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Topology Trade-offs in the Synthesis of Chip-based Electrophoretic Separation Systems

A.J. Pfeiffer, T. Mukherjee and S.Hauan
Carnegie Mellon University, US

Keywords: microscale electrophoresis , synthesis, topology

Micro-scale electrophoretic separation systems provide a highly effective, versatile and inexpensive method for separating a wide variety of chemical components. Particularly useful applications include separation of biological molecules, chemical sensing, and mobile drub delivery systems. Micro-scale electrophoretic separation systems are anintegral part of 'lab-on-chip' technology. From a design point of view, it is desired to bridge the gap between current analytical models and practical chip design [4,6]. A flexible simulation engine based entirely of closed-form algebraic models was implemented to capture the effects of channel topology on separation efficiency. By combining dispersion models for turns [3,5,2] and skewed band in straight channel sections between complimentary turns [1], the performance of arbitrary serpentine channel topologies may be predicted 2-3 orders of magnitude faster than rigorous solution of the underlying partial differential equations while retaining accurate results. The simulation engine enables the rapid investigation of various input conditions, channel geometries and flow regimes and serves as the basis for a generalized optimization framework. A key aspect of microscale electrophoresis is the trade-off between the resolution of analyte bands and the chip-area occupied by the separation subsystem. At constant temperature the unknown buffer and surface properties, the species mobilities are given and analyte resolution becomes inversely proportional to the dispersion squared. Based on detector accuracy and voltage source available, on may - a priori - calculate the required total length of the separation system. While minimum dispersion is achieved by a single straight channel, the most compact designs arise from serpentine and spiral topologies. Further, in straight sections immediately following a turn exhibit, the per-length dispersion [1] is increased due to geometrically skewed analyte bands. This paper aims to answer the following question: When can - and should - designs with increased dispersion, but less area, be preferred to those with minimum dispersion but a larger areas? The approach is schematically illustrated in Figure 1 where separation of the same two analytes are being perfomed in three simple channel systems (1a) consisting of a single straight channel (A) as well as two topologically different 5-section serpentines. The channels have the same (constant) width and voltage source as well as identical buffer properties. All turn lengths shown have been fixed at twice their minimum value [4] and the serpentine channels differ only by the length of the straight section in between the two complementary turns. As shown in subfigures (b) and (c) the amount of dispersion generated as well as the area occupied varies significantly between the different topologies. Figure (d) depicts the design trade-off for this elementary system in a plot of relative dispersion versus relative area. The straight channel (A) is reduced to a single point located at coordinates (1,1) while design (B) is generally smaller but gets increasingly worse with respect to dispersion as the total separation length decreases. While design (C) is close to (A) in dispersion (Fig. 1 (b)), the area penalty is significant for all but very short separation systems. We will extend the above analysis both to multi-turn serpentine channels and spiral topologies in order to determine the most promising trade-offs between chip area and "excess" analyte resolution for a range of relevant flow regimes. Unlike the schematic cases shown, the distribution of channel lengths between all individual sections will be optimized independently to ensure that we compare the best possible designs for each proposed topology. The results will be summarized graphically.

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