrodynamic drag, the response of the
microions close to the colloid surface is different from that of the microions
far away from the colloid. Both the mobility and polarizability exhibit a
dependency on the frequency of the external fields, which can be attributed to
the concentration polarization, the mobility of the microions, and the inertia
of microions. The effects of the colloidal charge, the salt concentration, and
the frequency of the external fields are investigated systematically.Comment: 12 pages, 8 figures, submitted to J. Chem. Phy