The induction of vortices in rectangular open tubular channels was demonstrated in in 5 and 3 µm channels for ARs (depth/width) up to around 7.
It was observed that the reduction in dispersion reduction due to lateral mixing becomes smaller with increasing salt concentration. This is expected, as higher ionic strengths decrease the Debye length and the electroosmotic flow scales with the Debye length. We find that the frequency at which the largest reduction in dispersion is found does not increase with higher salt concentration. This is surprising, as we expect the frequency of maximum AC-EOF to linearly increase with the inverse of the RC time of the system.
When working with 5 µm channels, it is interesting to note that lateral mixing (κ_aris) reduces κ_aris in an AR = 4 channel from 5.33/210 to 2.88/210 at 6 Vpp applied voltage, approaching the value of 1.76/210 for an AR=1 channel. It is well known that OT columns (AR=1) are the best conceivable column format, but that unfortunately for most applications the volume loadability is too small for practical applications. By introducing lateral mixing, the price to be paid for increasing volume loadability (a factor of 8 increase in C-term for ARs above 8) can therefore be greatly reduced.
In the 6 Vpp vortex mode, the experimentally obtained κ_aris value thus is reduced by a factor of 4. From Fig. 2D it can be appreciated that at a flow rate of 1 mm/s an H value of around 4 µm is achieved, close to the optimal value of the van Deemter curve in absence of lateral flow operated at around 200 µm/s. The same dispersive behavior is therefore attained in a residence time that is 5-fold shorter. When operating this column at a flow rate of around 1 mm/s, a pressure of only 5.7 bar/m column length is needed.19 A 20 cm long column for example would only need 1.14 bar applied pressure, and would deliver N=50,000 plates in 200 s. Thus pressure is not limiting when using commercial instrumentation. Under retained conditions the separation time will increase (e.g. 5-10 fold for practical applications), but the pressure requirement will relax as the optimal velocity will shift to lower values. With the extremely low pressures that thus are needed, the use of portable pumps such as the highly miniaturized EOF pumps (able to generate more than 10 bar nowadays becomes feasible.
For the work in 3 µm channels, van Deemter plots for applied voltages of 2 to 8 Vpp in the 3 µm x 20 µm channel were obtained. When peak-to-peak voltages of 2 and 4 V are applied, a gradual decrease in C-term dispersion occurs. κ_aris as calculated from the experimental results decreases from κ_aris = 10.5/210 in the absence of lateral mixing, to 8.13/210 (-23 %) at 2Vpp and 5.96/210 (-44 %) at 4 Vpp. The 44 % reduction in κ_aris is significantly smaller than for the 5 µm wide channel (reduction of 79 %), which we ascribe to the fact that the contribution of diffusion to dispersion becomes more and more significant when downscaling the channel width. Nevertheless, an absolute plate height value of H=2.7 µm is obtained at the velocity of 600 µm/s, very close to the optimal value of the van Deemter curve in the absence of EOF at 150 µm/s, hence reducing elution time 4-fold for a similar plate count. As the pressure drop needed for a 600 µm/s flow rate in a 3 µm channel is 14 bar/m, again pressure does not seem to be a limiting factor as instrumentation nowadays delivers standard 400 bar, a pressure that the silicon-glass devices furthermore can easily withstand. The corresponding plate count per m is 370370 plates/m, which is achieved in 28 min.
Next, we applied the macrotransport theory introduced previously by Brenner with the addition of surface adsorption on the channel walls. The proposed model considers both effect of lateral vortices, induced by AC-electroosmotic flows, and retention on Taylor-Aris dispersion. The presented results serve as a guideline for the manufacturing of (vortex chromatography) separation devices, taking into account retention, channel size, aspect ratio, applied potential to induce the lateral flow and molecular diffusion coefficent of the analyte (nanoparticles, HbA1c,dextran, etc.).
