Fluid Streaming in Micro Bifurcating Networks

The major challenges of Lab-On-Chip technology include cost-effective pumping, function integration, multiple detection, and system miniaturization. In this paper, we propose a novel and simple micro streaming-based fluid propulsion technology that has the potentials to address some of the challenging topics. The phenomenon of flow streaming can be found in zero-mean velocity oscillating flows for a wide range of channel geometries. Although there is no net flow (zero-mean velocity) across a channel cross section, the discrepancy in velocity profiles between the forward flow and backward flow causes fluid particles near the walls to drift toward one direction, while particles near the centerline drift to the other direction. The unique characteristics of flow streaming provide opportunities to transport, mix, separate and distribute particles entrained in flows. In this study, we investigate the phenomena of flow streaming in a network of symmetrical bifurcations using computer simulations. Dimensional analysis is first conducted. Results of streaming flow Reynolds number (Re) are presented as a function of Womerseley number and dimensionless oscillation amplitude. Computer simulation provides further insights of flow streaming phenomena. Results show that the oscillation amplitude has dominant effects on streaming velocity, which is is directly proportional to the oscillation frequency. Streaming flow can be an effective convective mass transport method when the Schmidt number is less than one. INTRODUCTION With technological advancements in micro-electromechanical systems (MEMS) and semiconductor micro-fabrication methods, along with the influx of genomic and proteomic data, microfluidic devices will continue to provide superior benefits in many fields including pharmaceuticals, biotechnology, life sciences, defense, public health, and food/agriculture. A true Lab-on-Chip (LOC) device needs to perform various testing functions on a single chip, including sampling, sample pre-treatment (filtration, concentration, mixing, reaction, separation, etc.) and detection [1]. The LOCs are low-cost, fast, portable and ideally free of human errors. Due to micro-scale dimensions, these devices consume an extremely low volume of sample material and reagents, drastically reducing sample size and processing time. The entire test procedure will be completed on a chip without human intervention. Experimental and analytical protocols developed in software, are translated into chip architectures consisting of interconnected fluid reservoirs and pathways. Micro-fluids, the fluids flowing in micro-channels, make LOC designs possible. The past few decades have witnessed a marked increase in research efforts on development of various novel microfluidics devices [1-11]. The major challenges of Lab-On-Chip technology include cost-effective pumping, function integration, multiple detection, and system miniaturization. While there are hundreds of papers describing many novel strategies of driving fluid through micro-channels, the two most common are electrokinetic-driven and pressuredriven flows, at the present time. Pressure-driven flow is the dominant flow type in macro-scale devices and has applications in microsystems technology as well. An advantage of pressure driven flow is that both charged and uncharged molecules, as well as cells, can be moved without separation. Typical micro-pumps used in pressure-driven flows are diaphragm pumps equipped with either check-valves or a pair of diffuser/nozzles [12]. Mixing two or more fluids quickly is also one key function in many biomedical testing routings. Rapid mixing is a challenge for micro-devices because flow is considered to be laminar. Micro channel cooling faces the same challenge: small dimensions lead to a low Re number and thus laminar heat transfer, which is usually associated with low heat transfer coefficients. Laminar flow has smooth streamlines and its mechanisms of shear, mass and heat transfer owe entirely to the fluid molecular viscosity and diffusivities. Based on the 1-D Einstein equation of Brownian diffusion, D x t 2 / 2 = where t is the time, x is the distance and D is the diffusivity, it will take molecules a short time to diffuse a short distance, while it will take 100 times longer to diffuse a distance only 10 times as great. In those cases, it becomes necessary to induce the flow disturbances for the enhancement of transport processes. In this study, we investigate a streaming flow-based micro fluid propulsion technique that may have potential to address some of the aforementioned problems. RESEARCH APPROACHES Mechanisms of Flow Streaming in Bifurcation The mechanisms of flow streaming in a bifurcating channel are illustrated in Figure 1. It shows a qualitative picture of the axial velocity profiles of a Newtonian fluid in a macro-channel bifurcation tube based on the work of [13]. During the inflow (to the right), the parabolic velocity profile in the mother tube is split in half at the location of when entering the daughter tubes, resulting in a nonsymmetrical profile with the maximum velocity skewed to the inner wall of the daughter tubes. During the backflow (to the left), two fully developed, parabolic flow profiles in the daughter tubes merge at the center of the bifurcation and result in an max U ε -shaped symmetrical profile in the mother tube with a zero velocity at the center. A discrepancy in velocity profiles between inflow and backflow causes fluid elements near the walls to drift toward the mother tube (negative drift) while fluids near the centerline drift to the daughter tubes (positive drift). We hypothesize that this unique phenomenon of flow streaming can be used for fluid propulsion in micro fluidic devices. One of the successful applications of flow streaming is the High-Frequency-Ventilation (HFV) technique used in emergency rooms of hospitals. In contrast to conventional ventilation, which mimics normal breathing, HFV operates with tidal volume much smaller than the anatomic dead space (or with a very small oscillation amplitude) of the lungs at a higher rate of breath. The successive bifurcation networks coupled with the tapered lung airways geometry promote two way fluid streaming within the entire human lungs. 2 2 / CO O We also hypothesize that the oscillation flow will provide unique opportunity for micro fluid mixing. Bifurcation channel network is an ideal configuration for parallel processing of multiple detections. There are two major types of micro-mixers, active and chaotic, reported in the literature [15-17]. Streaming-based mixers may inherit features of both mixers. Oscillations with variable intensity should effectively dismantle the layered flow structure and provide enormous sources of chaotic advection, making it a unique and inherently high-efficient micro mixer design. The parallel processing can be achieved by a stream-based micro array technique. A multi-generation and multi-channel microfluidic structure can be designed. The number of bifurcating generations as well as the number of channels per generation may vary accordingly in a wide range. Human lungs offer a perfect example of streaming-based micro array technique: millions of gas exchange processes occur simultaneously at the alveolar level with all the gases ventilated through the mouth at different directions. Various tree branch structures are other examples of natural selection. 2 2 / CO O The mechanisms of flow streaming we study are different from those of acoustic streaming. Acoustic flow streaming originates from attenuation of the acoustic field. The attenuation spatially reduces the vibrating amplitude of the acoustic wave and hence generates Reynolds stress distributions and drives the flow to form the acoustic streaming. Acoustic streaming occurs in most geometries when an acoustic field exists, while the streaming flows we study are induced by the pressure-driven asymmetrical oscillating flows. In addition, oscillating parameters are quite different. In most cases, the acoustic vibration has much higher frequency (>100 kHz vs. <0.1 kHz) and much smaller amplitude (< 0.1 mm vs. > 0.1 mm). Dimensional Analysis There are six major independent variables that characterize a streaming process, e.g., oscillation amplitude A, oscillation frequency , fluid kinematics viscosity f ν , mother channel width r, fluid streaming velocity V, and one or more geometry variables. The geometry variables could be the length of the mother or daughter channels L, the daughter channel width , the aspect ratio of the channel to width L/r, the bifurcation angle or the slope of the tapered channel, and others. There is a wide range of variations among these geometry variables. Considerable amount of work is needed to identify effects of these variables. They are not the focus of this study. It is also assumed that the fluid is in a single phase, surface tension and other surface forces are neglected. Using dimensional analysis, these six variables can be combined to yield four chosen non-dimensional groups; = function (Womerseley number, nondimensional oscillation amplitude, and non-dimensional geometry factor), where is the 1 r