Retention behavior of metal particle dispersions in aqueous and nonaqueous carriers in thermal field-flow fractionation

Until quite recently, theories on thermophoresis of particles predicted very low thermophoretic velocities of metal particles in liquids. This prediction was based on the understanding that the very high thermal conductivities of metals relative to most liquid media resulted in quite low temperature gradients across the metal particle thereby leading to low net force on the particle. In this paper, we report the retention behavior of submicrometer size metal particles of silver (Ag), gold (Au), palladium (Pd) and platinum (Pt) suspended in both aqueous and organic (specifically, acetonitrile and tetrahydrofuran) carrier liquids in thermal field-flow fractionation (ThFFF). The dependence of the metal particle retention on various factors such as particle composition, amount of added electrolyte, carrier liquid composition, field strength, channel thickness, and carrier flow-rate is evaluated and discussed. A comparison in particle retention behavior among equal-sized metal, latex and silica particles is also provided.     

Practical implications of ionic strength effects on particle retention in thermal field-flow fractionation

Modification of ionic strength of an aqueous or non-aqueous carrier solution can have profound effects on the particle retention behavior in thermal field-flow fractionation (ThFFF). These effects can be considered as either advantageous or not depending on the performance criteria under consideration. Aside from the general increase in retention time of particulate material (latexes and silica particles), our experiments indicate improvement in resolution with increases in electrolyte concentration. Absence of an electrolyte in the carrier solution causes deviations from the theoretically expected linear behavior between the retention parameter lambda (a measure of the extent of interaction between the applied field and the particle) and the reciprocal temperature drop across the channel walls. A negative interaction parameter delta(w), of about -0.170 was determined for 0.105- and 0.220-microm polystyrene (PS) latex particles suspended in either a 0.25 or a 1.0 mM TBAP-containing acetonitrile carrier and for 0.220 microm PS in 0.50 and 1.0 mM NaCl-containing aqueous medium. This work also demonstrates that optimum electrolyte concentrations can be chosen to achieve reasonable experimental run-times, good resolution separations, and shifts in the steric inversion points at lower field strengths, and that too high electrolyte concentrations can have deleterious effects such as band broadening and sample loss through adsorption to the channel accumulation surface. The advantages of using ionic strength rather than field strength to effect desired changes are lowered power consumption and possible application of ThFFF to high temperature-labile samples.     

Determination of calibration function in thermal field flow fractionation under thermal field programming

A new procedure for determining the calibration function able to relate retention and operative parameters to molecular weight of the species in thermal field flow (ThFFF) under thermal field programming (TFP) conditions is presented. The procedure involves determining the average values of retention parameters under TFP and determining a numerical function related to the temperature variations that occur during TFP. The calibration parameters are obtained by a procedure fitting the retention and operative parameters that hold true at the beginning of the TFP. The procedure is closely related to the one previously developed to calibrate the retention time axis under TFP ThFFF and, together, they constitute a full calibration procedure. Experimental validation was performed with reference to polystyrene (PS)-decalin and PS-THF systems. The calibration functions here obtained were compared to those derived by the classical procedure at constant thermal field ThFFF to obtain the calibration function at variable cold wall temperatures. Excellent agreement was found in all cases proving "universality" of the ThFFF calibration concept, i.e. it is independent of the particular system on which it was determined and can thus be extended to ThFFF operating under TFP. The new procedure is simpler than the classical one since it requires less precision in setting the instrumentation and can be obtained with fewer experiments. The potential applications for the method are discussed.     

A theory-based approach to thermal field-flow fractionation of polyacrylates

A theory-based approach is presented for the development of thermal field-flow fractionation (ThFFF) of polyacrylates. The use of ThFFF for polymer analysis has been limited by an incomplete understanding of the thermal diffusion which plays an important role in retention and separation. Hence, a tedious trial-and-error approach to method development has been the normal practice when analyzing new materials. In this work, thermal diffusion theories based on temperature dependent osmotic pressure gradient and polymer-solvent interaction parameters were used to estimate thermal diffusion coefficients (D(T)) and retention times (t(r)) for different polymer-solvent pairs. These calculations identified methyl ethyl ketone as a solvent that would cause significant retention of poly(n-butyl acrylate) (PBA) and poly(methyl acrylate) (PMA). Experiments confirmed retention of these two polymers that have not been previously analyzed by ThFFF. Theoretical and experimental D(T)s and t(r)s for PBA, PMA, and polystyrene in different solvents agreed to within 20% and demonstrate the feasibility of this theory-based approach.     

On void time determination in thermal field-flow fractionation

Because of the temperature dependence of the carrier liquid density, the mass of carrier which is contained in a thermal field-flow fractionation channel depends on the cold wall temperature and on the temperature difference across the channel thickness. It is observed that the void time of the solvent peak decreases when increasing the average temperature in the channel. The void time is found to be directly proportional to the average carrier density in the channel. The determination of the void time from the knowledge of the channel geometrical volume and the measurement of the volumetric flow-rate leads to significant errors if the thermal expansion of the carrier between the temperature of the measurement and the average channel temperature is not taken into account. Recommendations are given for proper void time determinations in thermal FFF.     

Characterization of macromolecules in liquid solutions by thermal diffusion. I. Dependence of the soret coefficient on the nature of the dispersing medium

Experiments have been carried out on thermal diffusion of macromolecular particles dispersed in various liquids, with the object of checking some predictions of the radiation-pressure theory of Soret effect in liquids and of establishing a method of physical characterization of macromolecules in liquid solutions. The experimental results confirm the importance of the ratio G between thermal conductivity K and (phase) velocity v of high-frequency elastic waves of the materials composing the mixture in determining the thermodiffusive behavior of a liquid solution. We have shown that the migration of the macromolecular component takes place in the same direction in which thermal energy is flowing or opposite to it, depending on whether G of the dispersed particles is smaller or larger relative to the G of the liquid. Another aspect of the same phenomenon may be observed when macroscopic pieces of nonmetallic materials are suspended in a liquid, and heat is made to flow through this solid plunger and the surrounding liquid. The experiments performed with molecular solutions and with macroscopic plungers mutually complement and confirm each other. Anomalous results obtained in the case of solutions of polyvinylpyrrolidone in methanol are also discussed, and the possibility that this might be the consequence of the existence of a marked velocity dispersion in the high-frequency region of the spectrum of thermal waves in both water and methyl alcohol is indicated. Finally the possibility is hinted that thermal diffusion might have been responsible for the phenomena of molecular selection and evolution which ultimately led to the origin of life on our planet.     

Flow-induced thermal effects on spatial DNA melting

Continuous-flow temperature gradient microfluidics can be used to perform spatial DNA melting analysis. To accurately characterize the melting behavior of PCR amplicon across a spatial temperature gradient, the temperature distribution along the microfluidic channel must be both stable and known. Although temperature change created by micro-flows is often neglected, flow-induced effects can cause significant local variations in the temperature profile within the fluid and the closely surrounding substrate. In this study, microfluidic flow within a substrate with a quasi-linear temperature gradient has been examined experimentally and numerically. Serpentine geometries consisting of 10 mm long channel sections joined with 90 degrees and/or 180 degrees bends were studied. Infrared thermometry was used to characterize the surface temperature variations and a 3-D conjugate heat transfer model was used to predict interior temperatures for multiple device configurations. The thermal interaction between adjacent counter-flow channel sections, which is related to their spacing and substrate material properties, contributes significantly to the temperature profile within the microchannel and substrate. The volumetric flow rate and axial temperature gradient are directly proportional to the thermal variations within the device, while these flow-induced effects are largely independent of the cross-sectional area of the microchannel. The quantitative results and qualitative trends that are presented in this study are applicable to temperature gradient heating systems as well as other microfluidic thermal systems.     

Study of continuous two-dimensional thermal field-flow fractionation of polymers

Two-dimensional thermal field-flow fractionation (2D-ThFFF) is a new instrumental technique devised for continuous fractionation of soluble macromolecules and particles. The sample mixture is introduced into a disc-shaped channel and the separated sample components are collected continuously from the channel outlets. The method is based on a two-dimensional fractionation mechanism with radial and tangential flow components in the channel. The effects of flow components and thermal gradient on the fractionation were studied in the separation of polystyrene samples of different molecular masses using cyclohexane or a binary solvent consisting of 25% ethylbenzene and 75% cyclohexane as carrier. The continuous separation of polystyrene samples was improved with increasing thermal gradient and with the use of slow radial and tangential flow rates. The technique can be applied to preparative continuous separation of macromolecules.     

A contribution to Semenov's general theory of thermal ignition regarding thermal analysis

The general theory of thermal ignition under the conditions of thermal analysis of flammable substances is discussed. For a linear heating rate of the specimen the ignition temperature is obtained from the relationship $$(dT/dt)_b - \frac{q}{{(dT/dt)_b }} = \frac{E}{{RT_b^2 }}(T_b - T_c^\prime )$$ whereT′_c is the temperature of the reactor wall (heated at the rateq) at the starting moment of the development of the thermal explosion.     

Investigation of the thermal lens effect in water-ethanol mixtures: composition dependence of the refractive index gradient, the enhancement factor and the Soret effect.

The thermal lens effect produced in binary mixtures of water and ethanol has been investigated. It is shown that the sensitivity of the thermal lens method upon the addition of ethanol in water varies as the temperature-dependent refractive index gradient to thermal conductivity ratio of the mixture. The dependence of k and dn/dT upon the ethanol volume fraction follows a second-order and fourth-order polynomial, respectively, and cannot be precisely predicted using the additive rule. Moreover, depending on the experimental conditions and the mixture composition, the temperature gradient produced subsequently to relaxation of the excited species induces mutual migration of the solvent molecules and the formation of a concentration gradient in the irradiated area. This effect, known as the Soret effect, can locally change the thermo-optical properties of the solution and produce an additional signal, especially when steady-state experiments are done. This may result in errors as large as 20% when quantitative informations have to be derived from experimental data.     

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.     

Lateral and cross-lateral focusing of spherical particles in a square microchannel

The inertial migration of particles in micro-scale flows has received much attention due to its promising applications, such as the membrane-free passive separation of particles or cells. The particles suspended in rectangular channels are known to be focused near the center of each channel face as the channel Reynolds number (R(C)) increases due to the lift force balance and the hydrodynamic interactions of the particles with the wall. In this study, the three-dimensional positions of neutrally buoyant spherical particles inside a square microchannel are measured using the digital holographic microscopy technique, and a transition from the lateral tubular pinch to the cross-lateral focusing with increasing R(C) is reported. The particles are found to migrate first in the lateral direction and then cross-laterally toward the four equilibrium positions. A general criterion that can be used to secure the fully developed state of particle focusing in Lab-on-a-Chip applications is also derived. This criterion could be helpful for the accurate estimation of the design parameters of inertial microfluidic devices, such as R(C), channel length and width, and particle diameter.     

Electrokinetic Separation Methods

Electrophoresis is the transport of dissolved molecules or suspended particles in a homogeneous polar liquid (such as water) under the influence of an electric field. Most molecules or particles acquire a surface electric charge when dissolved or suspended in buffered water (or other polar liquids), owing to ionization or adsorption of ions present in the water. The sign of the surface charge of molecules or particles determines whether they will migrate towards the positive or the negative electrode of the applied electric field, and the velocity of migration depends on the surface potential of the molecules or particles, as well as on the potential of the electric field.     

Dissipative particle dynamics simulation of depletion layer and polymer migration in micro- and nanochannels for dilute polymer solutions

The flows of dilute polymer solutions in micro- and nanoscale channels are of both fundamental and practical importance in variety of applications in which the channel gap is of the same order as the size of the suspended particles or macromolecules. In such systems depletion layers are observed near solid-fluid interfaces, even in equilibrium, and the imposition of flow results in further cross-stream migration of the particles. In this work we employ dissipative particle dynamics to study depletion and migration in dilute polymer solutions in channels several times larger than the radius of gyration (Rg) of bead-spring chains. We compare depletion layers for different chain models and levels of chain representation, solvent quality, and relative wall-solvent-polymer interactions. By suitable scaling the simulated depletion layers compare well with the asymptotic lattice theory solution of depletion near a repulsive wall. In Poiseuille flow, polymer migration across the streamlines increases with the Peclet and the Reynolds number until the center-of-mass distribution develops two symmetric off-center peaks which identify the preferred chain positions across the channel. These appear to be governed by the balance of wall-chain repulsive interactions and an off-center driving force of the type known as the Segre-Silberberg effect.     

Numerical simulations of viscoelastic particle migration in a microchannel with triangular cross-section

The migration of a spherical particle immersed in a viscoelastic liquid flowing in a microchannel with a triangular cross-section is investigated by direct numerical simulations under inertialess conditions. The viscoelastic fluid is modeled through two constitutive equations to investigate the effect of the second normal stress difference and the resulting secondary flows on the migration phenomenon. The results are presented in terms of trajectories followed by the particles released at different initial positions over the channel cross-section in a wide range of Weissenberg numbers and confinement ratios. Particles suspended in a fluid with a negligible second normal stress difference migrate toward the channel centerline or the closest wall, depending on their initial position. A much more complex dynamics is found for particles suspended in a fluid with a relevant second normal stress difference due to the appearance of secondary flows that compete with the migration phenomenon. Depending on the Weissenberg number and confinement ratio, additional equilibrium positions (points or closed orbits) may appear. In this case, the channel centerline becomes unstable and the particles are driven to the corners or “entrapped” in recirculation regions within the channel cross-section. The inversion of the centerline stability can be exploited to design efficient size-based separation devices.     

Repeatability and reproducibility of thermal field-flow fractionation in molecular weight determination of processed natural rubber

The purpose of this study is (1) to determine the repeatability and reproducibility of thermal field-flow fractionation (ThFFF) in measuring the molecular weight of compounded natural rubber, and (2) to examine the correlation between the molecular weights obtained from ThFFF and the rheological data. 8 batches of compounded natural rubber were obtained from a thermo-mechanical mastication process, and were analyzed by ThFFF in a designed testing sequence. ThFFF analysis showed the compounded natural rubbers range in weight-average molecular weight (M(w)) from 143,000 to 360,000. By taking into account both the short term variability (repeatability) as well as the long term variability (reproducibility) of the instrument, ThFFF was shown to be able to distinguish between samples differing by as little as 21,000 in M(w) and 15,600 in number-average molecular weight, M(n) (based on cis-polyisoprene calibration); and thus is a useful tool for the molecular weight analysis of natural rubber-related materials. It was also found that the rheological data (G' and tan delta) measured on both the virgin and the compounded natural rubber correlated well with the molecular weights obtained from ThFFF when normalized.     

High temperature thermal field-flow fractionation of polyethylene and polystyrene

In this paper the high-temperature thermal field flow fractionation method is exploited for the analysis of polyethylene (PE). The experimental apparatus set-up, obtained by simply modifying a commercial instrument, is presented. The numerical procedure for deriving retention calibration plot versus molecular weight is discussed with reference to the specific polymer-solvent pair, PE-o-dichlorobenzene (ODCB), here employed. Different methods for computing the physicochemical data set of the solvent, necessary for calibration, are compared. The selectivity of the checked PE-ODCB system proves comparable with respect to the values currently found in thermal field-flow fractionation (ThFFF) analysis. Differences are found between PE and polystyrene (PS) analysis in the same solvent. The conditions for high temperature ThFFF operation in PE analysis and their advantages are discussed with respect to the standard SEC technique for PE, PS, and PE-PS copolymer analysis. Molecular weight distributions obtained by ThFFF of two PE commercial samples agree with those obtained by SEC. © 1995 John Wiley & Sons, Inc.     

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.     

Improvement of energy dissipative particle dynamics method to increase accuracy

In this article, dissipative particle dynamics with energy conservation eDPD is used for simulating hydrodynamic behavior and heat transfer of DPD particles in a two-dimensional channel with parallel planes. To this end, a Fortran programming code is developed and the results are presented as dimensionless velocity and temperature profiles on the cross section perpendicular to the flow direction inside the channel. For the indented geometry, thermal and dynamic boundary conditions have been considered. The dynamic boundary condition of solution domain in the flow’s direction is periodic, and for modeling the walls, freezing layers of DPD particles with Bounce-Back reflection has been used. For the thermal boundary condition, it is assumed that the wall temperature is constant and the temperature of each DPD particle in contact with the wall is the same as the wall temperature. In this article, for the first time, for modeling the walls four frozen layers with Bounce-Back reflection are used and the effect of particle exit on two and three-layers configurations is investigated. Furthermore, for the first time, modified velocity Verlet integration algorithm is improved by adding heat transfer equations. And considering λ?=?0.65 in the algorithm; the indented geometry is well simulated. In order to validate the results, first, the effect of regular and random initial distribution is compared. Furthermore, the results of wall alignment are compared with those obtained from CFD approach. In this paper, in addition to studying the effect of wall alignment and initial particle arrangement, the influence of the size of cells for averaging and the time steps in the output results are investigated.

     

Diffusioosmosis of electrolyte solutions in a fine capillary slit

The steady diffusioosmotic flows of an electrolyte solution along a charged plane wall and in a capillary channel between two identical parallel charged plates generated by an imposed tangential concentration gradient are theoretically investigated. The plane walls may have either a constant surface potential or a constant surface charge density. The electrical double layers adjacent to the charged walls may have an arbitrary thickness and their electrostatic potential distributions are determined by the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the tangential direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the lateral position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect in the double layer on the diffusioosmotic flow are found to be very significant.