Schematic of the cross-patterned COP chip used in the experiments. The three different gray shadings denote TE (channel W/C), TE with fluorescent sample (channel N/C), and LE (channel E/C). The figure shows the initial condition. After application of the external voltage a sample zone migrates from C to reservoir E, driven by ITP and EOF.
Experimental result showing the combined transport of a fluorescent sample by ITP and EOF, 13, 21, 28, and 76 s after application of the electrostatic potential—from left to right. The figure is composed of micrographs showing sections of the separation channel C/E, see Fig. 1. The single frames have been taken in the course of an ITP run. Both electrophoretic and electro-osmotic transports proceed from left to right. The solid lines denote the side walls of the channel, being apart. The dashed-dotted line denotes the channel center.
Sketch of the model domain showing various geometric parameters. The LE and TE regions are marked by vertical and slanted hatchings. The domain considered in the numerical model is denoted by dashed lines and with corresponding hatchings having a higher contrast. The numbers refer to the boundaries of the model geometry. The corresponding boundary conditions are discussed in the text. Moreover, the polarization of the applied voltage, the direction of electrokinetic transport and the coordinate system are shown.
Time evolution of the natural logarithm of concentration ratios and comparison with the analytical approach of MacInnes and Longsworth (Ref. 18). The data are plotted as a function of the distance from the initial interface position in a comoving frame of reference. The inset shows the fully developed concentration fields in the transition region and the bar marks the characteristic broadening given by Eq. (17).
LE concentration and relative velocity field at different time steps of an ITP/EOF simulation. The images show the central part of the 2D model geometry, cf. Fig. 3, where the upper boundary represents the channel wall and the lower one the symmetry axis. The grayscale denotes the concentration of leading cations, black maximum, light gray zero. The arrows mark the confluence points, i.e., the position of the interface at the symmetry boundary in the middle of the channel. Top: right after the start of the simulation ; center: ; bottom: .
Schematic of the transport processes close to a transition zone in the comoving frame of reference. Thin black arrows denote the direction of convection in the frame of reference comoving with the interface. Thick black straight arrows denote the electrophoretic velocity relative to the flow. The thick white arrow symbolizes radial diffusion.
LE concentration at the end of an ITP/EOF run, . The grayscale denotes the concentration of leading cations, cf. Fig. 5. The deformation of the interface gradually decreases for (left), (center), and (right).
Dispersive broadening derived within the FEM approach for the “steady state” at a fixed position in the channel as a function of . The lines show linear fits to the data points in the cases and , respectively. Below the corresponding LE concentration profiles and velocity fields in a frame of reference comoving with the average EOF speed are displayed for the cases and .
TE concentration profiles resulting from FEM simulations for different values of the electro-osmotic mobility (, , ; from top to bottom). The axial position of the interface is . The arrows show the flow velocity field in the frame of reference comoving with the average EOF velocity.
Dependence of the interface deformation as a function of the electro-osmotic mobility (left) and as a function of the diffusion timescale (right). The squares on the right figure were obtained by changing the diffusion constant while keeping the electrophoretic mobility constant. The circles stem from changing the channel diameter while fixing the diffusion constant. The line fit is based solely on the squares.
Product of cationic concentration fields resulting from the FEM simulation shown in Fig. 5. Black and light gray denote large and small values of the concentration product. The axial positions of the interface are , 0.5, 0.7, and 0.9, from left to right.
Top: LE concentration as in Fig. 5; bottom: as defined in Eqs. (B1) and (B2) computed within the FEM simulation, where dark (light) gray tones denote large (small) values. Maximum and minimum values are given in the figure. For clarity isolines of the LE cation concentration are included.
Boundary conditions applied in the FEM model. See Fig. 3 for the numbering of the boundaries (left column). denotes the unit vector being orthogonal to the respective boundary, the other symbols are defined in the text.
Model parameters used in the FEM simulations, the results of which are shown in the respective figures. The arrows indicate that the same value as in the left neighbor cell has been used.
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