Tomasz Glawdel and Carolyn Ren*
Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Ave West, Waterloo, ON, Canada, N2L3G1, Tel: 1-519-88-4567 X 33030, Fax: 1-519-885-5862, Email: c3ren@uwaterloo.ca
Introduction
Electrical current monitoring is a technique for measuring the area average velocity of electro-osmotic flow (EOF) by monitoring the electrical current change for a solution replacement process, where one electrolyte solution is replacing another slightly less concentrated one (or slightly concentrated one) via EOF. EOF is the bulk liquid motion generated when an external electrical field is applied to the liquid in a microchannel tangentially, due to the presence of a thin layer with net charges near the solid-liquid interface which is called the electrical double layer (EDL) [1].
In electrical current monitoring methods, the microchannel is initially filled with one electrolyte solution producing a constant electrical current through the microchannel. After the replacement process starts via EOF, the overall electrical resistance of the liquid and hence the current in the microchannel changes, as illustrated in Figure 1. Once the replacement process is completed, the current will reach a plateau again. This current-time relationship allows the area average velocity of EOF to be determined using the total length method and the slope method as explained later. For the purpose of measuring the area average EOF velocity for one particular solution, the two electrolyte solutions are the same in chemical species with a slight difference in concentration, i.e. 5% difference. It is important to maintain a small difference in concentration to avoid: i) the once sharp front surface to become blurred and ii) dramatic change in the electrical current at a certain point and very slow change at the beginning and the end of the replacement process; both of which cause difficulties in determining the replacement time accurately [2].
Figure 1. A typical current–time relationship measured for a 1× TAE buffer solution replacing a 95% 1× TAE buffer solution in a 10-cm length of 100-μm-i.d. capillary, under an applied electrical field of 7.5 kV/m. |
Total Length Method
The total length method uses the following equation to calculate the average velocity:
(1) |
where Δt is the measured time between the two plateaus values of the current, which is also the time required for the second solution to travel through the entire channel length, L. This method requires the determination of the starting and ending time for the current change during a replacement process via EOF. Experimentally it is very difficult to determine the exact starting and ending time of a replacement process because the gradual changing of the current with time and the small current fluctuations exist at both the beginning and the end of the replacement process, as shown in Figure 1. In addition, for low concentration solutions, the average electro-osmotic velocity is very low, which requires a longer time to complete the replacement process. Two concerns arise from this situation. First, Joule heating is dependent on the running time of the replacement process, therefore, it may become an issue especially when the channel is made of polymer material such as poly (dimethylsiloxane) (PDMS) which has a low thermal conductivity. Second, the once sharp concentration front between the two solutions becomes progressively blurred. This mixing causes the sloped and plateau region of the current-time relationship to be smoothed together, which makes it difficult to determine the beginning and the end point for the replacement process. Consequently, significant errors could be introduced in the average velocity determined in this way. Therefore an improved method was developed which is called the slope method [3].
Figure 2. (a) A schematic describing of the operation of the Y-channel design with the current monitoring method, and (b) Actual current–time plot obtained for 1XTBE during experiments with notations added to explain the calculation of the zeta potential from the total length and slope methods. |
An improved method – Slope method
It has been observed that, despite the curved beginning and ending sections, the measured current–time relationship is linear in most part of the process when the concentration difference is small. This may be understood in the following way. As one solution flows into the microchannel, the same amount of the other flows out of the microchannel at essentially the same speed. The two solutions have different electrical conductivity values, therefore, the overall electrical resistance of the liquid changes linearly, and hence the slope of the current–time relationship is constant during this process. The slope of the linear current–time relationship can be described as
(2) |
where I is the electrical current, E the applied electrical field strength, and (λ_{b2} − λ_{b1}) the difference in the bulk conductivity between the two solutions. In Eq. (2), all the parameters are known and constant during the replacing process. If we group all the known parameters and denote Γ = EA(λ_{b2} - λ_{b1})/L, Eq. (2) can be rewritten as
(3) |
Eq. (3) shows that the average EOF velocity can be determined by measuring the slope of the current–time relationship. Figure 2 shows a Y-channel design for the current monitoring method which significantly improved the accuracy in measurements [2] as compared with the previously reported studies.