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 ͑BSA͒ in Tris buffer. Albumin passively adsorbs on the PDMS surface. Electrokinetic characteristics ͑electro-osmotic velocity, electro-osmotic mobility, and zeta potential͒ of the coated PDMS channels are experimentally determined as functions of the electric field strength and the characteristic electrolyte concentration. Atomic force microscopy ͑AFM͒ 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.
AC electroosmotic micropumps are suggested to be powerful tools for electrolyte dosing in various microand nanofluidic systems. In this paper, we compare two modeling approaches for studying the AC electroosmosis in the following micro and nanochannel systems: (i) a traveling-wave AC pump with a spatially continuous wave of electric potential applied on a planar boundary, (ii) a traveling-wave AC pump with a wave of electric potential applied on a set of discrete planar electrodes, and (iii) an AC pump with a set of non-planar electrodes. The equilibrium approach is based on the use of capacitor-resistor boundary conditions for electric potential and the slip boundary conditions for velocity at electrode surfaces. The non-equilibrium approach uses the mathematical model based on the Poisson equation and the non-slip boundary conditions. We have observed discrepancies between the predictions given by the both models and then we have identified their possible reasons. The comparison of the equilibrium and non-equilibrium results further showed three important actualities: (a) how the equilibrium model overestimates or underestimates the net velocity, (b) how the velocity maxima in the frequency characteristics can be shifted, if the equilibrium model assumptions are not satisfied, (c) the parametric region where the equilibrium model is applicable. Because the data are obtained in a dimensionless form, they can be exploited for AC electroosmotic studies. We discuss the limitations of the equilibrium and non-equilibrium models and compare selected predictions with available experimental data. List of symbolsDiffusivity (2 9 10 -9 m 2 s -1 ) fFrequency (s -1 ) F The Faraday constant (96,485 C mol -1 ) g Gap width (m) g = x m?1 L -x m R h Electrode height (m) H Height of a periodic segment (m) J Ion flux intensity (mol m -2 s -1 ) k Wave number (m -1 ) k = 2p/L L Length of a periodic segment (m) L e Electrode width (m) L e = x m R -x m L n Number of electrodes n Fx Number of finite elements in the x-direction n Fy Number of finite elements in the y-direction n Normal unit vector p Pressure (Pa) q Electric charge density (C m -3 ) R Molar gas constant (8.314 J K -1 mol -1 ) t Time (s) t Tangential unit vector T Temperature (298.15 K) T t Period of the electric signal (s) T t = f -1 v Horizontal component of velocity (m s -1 ) hv i Net velocity (m s -1 ) vVelocity (m s -1 ) wElectric potential wave velocity (m s -1 ) w = L/T t = x/kx Spatial coordinate (m) y Spatial coordinate (m)Greek symbols a Phase of an AC signal e Electrolyte permitivity (6.9503 9 10 -10 F m -1 ) u Electric potential (V) gDynamic viscosity (0.001 Pa s) k D The Debye length (m) k 2 D ¼ eD r w Complex electric potential (V) qDensity (1,000 kg m -3 ) rSpecific conductivity (S m -1 ) r ¼ 2c D F 2
This paper deals with the mathematical modeling of traveling-wave ac electro-osmotic micropumps with a zig-zag arrangement of microelectrodes. A mathematical model based on the Poisson-Nernst-Planck-Navier-Stokes description is used in this study within the physically relevant ranges of the model parameters. We present an extensive set of parametrical studies concerning the dependence of the net velocity on a variety of parameters. We also demonstrate limits of the validity of the commonly used Capacitor-Resistor-Capacitor model. In order to achieve high net velocities, we found that there are the optimal values of the electrode length, the shift between the top and bottom electrode arrays, and the signal frequency. Performance of the zig-zag micropumps is evaluated by the means of back-pressure loads. The suggested zig-zag design brings two main benefits: (i) it allows an easier construction of four-phase traveling-wave micropumps without the need of spatially complicated electrode connections, and (ii) the zig-zag pumps can provide higher flow rates than those with single-sided coplanar arrangements. Another robust feature of the proposed zig-zag system is that a single flow reversal is observed at the ac frequency approximately six times higher than the reciprocal resistor-capacitor time even in low-amplitude regimes.
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