Electroneutral Layer Dynamics Drive Ion Migration in Low Frequency AC Electrophoresis Below the Water Electrolysis Threshold.

Low-frequency AC electrophoresis lies in a regime between DC microchannel electrophoresis and dielectrophoresis, which typically utilizes frequencies above 1000 Hz. Although few electrophoretic methods have been reported in this ≤100 Hz range, traveling wave electrophoresis (TWE) and transverse AC electrophoresis (TrACE) operate in this frequency range, and use low voltages to avoid bubble formation from water electrolysis. TWE provides molecular separations with enhanced control and TrACE provides multiplexed, multiparameter particle characterization.

Hybrid finite-amplitude periodic modes for two uniformly magnetized spheres.

We analyze a system of two uniformly magnetized spheres, one fixed and the other free to slide in frictionless contact with the surface of the first. The centers of the two magnets, and their magnetic moments, are restricted to a plane. We search for sets of initial conditions that yield finite-amplitude oscillatory periodic solutions.

Correction: Measuring the electrophoretic mobility and size of single particles using microfluidic transverse AC electrophoresis (TrACE).

Correction for 'Measuring the electrophoretic mobility and size of single particles using microfluidic transverse AC electrophoresis (TrACE)' by M. Hannah Choi , , 2023, https://doi.org/10.

Measuring the electrophoretic mobility and size of single particles using microfluidic transverse AC electrophoresis (TrACE).

The ability to measure the charge and size of single particles is essential to understanding particle adhesion and interaction with their environment. Characterizing the physical properties of biological particles, like cells, can be a powerful tool in studying the association between the changes in physical properties and disease development. Currently, measuring charge the electrophoretic mobility () of individual particles remains challenging, and there is only one prior report of simultaneously measuring and size.

Inertial motion on the earth's spheroidal surface.

As seen by an observer in the rotating frame, the earth's small spheroidal deformations neutralize the centrifugal force, leaving only the smaller Coriolis force to govern the "inertial" motion of objects that move on its surface, assumed smooth and frictionless. Previous studies of inertial motion employ weakly spheroidal equations of motion that ignore the influence of the centrifugal force and yet treat the earth as a sphere. The latitude dependence of these equations renders them strongly nonlinear.

Normal-mode oscillations for the circular and dipolar states of a filled hexagonal magnetic dipole cluster.

We analyze the rotational dynamics of six magnetic dipoles of identical strength at the vertices of a regular hexagon with a variable-strength dipole in the center. The seven dipoles spin freely about fixed axes that are perpendicular to the plane of the hexagon, with their dipole moments directed parallel to the plane. Equilibrium dipole orientations are calculated as a function of the relative strength of the central dipole.

Periodic bouncing modes for two uniformly magnetized spheres. I. Trajectories.

We consider a uniformly magnetized sphere that moves without friction in a plane in response to the field of a second, identical, fixed sphere, making elastic hard-sphere collisions with this sphere. We seek periodic solutions to the associated nonlinear equations of motion. We find closed-form mathematical solutions for small-amplitude modes and use these to characterize and validate our large-amplitude modes, which we find numerically.

Periodic bouncing modes for two uniformly magnetized spheres. II. Scaling.

A uniformly magnetized sphere moves without friction in a plane in response to the field of a second, identical, fixed sphere and makes elastic hard-sphere collisions with this sphere. Numerical simulations of the threshold energies and periods of periodic finite-amplitude nonlinear bouncing modes agree with small-amplitude closed-form mathematical results, which are used to identify scaling parameters that govern the entire amplitude range, including power-law scaling at large amplitudes. Scaling parameters are combinations of the bouncing number, the rocking number, the phase, and numerical factors.

Periodic nonlinear sliding modes for two uniformly magnetized spheres.

A uniformly magnetized sphere slides without friction along the surface of a second, identical sphere that is held fixed in space, subject to the magnetic force and torque of the fixed sphere and the normal force. The free sphere has two stable equilibrium positions and two unstable equilibrium positions. Two small-amplitude oscillatory modes describe the sliding motion of the free sphere near each stable equilibrium, and an unstable oscillatory mode describes the motion near each unstable equilibrium.

Diffusion layer formation drives zone migration in travelling wave electrophoresis.

COMSOL finite element modeling software is used to simulate 2D traveling-wave electrophoresis for microfluidic separations and sample concentration. A four-phase AC potential is applied to a periodic interdigitated four-electrode array to produce a longitudinal electric wave that travels through the channel. Charged particles are carried along with the electric wave or left behind, depending on their mobilities.

Velocity plateaus in traveling-wave electrophoresis.

One-dimensional models are used to study traveling-wave electrophoresis, a tunable method for separating charged analytes. A traveling-electrode model reveals the mechanism for longitudinal oscillations. A stationary-electrode model explains the origin of mode-locked plateaus in the average velocity, predicts devil's staircases with nested Farey sequences, and reduces to a continuum sinusoidal model in the high electrode-density limit.

Fabrication and performance of a microfluidic traveling-wave electrophoresis system.

A microfluidic traveling-wave electrophoresis (TWE) system is reported that uses a locally defined traveling electric field wave within a microfluidic channel to achieve band transport and separation. Low voltages, over a range of -0.5 to +0.

Simultaneous separation and detection of cations and anions on a microfluidic device with suppressed electroosmotic flow and a single injection point.

A rapid and simultaneous separation of cationic and anionic peptides and proteins in a glass microfluidic device that has been covalently modified with a neutral poly(ethylene glycol) (PEG) coating to minimize protein adsorption is presented. The features of the device allow samples that contain both anions and cations to be introduced from a central flow stream and separated in different channels with different outlets-all in the presence of low electroosmotic flow (EOF) imparted by the PEG coating. The analytes are electrophoretically extracted from a central hydrodynamic stream and electrophoretically separated in two different channels, in which pressure driven flow has been suppressed through the use of hydrodynamic restrictors.

Self-similar nested sequences on a chaotic attractor for traveling-wave electrophoresis.

Oscillating electric potentials are applied to interdigitated arrays of cylindrical electrodes above and below a stationary conducting viscous fluid. The phases of these potentials are chosen to produce a longitudinal traveling wave that traps high-mobility ions and partially traps intermediate-mobility ions in periodic and narrowband chaotic attractors with average velocities that are commensurate with the wave speed. Stable periodic attractors have periods up to 101 times the wave period.

A theoretical and experimental study of the electrophoretic extraction of ions from a pressure driven flow in a microfluidic device.

The electrophoretic extraction of ions from a hydrodynamic flow stream is investigated at an intersection between two microfluidic channels. A pressure gradient is used to drive samples through the main channel, while ions are electrophoretically extracted into the side channels. Hydrodynamic restrictors and a neutral coating are used to suppress bulk flow through the side channels.

Traveling-wave electrophoresis for microfluidic separations.

Models and microfluidic experiments are presented of an electrophoretic separation technique in which charged particles whose mobilities exceed a tunable threshold are trapped between the crests of a longitudinal electric wave traveling through a stationary viscous fluid. The wave is created by applying periodic potentials to electrode arrays above and below a microchannel. Predicted average velocities agree with experiments and feature chaotic attractors for intermediate mobilities.

Propagation velocities of chemical reaction fronts advected by Poiseuille flow.

Poiseuille flow between parallel plates advects chemical reaction fronts, distorting them and altering their propagation velocities. Analytical solutions of the cubic reaction-diffusion-advection equation resolve the chemical concentration for narrow gaps, wide gaps, and small-amplitude flow. Numerical solutions supply a general description for fluid flow in the direction of propagation of the chemical reaction front, and for flow in the opposite direction.

Poiseuille advection of chemical reaction fronts.

Poiseuille flow between parallel plates alters the shapes and velocities of chemical reaction fronts. In the narrow-gap limit, the cubic reaction-diffusion-advection equation predicts a front-velocity correction equal to the gap-averaged fluid velocity epsilon. In the singular wide-gap limit, the correction equals the midgap fluid velocity 3epsilon/2 when the flow is in the direction of propagation of the reaction front, and equals zero for adverse flow of any amplitude for which the front has a midgap cusp.

River meandering dynamics.

The Ikeda, Parker, and Sawai river meandering model is reexamined using a physical approach employing an explicit equation of motion. For periodic river shapes as seen from above, a cross-stream surface elevation gradient creates a velocity shear that is responsible for the decay of small-wavelength meander bends, whereas secondary currents in the plane perpendicular to the downstream direction are responsible for the growth of large-wavelength bends. A decay length D=H/2C(f) involving the river depth H and the friction coefficient C(f) sets the scale for meandering, giving the downstream distance required for the fluid velocity profile to recover from changes in the channel curvature.