Microfluidic Flow Modeling Study

Mathematical modeling and computer simulation have been applied for various flow studies in rectangular microchannels (see Table 3.1). An equation to describe the flow in a rectangular channel has been given [124]. Simulation of fluid flow can be conducted by solving the coupled Poisson and Navier-Stokes equation for fluid velocity [532]. However, this complicated computation has been simplified by solving the Laplace equation for the electric field because it is proportional to fluid velocity [321]. 

Caged fluorescent dyes have been used to measure EOF in microchannels [410], A nanosecond N2 laser pulse first activated a caged fluorophore, and its subsequent single-molecule detection was used to measure velocity of liquid flows, which 

FIGURE 3.12 Simulation (left column) and photobleached-fluorescence visualization (right column) of an analyte band traveling around a constant-radius corner. In both cases the channel is 250 pm wide. In the experiments, the channels were - 40 pm deep [535]. Reprinted with permission from the American Chemical Society. 

Other methods for flow measurement include the use of fluorescence correlation spectroscopy to trace the hydrodynamic flow of a fluorophore in a Si microchannel [412]. Velocity of flowing particles was measured using SCOFT detection as described in Chapter 7, Section 7.1.3 [413]. 

Flow measurement has been achieved without the use of beads or dyes. A short heating pulse generated by a C02 infrared laser (10.6 pm) was delivered through the IR-transparent Si wafer into the channel. The radiative image of the hot liquid plug was recorded by an IR camera [414]. 

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Despite the fact that much effort has been made to model the DMFC system, considerable work remains, particularly in support of the emerging portable designs and systems. Few have treated the dominating effects of two-phase flow. No model to date has sufficient detail to provide a microfluidic theory for portable systems including effects of channel geometry and wettability characteristics of the GDL on fluid flow in the anode or cathode. Modeling studies are needed to fully elucidate the intricate couplings of methanol, water, and heat-transport... 

Various Mathematical Modeling and Stimulation Methods to Study Microfluidic Flow... 

The development of microfluidics makes the study of the movement of a small particle in a laminar flow an especially dynamic topic nowadays. The eontents of this ehapter, without having gone into the detail of theoretioal developments, show the eomplexity and difficulty of the subject. A pertinent modeling of the movement of a particle, in order to encompass phenomena such as the lesuspension of particles from walls or the migration of particles in a direction perpendicnlar to the flow streamlines, should incorporate the lift force exerted on a partiele, even though it is much weaker than the drag force. 

The microneedle design and analysis involves strength modeling and CFD analysis. Many research studies have been conducted for structural and microfluidics (flow) analysis of the microneedles. [13] conducted numerical and... 

In order to further investigate and understand the unfavorable results regarding sample elution time of the weir-SMEC as compared to the grid-SMEC, microfluidic modeling of the flow profile immediately after the weir was performed. When the size of fluidic channels is in the dimensions of a few hundred micrometers or smaller and aqueous-based solutions are used, it is well known that pressure-driven fluid transport is usually heavily dominated by laminar flow. Therefore microfluidic modeling can be employed to investigate and study fluid flow characteristics in microchip designs prior to fabrication. 

The role of mixing has been studied in systems with more complex reaction schemes or considering more complex fluid-dynamical properties, and in the context of chemical engineering or microfluidic applications (for reviews on microfluidics see e.g. Squires (2005) or Ottino and Wiggins (2004)). Muzzio and Liu (1996) studied bi-molecular and so-called competitive-consecutive reactions with multiple timescales in chaotic flows. Reduced models that predict the global behavior of the competitive-consecutive reaction scheme were introduced by Cox (2004) and by Vikhansky and Cox (2006), and a method for statistical description of reactive flows based on a con-... 

The liver is a vital organ in the body that plays a primary role in the digestive system in detoxification, protein synthesis, and filtering of blood [56]. Liver-on-a-chip platforms have been developed to understand liver function better and to study drug hepatotoxicity and metabolism [29, 57, 58]. A microfluidic-based device fabricated to mimic the permeable sinusoid endothelial barrier between hepa-tocytes and liver [29] includes three main sections—a central channel to pack the hepatocytes, a microfluidic sinusoid barrier consisting of a set of narrow (2 mm wide) microchannels to model the endothelial barrier, and a convection microfluidic channel surrounding the barrier (Fig. 5A). The flow of nutrients through the convection microfluidic channel feeds the hepatocytes. This system mimics the transportation between blood flow and hepatocytes, and the shear stress over hepatocytes with a patterned set of microchannels. 

Microfluidics is an area where the fluid flow and its properties are manipulated in a micron scale for various applications. Some of the microfluidic techniques developed for biological studies have been primarily focused to study, understand, and develop possible diagnostic tools and remedies for human diseases. In the last decade, research in this area has developed rapidly and extensively owing to the possibility of creating and controlling a microenvironment by the enabling microfluidic-based lab-on-a-chip technology, which can mimic the cellular microenvironment in vivo and hence perform individual cell-based studies that are not possible in an actual in vivo model. 

In microfluid mechanics, the direct simulation Monte Carlo (DSMC) method has been applied to study gas flows in microdevices [2]. DSMC is a simple form of the Monte Carlo method. Bird [3] first applied DSMC to simulate homogeneous gas relaxation problem. The fundamental idea is to track thousands or millions of randomly selected, statistically representative particles and to use their motions and interactions to modify their positions and states appropriately in time. Each simulated particle represents a number of real molecules. Collision pairs of molecule in a small computational cell in physical space are randomly selected based on a probability distribution after each computation time step. In essence, particle motions are modeled deterministically, while collisions are treated statistically. The backbone of DSMC follows directly the classical kinetic theory, and hence the applications of this method are subject to the same limitations as kinetic theory. 

The applications related to non-Newtonian fluid flow through microchannels are mostly associated with the transport of biofluids, with blood as the most common example. Utilizing the mathematical model outlined as above, recent efforts have been directed to understand the implications of various rheological characteristics of blood on electrokinetically driven microfluidic transport [9]. The simulation studies based on the above-mentioned mathematical model clearly revealed... 

When handling strong exothermic processes or hazardous substances, safety issues also became a major driver for the use of microreactors. Finally, several academic studies can be found in the literature focusing on the analysis of mass transport and flow characteristics within microfluidic charmels by using electrophilic aromatic substitutions as model reactions. 

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