Pressure Driven Micro-flow Through a Double-T Metering Junction Luke Hunter and Daniel Dedrick University of California, Berkeley December 10, 2001 Abstract Discrete fluid volumes (plugs) are often needed for micro bioassay. Current methods of isolating discrete volumes use electrokinetic forces that require high voltages and result in ionic component separation of the sample. Pressure-driven flow through a double-T metering junction is a suggested alternative to this electrokinetic method. There has been no extensive analysis of pressure-driven plug flow. This paper outlines a method to characterize the effects of diffusive mixing of plug flow through a double-T metering junction and determine the viability of pressure driven flow as an alternative to electrokinetically driven flow for bioassay. Introduction “Lab on a chip” systems have undergone rigorous development in recent years. These bioassay systems are typically comprised of pumps, valves, mixing chambers, and complex channeling [1,2]. Many of these designs analyze discrete volumes of high-purity liquid. These volumes are often times defined by geometry and electrokinetic forces [3,4]. Electrokinetic forces separate ionic components of the fluid by applying a high potential (approximately 400V-1000V) across the sample. Although the use of electric fields is a powerful tool for separation of molecules, there are shortcomings in using this as a general method of fluidic transport. For example, electrophoretic de-mixing occurs when pumping heterogeneous solutions due to the separation of the different ionic components. This problem can be partially compensated by alternating plugs of low and high-conductivity buffer, but other problems can arise [5]. The use of high voltages is also problematic for developing mobile, low power, µ-assay systems. These types of systems are being pursued for military and public health applications [6]. To avoid ionic separation and exceeding the energy budget of self-contained low-power micro systems, pressure-driven flow through a double-T metering junction is suggested. This method of metering utilizes geometry and pressure differences rather than an electronic potential to isolate a discrete volume of sample between two plugs of buffer fluid. Although plug transport has been demonstrated with electrophoretic forces [3-5], extensive analysis of pressure driven plug flow has not been pursued. Mixing between sample and buffer will be analyzed by optical imaging of dyes and particle image velocimetry (PIV). PIV can be used to characterize flow velocity profiles, and possibly, buffer and sample interface diffusion. Test structures will be fabricated using standard glass micro machining processes or hot embossing of plastic. A cover plate with through holes will be required for liquid input and output. The cover plate can then be bonded to the micro machined glass wafer or hot embossed plastic. Different structures will be fabricated in a single process allowing for flow analysis of straight channels and t-junctions. This paper will outline a method for characterization of pressure driven plug flow including the development of test structures for comparing modeled and experimental results. The results produced will be used to determine the viability of pressure-driven plug flow as an alternative to electrokinetic methods. Design Pressure-driven flow through a double-T metering junction is suggested as a low power option to electrokinetic metering systems. A double-T metering junction utilizes geometry to isolate a discrete volume of sample between two plugs of buffer fluid. A schematic of the double-T metering junction is shown in Figure 1. The following steps define a discrete volume: 1. Flood system with buffer and stop flow. 2. Drive sample towards waste outlet past point b and stop flow. 3. Drive buffer towards assay outlet.(1) These steps result in a volume of sample defined by the distance between points a and b and the depth and width of the channel. Buffer in Sample in To WasteTo Assay x z y a b Figure 1: Schematic of double-T metering junction A sample volume of approximately 20 nano-liters and a flow rate of 1 µL/min (60 µL/hr) are reasonable values for “lab on a chip” systems. If the channels shown in Figure 1 are 100 µm X 100 µm, an average flow velocity of ~1.67 mm/s and thus a Reynolds number of ~0.167 will result. This low Reynolds number indicates laminar flow and implies mixing will be dominated by diffusion. The average velocity and Reynolds number will change with different geometries but not enough to enter a turbulent regime. Micro-syringe pumps will be used to provide pressure sources to drive flow through the test structures. These pumps are capable of delivering flow rates as low as 0.001 µL/hr (well below the specified 60 µL/hr). After volume definition, mixing and velocity profiles can be determined. Particle image velocimetry (PIV) will be used to characterize the flow velocity profile. PIV requires that the flow be seeded with particles that can scatter laser light. A CCD captures images of the scattering and software cross-correlates the pictures to develop a vector field describing the flow velocity. Diffusion can be characterized by capturing images of dyed fluid plugs as they travel through the channel. Image intensity changes will represent dye diffusion between plugs. Measuring pH may be another method of measuring diffusion. Two fluids of differing pH will represent a sample and buffer. By measuring the pH of these fluid volumes after the double-t, an estimation of mixing can be determined. This would require integration of electrodes into the cover plate. Theory Due to the very small channel size, the Reynolds number for µ-flow is typically < 1, well below turbulent regimes. For flow analysis, we can use the Navier-Stokes equation (eq. 1). For steady flow in the x-direction, at very low Reynolds numbers, this equation simplifies to the Stokes equation (eq. 2). If we also assume that the flow is much more dependent on the y direction (i.e. the channel is much wider than it is deep) and the pressure gradient is constant, then the equation simplifies further to By solving this equation we find that the velocity profile across the depth of a channel is where h is the height of the channel, µ is the viscosity, ρ is the density, P is pressure, and K is a constant equal to the pressure gradient [7]. Diffusion affects
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