Multiscale phenomena in microfluidics and nanofluidics

Abstract

A lab-on-a-chip device typically integrates many microfluidic components and has similar functions to the room-sized laboratory. However, developing such a lab-on-a-chip device is not simply to scale down the conventional instruments. It requires the understanding and controlling of many multiscale physical and chemical phenomena, spanning from centimeter to nanometer. In this paper, we provide an overview of the multiscale fluidic phenomena encountered in lab-on-a-chip devices, with focus on electrokinetics. We review different computational models for the studies of microfluidics and nanofluidics. Several application examples using microfluidics and nanofluidics, including micromixing, particle/cell separation, and DNA separation, are given.

Introduction

Size generally means the physical dimensions, proportions, magnitude, or extent of an object. In the real world, length is one of the most important dimensions of measurement, spanning from ${10}^{25}\mathrm{m}$ (our entire universe) down to ${10}^{-16}\mathrm{m}$ (lepton and quark). Many fundamental processes of biology, however, do not cover quite as large a range of sizes as mentioned above. For instance, translation, gene regulation, and cell communication occur on the micrometer to nanometer scale (Tegenfeldt et al., 2004). Table 1lists the typical length scales of some of the biological objects. In order to study the various biological phenomena and processes at the molecular level and at the cellular level, researchers must be able to access these relevant length scales. This requires the experimental devices to have characteristic sizes of a few nanometers up to several micrometers. During the past decade, micromachining and microfabrication technology has become available to make nano- and micron-sized devices, thus enabling studies of objects with these length scales.

Since Manz et al. (1990) developed the concept of miniaturized total analysis system ($\mu$ TAS) or lab-on-a-chip, the miniaturization of biological or chemical devices has attracted substantial attention and remarkable progress has been achieved (refer to the reviews by Reyes et al., 2002, Auroux et al., 2002, Erickson and Li, 2004). An integrated lab-on-a-chip device can incorporate many of the necessary components and functionality of a typical room-sized laboratory into a small chip that performs a specific biological or chemical analysis, including sample treatment, transport, reaction, and detection. Originally it was thought that the most significant benefit of the miniaturization would be the analytical improvements associated with the scaling down of the size (Manz et al., 1990). Further development revealed other advantages such as minimized reagents, increased automation, and reduced manufacturing costs (Kock et al., 2000).

Lab-on-a-chip devices are not just a simple smaller version of the conventional instruments. Miniaturization raises many new challenges. Fluid and sample transport is a crucial issue in these lab-on-a-chip devices because many biological and chemical processes and experiments take place in aqueous environments. The fundamental properties of fluidi in micro/nanoscale may differ significantly from those in larger devices. For gaseous flows, the continuum Navier–Stokes equations are valid only if the Knudsen number $\mathit{Kn}<0.1$, while the non-slip boundary condition holds for the stricter limit of $\mathit{Kn}<0.001$. For liquid flows, the fluidic phenomena in microscale $(100\mathrm{nm}\sim 100\mathrm{\mu }\mathrm{m})$ still can be described by the continuum theory but the decrease of length scale makes surface force and electrokinetic effects important and inertial force unimportant. One of the well-known examples is that mass transportation in microfluidic device is normally dominated by viscous force rather than inertial force. Dimensions of fluidic channels continue to be scaled down to below 100 nm, entering the region of nanofluidics. The liquid can no longer be fully considered as a continuum but as an ensemble of individual molecules. In these scales, the surface-to-volume ratio is very high, the non-slip boundary condition does not hold fully, and fluid constitutive relations are strongly affected by the existence of the boundary. The study of micro/nanoscale fluid mechanics is important for the understanding and development of the lab-on-a-chip devices at the corresponding scales.

The fluid motion in microfluidics and nanofluidics is generated typically by applying a pressure difference to a channel or by applying an electric field along the channel. Pressure-driven flow has in general a parabolic flow profile that may degrade separation efficiency. Moreover, very large hydrodynamic pressure is required to generate liquid flow in microfluidic and nanofluidic devices since the hydraulic resistance is reversely proportional to the fourth power of transverse channel dimension, which makes many designs using pressure-driven flow impractical. An alternative to pressure-driven flow is electrokinetic pumping that is easy to control and is insensitive to channel sizes compared to pressure-driven flow (Probstein, 1994, Li, 2004). The advantage of electrokinetic pumping is that the flow is plug-like and independent of the size of the channels provided that the diameter of channel $⪢$ Debye length ($1\sim 10\mathrm{nm}$ for standard buffer conditions). Electrokinetic mechanisms, including electroosmosis, electrophoresis, and (AC and DC) dielectrophoresis, are playing more and more important roles in micro/nanoscale devices. They have been extensively used for flow control (Hu et al., 2005), micromixing (Erickson and Li, 2003, Biddiss et al., 2004), concentration gradient generation (Lee et al., 2005), separation (Kang et al., 2006), sorting (Xuan and Li, 2005), and DNA detection (Paegel et al., 2002) on lab-on-a-chip platforms.

Along with experimental and theoretical studies, numerical simulation has been an indispensable tool in almost every research and application field for many years. It also provides great help in the design of microfluidic and nanofluidic devices (Erickson, 2005). Simulations allow researchers to rapidly determine how design change will affect chip performance, thereby reducing the number of prototyping iterations. However, there are several factors that complicate the numerical simulation of micro/nanoscale phenomena and thus distinguish it from the macroscale counterpart. The first and most important one is the large range of relevant length scales, which can vary up to seven orders (from Debye layer, nm, to channel length and substrate thickness, cm). Secondly, the downscaling of the size dramatically increases the relative importance of surface and interfacial phenomena. Rapid and localized changes of fluidic and material properties often occur in the miniature devices. Another challenge in numerical simulation is the intrinsic multiphysics phenomena that usually combine less or more fluid mechanics, heat transfer, electrokinetics, chemical and biological thermodynamics, and reaction kinetics. In general, one must consider all these aspects in order to provide a numerical picture for a true lab-on-a-chip device.

In this paper, we first discuss the fundamental electrokinetic phenomena and then give an overview of some of the most important scale parameters in microfluidics and nanofluidics. We will continue to review the theoretical and numerical models employed in micro/nanoscales. Finally, we will focus on application-based devices and prototypes using microfluidics and nanofluidics.