Study on surface properties of PDMS microfluidic chips treated with albumin

Electrokinetic properties and morphology of PDMS microfluidic chips intended for bioassays are studied. The chips are fabricated by a casting method followed by polymerization bonding. Microchannels are coated with 1% solution of bovine serum albumin (BSA) in Tris buffer. Albumin passively adsorbs on the PDMS surface. Electrokinetic characteristics (electro-osmotic velocity, electro-osmotic mobility, and zeta potential) of the coated PDMS channels are experimentally determined as functions of the electric field strength and the characteristic electrolyte concentration. Atomic force microscopy (AFM) analysis of the surface reveals a “peak and ridge” structure of the protein layer and an imperfect substrate coating. On the basis of the AFM observation, several topologies of the BSA-PDMS surface are proposed. A nonslip mathematical model of the electro-osmotic flow is then numerically analyzed. It is found that the electrokinetic characteristics computed for a channel with the homogeneous distribution of a fixed electric charge do not fit the experimental data. Heterogeneous distribution of the fixed electric charge and the surface roughness is thus taken into account. When a flat PDMS surface with electric charge heterogeneities is considered, the numerical results are in very good agreement with our experimental data. An optimization analysis finally allowed the determination of the surface concentration of the electric charge and the degree of the PDMS surface coating. The obtained findings can be important for correct prediction and possibly for robust control of behavior of electrically driven PDMS microfluidic chips. The proposed method of the electro-osmotic flow analysis at surfaces with a heterogeneous distribution of the surface electric charge can also be exploited in the interpretation of experimental studies dealing with protein-solid phase interactions or substrate coatings.     

Electro-osmotic mobility of non-Newtonian fluids

Electrokinetically driven microfluidic devices are usually used to analyze and process biofluids which can be classified as non-Newtonian fluids. Conventional electrokinetic theories resulting from Newtonian hydrodynamics then fail to describe the behaviors of these fluids. In this study, a theoretical analysis of electro-osmotic mobility of non-Newtonian fluids is reported. The general Cauchy momentum equation is simplified by incorporation of the Gouy–Chapman solution to the Poisson–Boltzmann equation and the Carreau fluid constitutive model. Then a nonlinear ordinary differential equation governing the electro-osmotic velocity of Carreau fluids is obtained and solved numerically. The effects of the Weissenberg number (Wi), the surface zeta potential (ψ¯s), the power-law exponent(n), and the transitional parameter (β) on electro-osmotic mobility are examined. It is shown that the results presented in this study for the electro-osmotic mobility of Carreau fluids are quite general so that the electro-osmotic mobility for the Newtonian fluids and the power-law fluids can be obtained as two limiting cases.     

dc electrokinetic transport of cylindrical cells in straight microchannels

Electrokinetic transport of cylindrical cells under dc electric fields in a straight microfluidic channel is experimentally and numerically investigated with emphasis on the dielectrophoretic (DEP) effect on their orientation variations. A two-dimensional multiphysics model, composed of the Navier–Stokes equations for the fluid flow and the Laplace equation for the electric potential defined in an arbitrary Lagrangian–Eulerian framework, is employed to capture the transient electrokinetic motion of cylindrical cells. The numerical predictions of the particle transport are in quantitative agreement with the obtained experimental results, suggesting that the DEP effect should be taken into account to study the electrokinetic transport of cylindrical particles even in a straight microchannel with uniform cross-sectional area. A comprehensive parametric study indicates that cylindrical particles would experience an oscillatory motion under low electric fields. However, they are aligned with their longest axis parallel to the imposed electric field under high electric fields due to the induced DEP effect.     

Effects of non-Newtonian power law rheology on mass transport of a neutral solute for electro-osmotic flow in a porous microtube

Mass transport of a neutral solute for a power law fluid in a porous microtube under electro-osmotic flow regime is characterized in this study. Combined electro-osmotic and pressure driven flow is conducted herein. An analytical solution of concentration profile within mass transfer boundary layer is derived from the first principle. The solute transport through the porous wall is also coupled with the electro-osmotic flow to predict the solute concentration in the permeate stream. The effects of non-Newtonian rheology and the operating conditions on the permeation rate and permeate solute concentration are analyzed in detail. Both cases of assisting (electro-osmotic and poiseulle flow are in same direction) and opposing flow (the individual flows are in opposite direction) cases are taken care of. Enhancement of Sherwood due to electro-osmotic flow for a non-porous conduit is also quantified. Effects if non-Newtonian rheology on Sherwood number enhancement are observed.     

Long-range and superfast trapping of DNA molecules in an ac electrokinetic funnel

In this work we report a microfluidic platform capable of trapping and concentrating a trace amount of DNA molecules efficiently. Our strategy invokes nonlinear electro-osmotic flow induced by charge polarization under high-frequency ac fields. With the asymmetric quadrupole electrode design, a unique converging flow structure can be created for generating focusing effects on DNA molecules. This focusing in turn transforms into a robust funnel that can collect DNA molecules distantly from the bulk and pack them into a compact cone with the aid of short-range dipole-induced self-attraction and dielectrophoresis. Our results reveal that not only can DNA molecules be concentrated within just a few seconds, but also they can be focused into threads of 1 mm in length, demonstrating the superfast and long-range trapping capability of this funnel. In addition, pico M DNA solutions can be concentrated with several decades of enhancement without any continuous feeding. Alternating concentration and release of DNA molecules is also illustrated, which has potentials in concentrating and transporting biomolecules in a continuous fashion using microdevices.     

Effect of electrical double layer on electric conductivity and pressure drop in a pressure-driven microchannel flow

The effect of an electrical double layer (EDL) on microchannel flow has been studied widely, and a constant bulk electric conductivity is often used in calculations of flow rate or pressure drop. In our experimental study of pressure-driven micropipette flows, the pipette diameter is on the same order of magnitude as the Debye length. The overlapping EDL resulted in a much higher electric conductivity, lower streaming potential, and lower electroviscous effect. To elucidate the effect of overlapping EDL, this paper developed a simple model for water flow without salts or dissolved gases (such as CO₂) inside a two-dimensional microchannel. The governing equations for the flow, the Poisson, and Nernst equations for the electric potential and ion concentrations and the charge continuity equation were solved. The effects of overlapping EDL on the electric conductivity, velocity distribution, and overall pressure drop in the microchannel were quantified. The results showed that the average electric conductivity of electrolyte inside the channel increased significantly as the EDL overlaps. With the modified mean electric conductivity, the pressure drop for the pressure-driven flow was smaller than that without the influence of the EDL on conductivity. The results of this study provide a physical explanation for the observed decrease in electroviscous effect for microchannels when the EDL layers from opposing walls overlap.     

Dynamic superconcentration at critical-point double-layer gates of conducting nanoporous granules due to asymmetric tangential fluxes

A transient 10⁶-fold concentration of double-layer counterions by a high-intensity electric field is demonstrated at the exit pole of a millimeter-sized conducting nanoporous granule that permits ion permeation. The phenomenon is attributed to a unique counterion screening dynamics that transforms half of the surface field into a converging one toward the ejecting pole. The resulting surface conduction flux then funnels a large upstream electro-osmotic convective counterion flux into the injecting hemisphere toward the zero-dimensional gate of the ejecting hemisphere to produce the superconcentration. As the concentrated counterion is ejected into the electroneutral bulk electrolyte, it attracts co-ions and produce a corresponding concentration of the co-ions. This mechanism is also shown to trap and concentrate co-ion microcolloids of micron sizes too (macroions) and hence has potential application in bead-based molecular assays.     

On the qualitative behaviors of solutions of some differential equations of higher order with multiple deviating arguments

We study the boundedness of the solutions to a non-autonomous and non-linear differential equation of second order with two constant deviating arguments. We give two examples to illustrate the main results. By this work, we extend some boundedness results obtained for a differential equation with a constant deviating argument in the literature to the boundedness of the solutions of a differential equation with two constant deviating arguments.     

Contactless microfluidic pumping using microchannel-integrated carbon black composite membranes

The ability to pump and manipulate fluid at the micron-scale is a basic requirement for microfluidic platforms. Many current manipulation methods, however, require expensive and bulky external supporting equipment, which are not typically compatible for portable applications. We have developed a contactless metal electro-osmotic micropump capable of pumping conductive buffers. The pump operates using two pairs of gallium metal electrodes, which are activated using an external voltage source and separated from a main flow channel by a thin micron-scale polydimethylsiloxane (PDMS) membrane. The thin contactless membrane allows for field penetration and electro-osmotic flow within the microchannel, but eliminates electrode damage and sample contamination commonly associated with traditional DC electro-osmotic pumps that utilize electrodes in direct contact with the working fluid. Our previous work has demonstrated the effectiveness of this method in pumping deionized water. However, due to the high resistivity of PDMS, this method proved difficult to apply towards manipulating conductive buffers. To overcome this limitation, we fabricated conductive carbon black (CB) powder directly into the contactless PDMS membranes. The increased electrical conductivity of the contactless PDMS membrane significantly increased micropump performance. Using a microfluidic T-channel device and an electro-osmotic flow model, we determined the influence that CB has on pump pressure for CB weight percents varying between 0 and 20. The results demonstrate that the CB increases pump pressure by two orders of magnitude and enables effective operations with conductive buffers.     

Transport of particles and microorganisms in microfluidic channels using rectified ac electro-osmotic flow

A new method is demonstrated to transport particles, cells, and other microorganisms using rectified ac electro-osmotic flows in open microchannels. The rectified flow is obtained by synchronous zeta potential modulation with the driving potential in the microchannel. Experiments were conducted to transport both neutral, charged particles, and microorganisms of various sizes. A maximum speed of 50 μm∕s was obtained for 8 μm polystyrene beads, without any electrolysis, using a symmetrical square waveform driving electric field of 5 V∕mm at 10 Hz and a 360 V gate potential with its polarity synchronized with the driving potential (phase lag=0°).     

Estimate for the root-location of linear systems via the lyapunov matrix equation

It is well known that the Lyapunov matrix equation can be utilized to obtain the estimate for the transient behavior of linear constant systems. This paper shows that the equation gives information not only on the maximum real part of the characteristic roots of system matrix but also on other extremal values to these roots.     

The effect of the surface functionalization and the electrolyte concentration on the electrical conductance of silica nanochannels

It is known that the conductance of nanochannels as a function of electrolyte concentration deviates from a linearly proportional relationship and approaches a value independent of the concentration as the electrolyte concentration is lowered. Most of the proposed models account for this behavior by considering a constant surface charge density and an ideal electrolyte solution. However, at low electrolyte concentrations, the ideal electrolyte approximation is no longer valid because the ions that result from the atmospheric carbon dioxide dissolution in water dominate the ionic concentration. In this paper, arrays of silica nanochannels were electrically characterized via conductance measurements. The conductance at low salt concentrations is modeled by a variable surface charge model that accounts for all ionic species in solution. This model was used to determine the variable surface charge of the bare silica nanochannels as well as of chemically modified nanochannels. The model correctly predicted the variation of the nanochannel conductance observed after silane (aminopropyldimethylethoxysilane) functionalization and single-strand DNA immobilization. Finally, pH modification of bulk KCl solutions was employed as an alternative method of changing the surface charge of silica nanochannels. Surface charge calculated from conductance measurements performed at different bulk pH values confirmed that the surface charge of the silica nanochannel walls is sensitive to the H⁺ concentration.     

Understanding electrokinetics at the nanoscale: A perspective

Electrokinetics promises to be the microfluidic technique of choice for portable diagnostic chips and for nanofluidic molecular detectors. However, despite two centuries of research, our understanding of ion transport and electro-osmotic flow in and near nanoporous membranes, whose pores are natural nanochannels, remains woefully inadequate. This short exposition reviews the various ion-flux and hydrodynamic anomalies and speculates on their potential applications, particularly in the area of molecular sensing. In the process, we revisit several old disciplines, with some unsolved open questions, and we hope to create a new one.     

Induced charge electro-osmotic concentration gradient generator

Biomolecule gradients play an important role in the understanding of various biological processes. Typically, biological cells are exposed to linear and nonlinear concentration gradients and their response is studied for understanding cell growth, cell migration, and cell differentiation mechanisms. Recent studies have demonstrated the use of microfluidic devices for precise and stable concentration gradient generation. However, most of the reported devices are geometrically complex and lack dynamic controllability. In this work, a novel microfluidic gradient generator is presented which utilizes the induced charge electro-osmosis (ICEO) by introducing conducting obstacle in the microchannel. With the ICEO flow component, significant transverse convection can be generated within the microchannel, which can, in turn, be used to create nonlinear as well as asymmetric gradients. The characteristics of the developed concentration gradient are dependent on the interplay between fixed charge electro-osmotic and ICEO flows. It is shown that the proposed device can switch between linear and nonlinear gradients by just altering the applied electric field. Finally, the formation of user-defined concentration profiles (linear, convex, and concave) is demonstrated by varying the conducting obstacle size.     

Extensional flow of blood analog solutions in microfluidic devices

In this study, we show the importance of extensional rheology, in addition to the shear rheology, in the choice of blood analog solutions intended to be used in vitro for mimicking the microcirculatory system. For this purpose, we compare the flow of a Newtonian fluid and two well-established viscoelastic blood analog polymer solutions through microfluidic channels containing both hyperbolic and abrupt contractions∕expansions. The hyperbolic shape was selected in order to impose a nearly constant strain rate at the centerline of the microchannels and achieve a quasihomogeneous and strong extensional flow often found in features of the human microcirculatory system such as stenoses. The two blood analog fluids used are aqueous solutions of a polyacrylamide (125 ppm w∕w) and of a xanthan gum (500 ppm w∕w), which were characterized rheologically in steady-shear flow using a rotational rheometer and in extension using a capillary breakup extensional rheometer (CaBER). Both blood analogs exhibit a shear-thinning behavior similar to that of whole human blood, but their relaxation times, obtained from CaBER experiments, are substantially different (by one order of magnitude). Visualizations of the flow patterns using streak photography, measurements of the velocity field using microparticle image velocimetry, and pressure-drop measurements were carried out experimentally for a wide range of flow rates. The experimental results were also compared with the numerical simulations of the flow of a Newtonian fluid and a generalized Newtonian fluid with shear-thinning behavior. Our results show that the flow patterns of the two blood analog solutions are considerably different, despite their similar shear rheology. Furthermore, we demonstrate that the elastic properties of the fluid have a major impact on the flow characteristics, with the polyacrylamide solution exhibiting a much stronger elastic character. As such, these properties must be taken into account in the choice or development of analog fluids that are adequate to replicate blood behavior at the microscale.     

Velocity effect of a lightning charge wave moving along a single wire transmission line

A wave equation solution for a moving charge on a simple one-wire, lossless transmission line is presented using Laplace transforms. The effect of lightning charge velocity on line potential as the charge moves along the transmission line is shown mathematically to be discontinuous should the wave velocity become the speed of light.     

A formula for the potential of a polygon with varying charge density

Explicit formulae are derived giving the Newtonian potential and field of a polygon whose surface charge density is a linear or quadratic function. The formulae involve only the elementary functions, logarithm and arctangent. Special attention is given to triangles and rectangles because they appear in various finite element calculations. The formulae may be used, together with the Fredholm integral equation, to solve electric or magneticfield problems.     

CHARACTERISTICS OF THE FRACTALS APPEARED ON ALUMINIUM FOIL IRRADIATED BY INTENSE RELATIVISTIC ELECTRON BEAM

ＣＨＡＲＡＣＴＥＲＩＳＴＩＣＳＯＦＴＨＥＦＲＡＣＴＡＬＳＡＰＰＥＡＲＥＤＯＮＡＬＵＭＩＮＩＵＭＦＯＩＬＩＲＲＡＤＩＡＴＥＤＢＹＩＮＴＥＮＳＥＲＥＬＡＴＩＶＩＳＴＩＣＥＬＥＣＴＲＯＮＢＥＡＭ￥ＧａｏＨｕａｉ－ｌｉｎ；ＰａｎＹｕ－ｌｉ（ＣｈｉｎａＩｎｓｔ...     

Induced charge electro osmotic mixer: Obstacle shape optimization

Efficient mixing is difficult to achieve in miniaturized devices due to the nature of low Reynolds number flow. Mixing can be intentionally induced, however, if conducting or nonconducting obstacles are embedded within the microchannel. In the case of conducting obstacles, vortices can be generated in the vicinity of the obstacle due to induced charge electro-osmosis (ICEO) which enhances mixing of different streams: the obstacle shape affects the induced zeta potential on the conducting surface, which in turn influences the flow profile near the obstacle. This study deals with optimization of the geometric shape of a conducting obstacle for the purpose of micromixing. The obstacle boundary is parametrically represented by nonuniform rational B-spline curves. The optimal obstacle shape, which maximizes the mixing for given operating conditions, is found using genetic algorithms. Various case studies at different operating conditions demonstrated that the near right triangle shape provides optimal mixing in the ICEO flow dominant regime, whereas rectangular shape is the optimal shape in diffusion dominant regime. The tradeoff between mixing and transport is examined for symmetric and nonsymmetric obstacle shapes.     

Riccati differential equations : William T.^Reid. 216 pages,diagrams, 6x9 in. New York,Academic Press Inc. (Mathematics in Science and Industry Series), Vol. 86, 1972. Price, $14.00.

The paper describes methods of carrying out the minimum weight design of finned surfaces of various types. For each type of surface (flat, cylindrical, etc.) two cases are considered. First, a method is described by which it is possible to obtain the optimum surface profile of fins required to dissipate a certain amount of heat from the given surface, there being no restriction on the fin height. This analysis is then extended for the case when the fin height is given. The solutions are presented for a number of cases and the results are discussed to illustrate the importance of various parameters in the design.