Continuous cell washing and mixing driven by an ultrasound standing wave within a microfluidic channel

Ultrasound standing wave radiation force and laminar flow have been used to transfer yeast cells from one liquid medium to another (washing) by a continuous field-flow fractionation (FFF) approach. Two co-flowing streams, a cell-free suspending phase (flow rate > 50% of the total flow-through volume) and a yeast suspension, were introduced parallel to the nodal plane of a 3 MHz standing wave resonator. The resonator was fabricated to have a single pressure nodal plane at the centre line of the chamber. Laminar flow ensured a stable interface was maintained as the two suspending phases flowed through the sound field. Initiation of the ultrasound transferred cells to the cell-free phase within 0.5 s. This particle transfer procedure circumvents the pellet formation and re-suspension steps of centrifuge based washing procedures. In addition, fluid mixing was demonstrated in the same chamber at higher sound pressures. The channel operates under negligible back-pressure (cross-section, 0.25 [times] 10 mm) and with only one flow convergence and one flow division step, the channel cannot be easily blocked. The force acting on the cells is small; less than that experienced in a centrifuge generating 100g. The acoustically-driven cell transfer and mixing procedures described may be particularly appropriate for the increasingly complex operations required in molecular biology and microbiology and especially for their conversion to continuous flow processes.     

Coordinate measurements and operators

Relativistic quantum-field theory provides the machinery for calculating wave functions or probability amplitudes depending upon space-time coordinates. The currently accepted theory, however, fails to provide position operators and a means of measuring particle coordinates that are consistent with Dirac's properties of physical observables. This is because it calls for a space position probability distribution at a specified time. This paper shows, however, that space-time event coordinate operators, together with a corresponding measurement procedure, can be found that are consistent with Dirac's requirements. This is done through a reinterpretation of the amplitudes computed by field theory and does not involve any change in that mathematical formalism. The measurement of the space-time coordinates of an event is accomplished by detecting the absorption of a photon by a particle from each of two light pulses designed to overlap at a given point at a given time. If a final emitted photon has an energy whose sum with the final particle energy approximately equals the sum of the mean energies of the pulses, then the absorption of the two pulse photons must certainly have taken place within a distance the order of a Compton wavelength of the small space-time region of overlapping pulses. This is clear from the fact that the high energy required to confine the pulses to very small volumes must throw a particle absorbing them far off the mass shell. Thus the absorption of the two photons throws the particle into a narrowly confined spatial wave function that must decay extremely rapidly—to within a Compton wavelength, a delta function in space-time. This delta function is the eigenfunction of space-time coordinate operators X^μ and is the scalar product of vectors in a Hilbert space spanned by spin–space-time kets large enough to contain the operators of the Poincaré group. These event operators transform properly under the action of Poincaré operators but do not commute with the mass. If the Compton wavelength is not negligible compared to the accuracy desired in the coordinate measurements, individual coordinate measurements are no longer possible. Nevertheless, a large number of repeated coordinate measurements can be carried out to produce a coordinate probability distribution. This distribution can be unfolded to find a true coordinate probability distribution if the charge form factor is known from basic theory. An analysis of laboratory particle detection techniques shows that they actually determine space coordinates and energy rather than spatial coordinates at a given time. When this fact is included, the Klein–Nishina formula can be derived using the electromagnetic four-vector potential as the photon probability amplitude wave. To clarify the meaning of the observables, a mass-momentum measurement is described.     

Electrophoresis of large colloidal particles with surface charge layers. Position of the slipping plane and surface layer thickness

A theory is proposed for the electrophoresis of a large colloidal particle with a surface charge layer. The slipping plane is assumed to be located within the surface layer but may not be located at the boundary between the surface layer and the particle core. In previous studies, the depth of the slipping plane is assumed to coincide with the surface layer thickness. The present theory makes it possible to examine the separate dependence of the electrophoretic mobility on the position of the slipping plane and on the surface layer thickness. It is shown that, at constant amount of particle-fixed charges in the surface layer, the mobility increases as the depth of the slipping plane (d _s ) increases, while it decreases as the surface layer thickness (d _c ) increases, causing a mobility maximum in some cases ifd _s =d _c . Several approximate analytic expressions for the mobility are presented.     

On probability flow descriptors in position and momentum spaces

The current density concepts of the position and momentum probability distributions are examined and the associated continuity equations are explored. The modified flow measure in the momentum-space is introduced in terms of which the nonclassical (current-related) functionals of the entropy/information content in quantum states assume forms isomorphic with the corresponding position-space expressions, when expressed in terms of the state modulus (density) and phase (current) degrees-of-freedom. These concepts are illustrated for the stationary states as well as the plane waves and wave packets of the free particle.     

Diffusiophoresis and electrophoresis of a charged sphere perpendicular to two plane walls

The problem of diffusiophoretic and electrophoretic motions of a dielectric spherical particle in an electrolyte solution situated at an arbitrary position between two infinite parallel plane walls is studied theoretically in the quasisteady limit of negligible Peclet and Reynolds numbers. The applied electrolyte concentration gradient or electric field is uniform and perpendicular to the plane walls. The electric double layer at the particle surface is assumed to be thin relative to the particle radius and to the particle-wall gap widths, but the polarization effect of the diffuse ions in the double layer is incorporated. To solve the conservative equations, the general solution is constructed from the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the plane walls by the Hankel transforms and then on the particle surface by a collocation technique. Numerical results for the diffusiophoretic and electrophoretic velocities of the particle relative to those of a particle under identical conditions in an unbounded solution are presented for various cases. The collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the walls can reduce or enhance the particle velocity, depending on the properties of the particle-solution system and the relative particle-wall separation distances. The boundary effects on diffusiophoresis and electrophoresis of a particle normal to two plane walls are found to be quite significant and complicated, and generally stronger than those parallel to the confining walls.     

Quantum trajectories for resonant scattering

Time‐dependent wave packet resonant scattering for the double square barrier has been studied in terms of Bohm quantum trajectories. The high transmission probability for the wave packet with a resonant energy can be explained by the behavior of the quantum trajectories under the influence of the relatively slow formation of a node within the first barrier. This node splits the trajectories into reflected and transmitted components. During this stage, many particle trajectories pass through the double‐barrier region and contribute to the transmitted part of the wave packet. Due to the transient nature of the nodes, trajectories in the reflected wave packet bunch together between the nodes for a finite period of time so that temporary structure (localization of particles and accompanying increase in the probability density) develops on small length scales. These calculations also show that the particles gain high momentum near the nodal points, and they reach a uniform momentum distribution after transmitting the barrier region. We have found that the presence of a node between the two barriers influences the different lifetimes of the quasi‐bound states. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 206–213, 2001     

Mechanism and Kinetics of Hexamethyldisilazane Reaction with a Fumed Silica Surface

An analytical study is presented on the thermocapillary migration of a fluid sphere within a constant applied temperature gradient in an arbitrary direction with respect to a plane surface. The Peclet and Reynolds numbers are assumed to be small so that the Laplace and Stokes equations, respectively, govern the temperature distributions and fluid velocities inside and outside the droplet. The asymptotic formulas for the temperature and the velocity fields in the quasi-steady situation are obtained by using a method of reflections. The plane surface can be a no-slip solid wall and/or a perfect-slip free surface. The boundary effect on the thermocapillary migration is found to be weaker than that on the motion driven by a body force. Even so, the interaction between the plane and the droplet can be very significant when the gap thickness approaches zero. For the motion of a droplet normal to a solid wall, the effect of the plane surface reduces the translational velocity of the droplet; however, this solid wall can be an enhancement factor on the particle migration as it is translating parallel to the wall. On the other hand, in case of a droplet migrating close to a free surface due to thermocapillarity, the droplet velocity can be either greater or smaller than that which would exist in the absence of the plane surface, depending on the relative thermal conductivity and the surface properties of the particle and its relative distance from the plane. Furthermore, the interacting thickness of the affected region by the presence of the plane is discussed by considering the droplet mobility. Generally speaking, a free surface exerts less influence on the particle movement than does a solid surface. Copyright 2000 Academic Press.     

Dissociative attachment in vinyl and allyl chloride,chlorobenzene and benzyl chloride

Relative cross sections for dissociative attachment are measured in vinyl and allyl chloride, chlorobenzene and benzyl chloride. For each pair, the compound with the Cl located out of the π nodal plane yields the larger cross section, by a factor of 5.3 and 17.5 respectively. In each case the maximum in the cross section occurs within 100 meV of the lowest π¹ resonance located by electron transmission spectroscopy.     

Direct measurement of the effective charge in nonpolar suspensions by optical tracking of single particles

The authors develop an ultrasensitive method for the measurement of the charge carried by a colloidal particle in a nonpolar suspension. The technique uses the phenomenon of the resonance of a particle held in an optical tweezer trap and driven by a sinusoidal electric field. The trapped particle forms a strongly damped harmonic oscillator whose fluctuations are a function of gamma, the ratio of the root-mean-square average of the electric and thermal forces on the particle. At low applied fields (gamma<1) the particle is confined to the optical axis, while at high fields (gamma>1) the probability distribution of the particle is double peaked. The periodically modulated thermal fluctuations are measured with nanometer sensitivity using an interferometric position detector. Charges, as low as a few elementary charges, can be measured with an uncertainty of about 0.25 e. This is significantly better than previous techniques and opens up new possibilities for the study of nonpolar suspensions.     

Feasibility and uniqueness of stationary states of nonideal recombinant fermentations?

Summary In recombinant fermentations the plasmid loss probability per generation depends on the specific growth rate, which is related linearly to the dilution rate. A model with this feature and incomplete mixing has been studied analytically for stationary state behavior. While the kinetic parameters place upper limits on the dilution rate for a feasible stationary state in a well-mixed bioreactor, the feasible and nonfeasible regions for an incompletely mixed reactor are separated by either a straight line or a plane, whose position is determined by the mixing conditions.</o:p>     

Adsorption of microstructured particles at liquid-liquid interfaces

The solid particles are adsorbed at interfaces and form self-assembled structures when the particles have suitable wettability to both liquids. Here, we show theoretically how the microstructure on the particle surface affects their adsorption properties. The physical properties of the interface adsorbing a particle will be described by taking into account the surface roughness due to the microstructure. The microstructure on the surface changes drastically the wettability and the equilibrium position of the adsorbed particle. Therefore, the contact angle of the particle at the three-phase contact line shifts with the particle surface area, because the surface roughness enhances the interfacial properties of the particle surface. Moreover, the range of the interfacial tensions at which the particle is adsorbed becomes narrower with the increase of the surface roughness. The effect of the particle shape on the adsorption properties is also studied. In the case of disk-shaped particles, the energy changes discontinuously when the plane surface of the particle contacts the liquid-liquid interface. The adsorbing position does not change with the surface roughness. The orientation of a parallelepiped particle at the liquid-liquid interface is governed by the aspect ratio and the surface area of the particle. On the other hand, the particle which is partially covered with the microstructured surface is adsorbed firmly at the interface in an oriented state. We should consider not only the interfacial tensions but also the surface structure and the particle shape to control the adsorption behavior of the particle.     

Transport through zeolite filled polymeric membranes

In this paper the effect of zeolite particles incorporated in rubbery polymers on the pervaporation properties of membranes made from these polymers is discussed. Pervaporation of methanol/toluene mixtures was carried out with membranes prepared from the toluene selective polymer EPDM and the methanol selective polymers Viton and Estane 5707. From the results of the pervaporation experiments it could be concluded that the addition of the hydrophilic zeolite NaX as well as the hydrophobic zeolite silicalite-1 leads to an increase in methanol flux and a decrease in toluene flux through the membranes. Pervaporation experiments with bi-layer membranes consisting of an unfilled polymer layer filled with zeolite particles demonstrated that the effect of addition of particles depends on their position in the membrane. Furthermore, the component flux through the membranes as a function of the volume fraction of zeolite is modelled with existing theories describing the permeability of heterogeneous materials. The results show that the apparent permeability of the dispersed phase is lower than the intrinsic permeability of the dispersed phase when the flux through the particle is restricted by the polymer phase. This phenomenon was confirmed by numerical simulation of the transport in the membrane through a plane parallel to the transport direction. The simulations are carried out for an unfilled membrane, a membrane filled with an impermeable particle, a rubber particle and with a particle which shows Langmuir sorption behaviour. The reason for the discrepancy between the apparent permeability and the intrinsic permeability is that the apparent permeability of the zeolite phase is calculated by dividing the flux with the driving force over the entire membrane which is larger than that over the particle. In case of numerical simulation the concentration in every position in the plane is known and therefore the intrinsic permeability of the filler can be calculated on basis of the actual driving force. This treatment results in a permeability which is correct over several orders of magnitude.     

Cavity ring-down spectroscopy measurement of single aerosol particle extinction. II. Extinction of light by an aerosol particle in an optical cavity excited by a cw laser

The authors present an analytical derivation of the scattered power from a spherical, homogeneous, nonabsorbing particle in a plane standing wave. The scattered power changes significantly with the position of the particle with respect to the peaks and nodes of the standing wave, even for particles whose diameters are many times the wavelength of the light. The analysis is applicable to continuous-wave cavity ring-down spectroscopy on aerosol particles, and the structure of the standing wave is expected to affect both the measured ring-down time and the shape of the ring-down trace. The dependence of the extinction on the phase of the standing wave at the location of the particle is captured in a parameter zeta which connects the current treatment to standard Mie scattering theory. Methods for calculating zeta are presented.     

Entropic Kullback-Leibler type distance measures for quantum distributions

Entropic distance measures for quantum mechanical probability distributions, which are characterized by nodal structure and symmetry holes, are considered. We illustrate how the Kullback-Leibler (KL) distance is not well defined in some instances and propose instead the use of the cumulative residual Kullback-Leibler (CRKL) distance. The KL and CRKL measures are compared and contrasted for some representative quantum mechanical systems: The particle in an infinite well, the harmonic oscillator, and hydrogenic systems. We present cases where CRKL can be used to obtain distances whereas KL cannot be used, and also highlight examples where the KL and CRKL measures yield different behaviors and interpretations. An extension of the CRKL definition is obtained for application to harmonic oscillator systems defined over [−∞, ∞]. Distance measures for two-variable (particle) distributions are also considered to address generalizations of the mutual information correlation measure. The use of CRKL in measuring distances between orbitals is also discussed.     

Tuning the Optical Properties of Sulfonylaniline Derivatives: Degeneracy Breaking of Benzene Orbitals and Linkage through Nodal Planes

The orbital degeneracy of benzene rings is resolved by an asymmetric push-pull system in 2,6-bis(methylsulfonyl)aniline (BMeSA), in which the highest occupied molecular orbital (HOMO) is located at the 4-position, while the lowest unoccupied molecular orbital (LUMO) is located at a different position and has a nodal plane through the carbon atoms at the 1- and 4-positions. Therefore, the π-extension of BMeSA at the 4-position reveals a strong overlap in the HOMO and a minimal overlap in the LUMO. Consequently, π-extended BMeSA derivatives exhibit longer absorbance and emission wavelengths in the order of the electron-donating abilities of their substituents at the 4-position, which is based on a decrease in an absolute HOMO-level-dependent HOMO-LUMO gap in accordance with the nodal arrangement. Positive fluorescent solvatochromism with polarity-dependent decrease in fluorescent intensity was also observed. The biaryls exhibited more planar geometries in the excited state than in the ground state. The charge transfer mechanism, which can be described as node-induced intramolecular charge transfer (NICT), differs from the planar intramolecular charge transfer (PICT) and twisted intramolecular charge transfer (TICT).     

Thermophoretic Motion of a Sphere Parallel to an Insulated Plane

An analytical study is presented for the thermophoresis of a sphere in a constant applied temperature gradient parallel to an adiabatic plane. The Knudsen number is assumed to be small so that the fluid flow can be described by a continuum model with a thermal creep and a hydrodynamic slip at the particle surface. A method of reflections is used to obtain the asymptotic formulas for the temperature and velocity fields in the quasisteady situation. The thermal insulated plane may be a solid wall (no-slip) and/or a free surface (perfect-slip). The boundary effect on the thermophoretic motion is found to be weaker than that on the axisymmetric thermophoresis of a sphere normal to a plane with constant temperature. In comparison with the motion driven by gravitational force, the interaction between the particle and the boundary is less significant under thermophoresis. Even so, the interaction between the plane and the particle can be very strong when the gap thickness approaches zero. For the thermophoretic motion of a particle parallel to a solid plane, the effect of the plane surface is to reduce the translational velocity of the particle. In the case of particle migration parallel to a free surface due to thermophoresis, the translating velocity of a particle can be either greater or smaller than that which would exist in the absence of the plane surface, depending on the relative thermal conductivity and the surface properties of the particle and its relative distance from the plane. Not only the translational velocity but also the rotational velocity of the thermophoretic sphere near the plane boundary is formulated analytically. The rotating direction of the particle is strongly dominated by its surface properties and the internal-to-external thermal conductivity. Besides the particle motion, the thickness of the thermophoretic boundary layer is evaluated by considering the thermophoretic mobility. Generally speaking, a free surface exerts less influence on the particle movement than a solid wall. Copyright 2000 Academic Press.     

Transport coefficients and orientational distributions of spheroidal particles with magnetic moment normal to the particle axis (Analysis for an applied magnetic field normal to the shear plane)

We have investigated the influence of the magnetic field strength, shear rate, and rotational Brownian motion on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. The rodlike particle is modeled as a magnetic spheroidal particle which has a magnetic moment normal to the particle axis; such a particle may typically be a hematite particle. In the present study, an external magnetic field is applied in the direction normal to the shear plane of a simple shear flow. The basic equation of the orientational distribution function has been derived from the balance of torques and solved numerically. The results obtained here are summarized as follows. Although the orientational distribution function shows a sharp peak in the shear flow direction for a very strong magnetic field, such a peak is not restricted to the field direction alone, but continues in every direction of the shear plane. This is due to the characteristic particle motion that the particle can rotate around the axis of the magnetic moment in the shear plane, although the magnetic moment nearly points to the magnetic field direction. This particle motion in the shear plane causes negative values of the viscosity due to the magnetic field. The viscosity decreases, attains a minimum value, and then converges to zero as the field strength increases. Additionally, the diffusion coefficient is significantly influenced by such characteristic particle motion in the shear plane for a strong magnetic field.     

Semiclassical wavepacket construction of quantum resonance states from classical resonant orbits for the F + H2 reaction

The semiclassical interpretation of reactive resonances as dynamically confined orbits is extended for the F + H₂ reaction by construction of resonant-state wavefunctions according to a time-dependent formalism for Gaussian wavepacket dynamics. The partitioning of nodal curves between entrance and exit channels for the collinear resonances agrees with adiabatic theory and nodal surfaces for the 3D probability density distribution qualitatively agree with quantal calculations.     

Diffusiophoresis of a highly charged soft particle normal to a conducting plane

Diffusiophoresis of a soft particle in electrolyte solutions normal to a conducting solid plane is investigated theoretically in this study, focusing on the highly charged particle in particular. A pseudo-spectral method based on Chebyshev polynomial is adopted to solve the resultant governing electrokinetic equations. It was found, among other things, that the closer the soft particle is to the plane, the faster it moves in general, provided only the chemiphoresis component of the diffusiophoresis is involved, i.e., no diffusion potential is present. The presence of the conducting plane is found to have three effects upon the particle motion nearby: the geometric boundary confinement effect, the electrostatic mirror-image force analog effect, and the hydrodynamic retarding effect. The enhancement of the double layer polarization by the first two effects leads to the seeming intriguing observation mentioned above. The particle always moves away from the plane in chemiphoresis. If a diffusion potential is present, however, then it is possible to drive the particle toward the plane. The results have potential applications in drug delivery.     

Stacking fault structure in shear-induced colloidal crystallization

We report measurements of the spatial distribution of stacking faults in colloidal crystals formed by means of an oscillatory shear field at a particle volume fraction of 52% in a system where the pair potential interactions are mildly repulsive. Stacking faults are directly visualized via confocal laser scanning microscopy. Consistent with previous scattering studies, shear orders the initially amorphous colloids into close-packed planes parallel to the shearing surface. Upon increasing the strain amplitude, the close-packed direction of the (111) crystal plane shifts from an orientation parallel to the vorticity direction to parallel the flow direction. The quality of the layer ordering, as characterized by the mean stacking parameter, decreases with strain amplitude. In addition, we directly observe the three-dimensional structure of stacking faults in sheared crystals. We observe and quantify spatial heterogeneity in the stacking fault arrangement in both the flow-vorticity plane and the gradient direction, particularly at high strain amplitudes (gamma> or =3). At these conditions, layer ordering persists in the flow-vorticity plane only over scales of approximately 5-10 particle diameters. This heterogeneity is one component of the random layer ordering deduced from previous scattering studies. In addition, in the gradient direction, the stacking registry shows that crystals with intermediate global mean stacking probability are comprised of short sequences of face-centered cubic and hexagonal close-packed layers with a stacking that includes a component that is nonrandom and alternating in character.