Peak tailing in electrophoresis due to alteration of the wall charge by adsorbed analytes a: Numerical simulations and asymptotic theory

When analytes containing cationic components, such as proteins, are separated in fused silica capillaries or micro-chips, they adsorb strongly to the negatively charged channel walls. Broadened and highly asymmetric peaks in the detector signal is symptomatic of the presence of such wall interactions. Band broadening is caused by the introduction of shear into the electroosmotic flow which leads to Taylor dispersion. The shearing flow in turn is caused by axial variations in zeta-potential due to adsorbed analytes. In this paper, numerical solutions of the coupled electro-hydrodynamic equations for fluid flow and the advection-diffusion equation for analyte concentration are presented in the limit of thin Debye layers. The simulations reproduce many of the qualitative effects of wall adsorption familiar from observation. Further, the simulation results are compared, and found to agree very well (to within a percent for characteristic values of the parameters) with a recently developed asymptotic theory.     

Motion of a drop on a solid surface due to a wettability gradient

The hydrodynamic force experienced by a spherical-cap drop moving on a solid surface is obtained from two approximate analytical solutions and used to predict the quasi-steady speed of the drop in a wettability gradient. One solution is based on approximation of the shape of the drop as a collection of wedges, and the other is based on lubrication theory. Also, asymptotic results from both approximations for small contact angles, as well as an asymptotic result from lubrication theory that is good when the length scale of the drop is large compared with the slip length, are given. The results for the hydrodynamic force also can be used to predict the quasi-steady speed of a drop sliding down an incline.     

Broadside mobility of a disk in a viscous fluid near a plane wall with no-slip boundary condition

The broadside motion of a disk in a viscous fluid towards a planar wall with no-slip boundary condition is studied on the basis of the steady-state Stokes equations. It is shown that flow velocity and pressure of the fluid can be found conveniently from a superposition of elementary complex stream functions. The two amplitude functions characterizing the superposition are found from the numerical solution of a pair of integral equations for the axial and radial velocity components at the disk. The numerical procedure converges fast, provided the distance to the plane is not much smaller than the radius of the disk. For small distance the flow is well approximated by lubrication theory.     

Unsteady transport phenomena in free-flow electrophoresis--prerequisite of ultrafast sample cleaning in microfluidic devices

The evolution partial differential equations describing the transport processes induced by hydrodynamic flow in free-flow electrophoresis (FFE) are solved by the generalized dispersion theory. Our theoretical analysis demonstrates that the central injection of solutes into a relatively fast hydrodynamic flow enables to transport them to the channel outlet well before they are spread through the width of the channel and their migration is negatively affected by a contact with walls. In this case, the axial zone spreading decreases by increasing the linear velocity of hydrodynamic flow. The resulting dependencies of convective and dispersion coefficients on the velocity of flow and parameters of the separation channel show the optimum separation conditions with respect to resolution and analysis time. Due to the unsteady character of transport processes, effective FFE separations can potentially be performed in a microfluidic device in seconds. This is a reasonable time to separate low-molecular mass impurities in the electric field. Thus, a fast and efficient sample cleaning before subsequent analysis by electrospray ionization-mass spectrometry (ESI-MS) or another separation method can be performed.     

Analysis of the microfluid flow in an evaporating sessile droplet

The axisymmetric time-dependent flow field in an evaporating sessile droplet whose contact line is pinned is studied numerically and using an analytical lubrication theory with a zero-shear-stress boundary condition on the free surface of the droplet at low capillary and Reynolds numbers. A finite element algorithm is developed to solve simultaneously the vapor concentration and flow field in the droplet under conditions of slow evaporation. The finite element solution confirms the accuracy of the lubrication solution, especially when terms of higher order in the droplet flatness ratio (the ratio of droplet height to radius, h/R) are included in the lubrication theory to account more accurately for the singular flow near the contact line.     

Effects of injector geometry and sample matrix on injection and sample loading in integrated capillary electrophoresis devices

The double-T injector design employed in many microchip capillary electrophoresis devices allows for the formation of very small (50-500 pL) sample plugs for subsequent analysis on-chip. In this study, we show that sample plugs formed at the channel junction can be geometrically defined. The channel width and injector symmetry prove to be of great importance to good performance. A unique pushback of solvent into the side channels can be induced when the side channels have a very low resistance to flow, and this helps to better define the injected sample plug. Samples and running buffers of differing ionic strength (e.g., 10 mM KCl buffer and 20 mM KCl sample) can yield widely variable results in terms of plug shape and amount injected (variations of 1.5 to 10x). Applying bias voltages to all the intersecting channels aids in controlling the plug shape. However, when the ionic strengths of buffer and sample are not matched, the actual amount injected (up to 10x variations) can be inconsistent with the appearance of the plug formed in the injector (up to only 30 % variations). Operating at constant pH and ionic strength produced the most consistent results. This report examines the effects of altering the injector geometry and solution ionic strengths, and presents the results of using bias voltages to control plug formation. The observed results should provide a benchmark for modeling of the fluid dynamics in channel intersections.     

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.     

The thermodynamic limit of linear gradient chromatography

The thermodynamic limit of the elution profile for solutes in linear gradient chromatography is obtained from the analytical solution of the equation for the ideal model of chromatography, Eq. (12). This limit is of great interest in both preparative and analytical chromatographies because it specifies the maximum possible concentration profile that can be achieved at elution. Elution profiles that are obtained from simulated experiments of the equilibrium dispersive model, Eq. (8), are compared with predictions made by the presented theory as well as the theory by Poppe [11]. It is found that for short injection times the simulated experimental peak is Gaussian like and its width agrees very well with the theory of Poppe. When the injection time increases, the experimental elution profile gradually approaches the profile that is obtained as the thermodynamic limit.     

Characterization and optimization of slanted well designs for microfluidic mixing under electroosmotic flow

Recently, a series of slanted wells on the floor of a microfluidic channel were experimentally shown to successfully induce off-axis transport and mixing of two confluent streams when operating under electroosmotic (EO) flow. This paper will further explore, through numerical simulations, the parameters that affect off-axis transport under EO flow with an emphasis on optimizing the mixing rate of (a). two confluent streams in steady-state or (b). the transient scenario of two confluent plugs of material, which simulates mixing after an injection. For the steady-state scenario, the degree of mixing was determined to increase by changing any of the following parameters: (1). increasing the well depth, (2). decreasing the well angle relative to the axis of the channel, and (3). increasing the EO mobility of the well walls relative to the mobility of the main channel. Also, it will be shown that folding of the fluid can occur when the well angle is sufficiently reduced and/or when the EO mobility of the wells is increased relative to the channel. The optimum configuration for the transient problem of mixing two confluent plugs includes shallow wells to minimize the well residence time, and an increased EO mobility of the well walls relative to the main channel as well as small well angles to maximize off-axis transport. The final design reported here for the transient study reduces the standard deviation of the concentration across the channel by 72% while only increasing the axial dispersion of the injected plug by 8.6 % when compared to a plug injected into a channel with no wells present. These results indicate that a series of slanted wells on the wall of a microchannel provides a means for controlling and achieving a high degree of off-axis transport and mixing in a passive manner for micro total analysis system (microTAS) devices that are driven by electroosmosis.     

Electrohydrostatically driven flow and instability in a vertical hele-shaw cell

The electrohydrostatic capillary-driven flow of a viscous poorly conducting Newtonian fluid rising between conducting parallel plates is studied both theoretically and experimentally. By scaling the problem with a pressure and time derived by considering Maxwell stresses along the interface, it is determined that the dimensionless parameters governing the flow are the hydrostatic bond (Bo(H)), electrostatic bond (Bo(E)) and electrostatic Reynolds (Re(E)) numbers. A lubrication theory analysis, in the limit Re(E) --> 0, of the momentum balance leads to an analytical solution for the elapsed time versus interface position that is analogous to one derived by Washburn (1921) for the capillary pressure-driven flow of a fluid in cylindrical capillaries (Washburn, E. W. Phys. Rev. 1921, 17 (3), 273-283). Experiments are performed using silicone and castor oil at gap spacing less than the capillary length for two ranges of electrostatic Reynolds numbers 0.001 < Re(E) < 0.01 and 10 < Re(E) < 1000. The experimental results for the interface displacement as a function of elapsed time are compared with the theoretical predictions. At large electrostatic Reynolds numbers (>1), a convective instability is observed in plots of the interface position as a function of time. The propagating front also reveals an interfacial instability for large electrostatic Reynolds numbers coupled with large fluid displacements. The theory and experiments for the static rise height show good agreement with theory while the flow dynamics show good qualitative agreement in the applicable limits at low electrostatic Reynolds numbers.     

Electrokinetic-vortex formation near a two-part cylinder with same-sign zeta potentials in a straight microchannel

Vortex formation near a two-part cylinder with zeta potentials of different values but the same sign under an external DC electric field is numerically investigated in this paper. The cylinder, inserted in a straight microchannel filled with an aqueous solution, is composed of an upstream part and a downstream part. When a DC electric field is applied in the channel, under certain conditions, the vortex will form near the cylinder due to the different velocities of electroosmotic flow generated on the cylinder surface. The numerical results reveal that the larger the velocity difference of electroosmotic flow generated on the two-part cylinder and the smaller the channel width, the more conducive to vortex formation in the channel. In addition, if the zeta potential ratios of cylinder downstream part to upstream part and channel wall to cylinder upstream part are unchanged, the DC electric field strength and the zeta potential value do not affect the pattern of vortices formed in the channel. This study provides a way for vortex formation in microchannels and has the potential application in microfluidic devices.     

Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet

We study the effects of Marangoni stresses on the flow in an evaporating sessile droplet, by extending a lubrication analysis and a finite element solution of the flow field in a drying droplet, developed earlier. The temperature distribution within the droplet is obtained from a solution of Laplace's equation, where quasi-steadiness and neglect of convection terms in the heat equation can be justified for small, slowly evaporating droplets. The evaporation flux and temperature profiles along the droplet surface are approximated by simple analytical forms and used as boundary conditions to obtain an axisymmetric analytical flow field from the lubrication theory for relatively flat droplets. A finite element algorithm is also developed to solve simultaneously the vapor concentration, and the thermal and flow fields in the droplet, which shows that the lubrication solution with the Marangoni stress is accurate for contact angles as high as 40 degrees. From our analysis, we find that surfactant contamination, at a surface concentration as small as 300 molecules/microm(2), can almost entirely suppress the Marangoni flow in the evaporating droplet.     

A note on the coating of an inclined plane in the presence of soluble surfactant

We consider the flow of a thin liquid film coating an inclined plane in the presence of a soluble surfactant. A two-dimensional three-equation model is derived using lubrication theory in the rapid diffusion limit and then used to investigate the stability of the fluid height and the surfactant surface and bulk concentrations. We present solutions for an insoluble surfactant system, which are then contrasted with those obtained for a system containing a soluble surfactant; both transient growth and fully nonlinear two-dimensional simulation results are discussed. Our results indicate that the characteristics of the fingering phenomena which accompany the flow are altered by the effects of solubility. In particular, we find that these effects de-stabilise the system further over an intermediate range of surfactant solubility.     

Nanoparticles in nematic liquid crystals: interactions with nanochannels

A mesoscale theory for the tensor order parameter Q is used to investigate the structures that arise when spherical nanoparticles are suspended in confined nematic liquid crystals (NLCs). The NLC is "sandwiched" between a wall and a small channel. The potential of mean force is determined between particles and the bottom of the channels or between several particles. Our results suggest that strong NLC-mediated interactions between the particles and the sidewalls of the channels, on the order of hundreds of k(B)T, arise when the colloids are inside the channels. The magnitude of the channel-particle interactions is dictated by a combination of two factors, namely, the type of defect structures that develop when a nanoparticle is inside a channel, and the degree of ordering of the nematic in the region between the colloid and the nanochannel. The channel-particle interactions become stronger as the nanoparticle diameter becomes commensurate with the nanochannel width. Nanochannel geometry also affects the channel-particle interactions. Among the different geometries considered, a cylindrical channel seems to provide the strongest interactions. Our calculations suggest that small variations in geometry, such as removing the sharp edges of the channels, can lead to important reductions in channel-particle interactions. Our calculations for systems of several nanoparticles indicate that linear arrays of colloids with Saturn ring defects, which for some physical conditions are not stable in a bulk system, can be stabilized inside the nanochannels. These results suggest that nanochannels and NLCs could be used to direct the assembly of nanoparticles into ordered arrays with unusual morphologies.     

Performance evaluation of an axially viewed horizontal inductively coupled plasma for optical emission spectrometry

A performance evaluation of a horizontal axially viewed inductively coupled plasma (ICP) for optical emission spectrometry is presented. The main contribution of this work is the elucidation of the sources of analytical performance differences using practical diagnostics in the comparison of axial and conventional radial viewing of the ICP. Figures of merit such as detection limit, background equivalent concentration, precision, and dynamic range are compared for both viewing arrangements. The detection limit improvements with axial viewing, known from previous work in the literature, are shown to be understood in the context of the signal-to-background-ratio relative-standard-deviation-of-the-background (SBR-RSDB) theory. The usefulness of the SBR-RSDB approach as a diagnostic tool for understanding the detection limit improvement and identifying performance differences is demonstrated. This approach can be further utilized for quality control and quality assurance of instrument performance and detection limit results. Other characteristic differences between axial and radial viewing are presented including matrix effects on line signals and the magnitudes of spectral interferences from OH bands. An overall improvement factor of five in detection power was observed when using axial viewing compared with radial viewing.     

Electrokinetic lift force for a charged particle moving near a charged wall — a modified theory and experiment

We present the refined theory of the electrokinetic lift force for a charged particle moving at a charged wall at the distance much larger than the double layer thickness. The theory is based on the lubrication approximation for the solution of the Stokes equation for the flow around a long cylinder moving near a solid wall. The “thin double layer” approximation is used to solve the ionic balance and electro-osmotic flow equations. The electrokinetic lift force is then obtained by integration of the viscous stress tensor as well as the Maxwell stress tensor over the particle surface. The resulting lift force for the cylinder translating, rotating at the wall as well as for the stationary cylinder in the wall shear flow, is considered. Following this, we apply the Derjaguin approximation to transform the obtained results to the sphere–wall geometry and we compare our theoretical predictions with the measurements of the electrokinetic lift force performed in the “colloidal particle collider” apparatus for the latex particles suspended in the glycerol–water solutions. Our theoretical results for the electrokinetic lift force exceeds by several orders of magnitude one obtained from the previously developed theory and are in a good agreement with experimental findings.     

Study of Joule heating effects on temperature gradient in diverging microchannels for isoelectric focusing applications

IEF is a high-resolution separation method taking place in a medium with continuous pH gradients, which can be set up by applying electrical field to the liquid in a diverging microchannel. The axial variation of the channel cross-sectional area will induce nonuniform Joule heating and set up temperature gradient, which will generate pH gradient when proper medium is used. In order to operationally control the thermally generated pH gradients, fundamental understanding of heat transfer phenomena in microfluidic chips with diverging microchannels must be improved. In this paper, two 3-D numerical models are presented to study heat transfer in diverging microchannels, with static and moving liquid, respectively. Through simulation, the temperature distribution for the entire chip has been revealed, including both liquid and solid regions. The model for the static liquid scenario has been compared with published results for validation. Parametric studies have showed that the channel geometry has significant effects on the peak temperature location, and the electrical conductivity of the medium and the wall boundary convection have effects on the generated temperature gradients and thus the generated pH gradients. The solution to the continuous flow model, where the medium convection is considered, shows that liquid convection has significant effects on temperature distribution and the peak temperature location.     

Diffusioosmotic flow in rectangular microchannels

The diffusioosmosis of an electrolyte solution inside a uniformly charged rectangular channel at steady locally developed conditions is the subject of this study. Utilizing a finite element based numerical procedure, we try to estimate the errors incurred by modeling the actual rectangular geometry of typical microchannels as a slit. We demonstrate that the flow pattern and direction are generally dependent upon the width‐to‐height ratio of the channel. Such a finding, besides showing the ineffectiveness of the slit geometry in representing a rectangular channel of small aspect ratio, informs us of another mechanism of controlling the diffusioosmotic flow. Inspections of the mean velocity reveal that, although it drastically grows by increasing the aspect ratio at smaller values of this parameter, no significant change is observed when the aspect ratio is 5 or higher. The same trend is observed when EDL is shrunk and is considered as a basis for the introduction of a slip‐like velocity, similar to the concept of the Helmholtz–Smoluchowski electroosmotic velocity, which will be of high practical importance when dealing with a micronsized channel. Because of its significance, an expression is presented for this slip velocity utilizing the curve fitting of the results, assuming a typical Peclet number.