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EML4930/6930 Introduction to Microfluidics & bioMEMS Spring 2020 1 | 3 P a g e Midterm Exam Problem 1. (10 pt) Select all correct answers that describe the image below (black patterns – electrodes): A. It shows a dielectrophoresis phenomenon. B. White particles and blue particles show same dielectrophoresis behavior. C. White particles and blue particles show different dielectrophoresis behavior. D. White particles show positive dielectrophoresis. E. The non-separated white and blue particles further away from electrodes are due to weak dielectrophoresis force. Problem 2. (20 pt) Consider flow of water ( = 1000 ; = 1 ) through a circular microchannel of length 5 cm. What is the largest magnitude pressure drop that can be applied while maintain strictly laminar flow if the microchannel diameter is (a) 5 and (b) 50 m. EML4930/6930 Introduction to Microfluidics & bioMEMS Spring 2020 2 | 3 P a g e Problem 3. (30 pt) Consider the following microfluidic channel with embedded microelectrodes on a side wall, a suspension of a mixture of two particle populations (blue and red) is focused in the center of the channel under a pressure-driven sheath flow. Under the influence of electric field, the trajectory of the focused particles will be biased due to dielectrophoresis (DEP) force. Depending on the sign of the real part of the CM factor, the particles can exhibit positive DEP or negative DEP so that they will be attracted towards to the electrodes or pushed away from the electrodes. Using this method, we can separate the two different types of particles. Given the dielectric properties in the following table, calculate the real part of the CM factor and identify an electrical frequency from a range of 1 kHz to 10 MHz to separate blue particles from red particles. Assume laminar flow and spherical particles with a same size. Using your selected electrical frequency, predict the collection sites (A, B, C) for each particle type. Show details of your calculation to support your prediction. parameter r, relative permittivity σ (S/m), electrical conductivity medium 78 0.03 Blue particle 40 0.2 Red particle 25 0.03 EML4930/6930 Introduction to Microfluidics & bioMEMS Spring 2020 3 | 3 P a g e Problem 4 (15 pt). The electrical permittivity o the electrolyte affects the thermodynamic efficiency of an electrokinetic pump owing to the dependence of electroosmotic flow on the permittivity. Read the attached reference and summarize: (a) The dependence of the flow rate on permittivity, (b) How can the permittivity of a solution be changed? (c) What other properties of a solution will also be changed that can affect the pumping efficiency? Problem 5. (25 pt) Access to the FAU library or Google Scholar, search for a journal publication showing microfabrication process. Understand the procedure of microfabrication described in the paper. Show explicitly in your answer regarding: (a) the cross-sectional view of the step-by-step fabrication process; (b) point out whether the photoresist material used in each step is positive or negative. Attach the full text of the paper together with your answer. doi:10.1016/S0925-4005(03)00128-X Increasing the performance of high-pressure, high-efficiency electrokinetic micropumps using zwitterionic solute additives David S. Reichmuth, Gabriela S. Chirica, Brian J. Kirby* Microfluidics Department, Sandia National Laboratories, P.O. Box 969, MS 9951, Livermore, CA 94551, USA Accepted 14 January 2003 Abstract A zwitterionic additive is used to improve the performance of electrokinetic micropumps (EK pumps), which use voltage applied across a porous matrix to generate electroosmotic pressure and flow in microfluidic systems. Modeling of EK pump systems predicts that the additive, trimethylammoniopropane sulfonate (TMAPS), will result in up to a 3.3-fold increase in pumping efficiency and up to a 2.5-fold increase in the generated pressure. These predictive relations comparewell with experimental results for flow, pressure and efficiency. With these improvements, pressures up to 156 kPa/V (22 psi/V) and efficiency up to 5.6% are demonstrated. Similar improvements can be expected from a wide range of zwitterionic species that exhibit large dipole moments and positive linear dielectric increments. These improvements lead to a reduction involtage and power requirements and will facilitate miniaturization of micro-total-analysis systems (mTAS) and microfluidically driven actuators. Published by Elsevier Science B.V. Keywords: Micropump; Electroosmosis; Zwitterion; Dielectric increment 1. Introduction Micro-total-analysis systems (mTAS) have received a great deal of recent attention owing to their ability to improve the performance of chemical analysis systems by reducing foot- print, reagent volumes, and electrical power needs. As a crucial component of mTAS research, micropumps have been investigated as a means to move fluids and actuate microscale mechanical components. Previous investigators have pre- sented micropumps in a variety of formats, as reviewed in recent papers [1,2]. Electrokinetic micropumps (EK pumps) have been shown to generate pressures above 57 MPa (8000 psi) [3] or flow rates above 1 ml/min [2], making them attractive for miniaturization of HPLC systems [4], cooling of microelectronics, and actuation of microscale mechanical components [5]. EK pumps use electroosmosis in charged porous media to generate a pumping function. Electroosmotic flow (EOF) in porous matrices has been used in a variety of applications, including capillary electrochromatography [6,7], and micro- fluidic pumping [2,3,8]. EK pumps are ideally suited for mTAS, since they can straightforwardly meter the very low flow rates (nl/min or ml/min) that are typically used, and can generate high pressure (>10 MPa) required for chromato- graphic separations. An EK pump is realized experimentally by applying voltage across a porous bed possessing a charged solid– liquid interface (Fig. 1). Electroosmosis due to the applied electrical field causes fluid flow and generates a pressure whose magnitude depends in part on the fluidic resistance of the channels downstream of the pump. Pump performance is dictated by substrate material and geometry as well as fluid properties. This paper presents the use of fluid additives to improve the pressure and flow rate performance of EK pumps. Important achievements include the demonstration of 156 kPa/V (22 psi/V) and 5.6% efficiency, both (to our knowledge) the highest performance reported for EK pumps. 2. Theory In certain limits, EK pumps can often be modeled by straightforward equations. This section derives performance relations for EK pumps, with special attention to the effect of solutes. These relations will be used throughout the paper to illustrate the effects of uncharged, zwitterionic solute addi- tives on pump performance. EK pump performance parameters were first derived for capillaries using a Helmholtz double layer model [9], and later expanded to incorporate Gouy–Chapman double layers Sensors and Actuators B 92 (2003) 37–43 * Corresponding author. Tel.: þ1-925-294-2898; fax: þ1-925-294-3020. E-mail address:
[email protected] (B.J. Kirby). 0925-4005/03/$ – see front matter. Published by Elsevier Science B.V. doi:10.1016/S0925-4005(03)00128-X of finite size [10]. Building on early work, which considered simple geometries and often linearized the Poisson–Boltz- mann equation [11], recent work has expanded this analysis to include detailed accounts of pore sizes and shapes [12] and fully explore the input parameter space [13] to evince nonlinear and limiting effects. Here, we are concerned primarily with the relative per- formance change caused by adding solute to the pumped buffer, and anticipate working with high enough buffer concentrations (�10 mM) that the Debye length [14] can be assumed small compared to the effective pore radius (�100–200 nm). For this simple case, the electroosmotic flow (EOF) may be treated as uniformly proportional to the electric field throughout the pump medium. Assuming a cylindrical capillary geometry with radius a and phenomenological zeta potential z (V), as well as a liquid with viscosity m (Pa s), Stokes’ flow equations can be combined with an electroosmotic forcing term to give the EOF profile as uðrÞ ¼ Px 4m ða2 � r2Þ � ee0zE m (1) where Px (Pa/m) is the pressure gradient along the axis, r the radial position, and E (V/m) is the uniform electrical field. In this paper we use e to denote the nondimensional dielectric constant such that the fluid permittivity is given by the product of the dielectric constant e and the permittivity of free space e0. Eq. (1) can be used to derive a number of performance relations for EK pumps that consist of linear capillaries and operate in the thin double layer limit. Practical EK pumps consist not of linear capillaries but rather a porous bed; thus Eq. (1) can quantitatively treat porous media only if additional parameters (e.g., formation factors, porosity, tortuosity) are used to adapt the microchannel geometry to that of the porous bed. These additional parameters add multiplicative factors to Eq. (1) and the derived results to follow. However, the theory in this section is concerned primarily with the relative per- formance increase observed upon addition of specific fluid additives; thus the treatment for an idealized linear capillary system will be retained; it is simple and sufficient for this purpose. This derivation has been presented in [9], but is repeated here for clarity. From Eq. (1) we can derive that the maximum pressure per volt generated in such a capillary (i.e., the pressure performance at zero net flow rate) is DPmax V ¼ 8ee0z a2 (2) Fig. 1. EK pump operation and characterization. (a) Schematic of experimental setup. Voltage applied across a capillary packed with silica microspheres leads to flow and pressure generation. The fluidic resistance of the output channel controls the pressure and flow rate. Pressure is measured with a transducer and flow is measured by observation of meniscus motion through the output channel. (b) Expanded view of EK pump. Voltage gradient induces EOF from left to right; pressure gradient induces Pouiseille flow from right to left. (c) Expanded view of pores in between microspheres. Flow pattern is a linear superposition of solenoidal EOF from left to right and pressure-driven Poiseuille flow from right to left. 38 D.S. Reichmuth et al. / Sensors and Actuators B 92 (2003) 37–43 where V is the applied voltage. As a practical example, we can use Eq. (2) to estimate that for a packed bed of 0.5 mm silica beads (effective pore radius a � 100 nm) and a fluid consisting of a 10 mM aqueous Tris (tris(hydroxymethyl)a- minomethane hydrochloride) buffer (z � 60 mV), the max- imum pressure achieved will be 35 kPa/V (4.9 psi/V). Expanding the microchannel model to consider an array of identical