Microfluidics

Theory and Practice for Beginners

Sebastian Seiffert, Julian Thiele

• Publisher: De Gruyter
• Year: 2019
• Print ISBN: 9783110487770
• eBook ISBN: 9783110487848
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Biotechnology
• Index: Technology & Engineering

Microfluidics introduces the theory and practice of fluid flow on small scales. The exquisite control of such flow at low Reynolds numbers allows liquids to be processed in either a well-defined co-flow or a well-defined segmented-flow fashion. Both lays a ground for high-throughput analytics and advanced materials design. With that, this book is ideal for research scientists and Ph.D. students in the fields of chemistry, chemical engineering, biotechnology, and materials science.

1 Theoretical background

1.1 Fluid physics on the microscale

1.1.1 Ideal fluids

Microfluidics is the art and science of fluid flow on small scales. On such scales, features such as efficient heat transfer, diffusion-based mixing, and a large surface-to-volume ratio (which, in turn, governs wetting phenomena as well as fluid resistance) characterize processes, as illustrated in Figure 1.1. The most important feature, however, is that fluid flow in microchannels is purely laminar. In this chapter, we focus on the fundamentals of these principles in microfluidics.

Figure 1.1: Key parameters that come into focus when moving from fluid flow at a macroscopic scale, such as in chemical distillation (left), to fluid flow inside a microfluidic flow cell. Image on the left reproduced from Wikimedia Commons (Luigi Chiesa/CC-BY-3.0).

In this context, a first and central question is how such flow occurs, and how it can be modeled and predicted in a quantitative fashion. The usual approach to tackle questions of this kind in physics is to balance over the forces involved or to appraise the sum of energies and then minimize it. We follow the first approach and consider the forces acting on a fluid volume element ΔV with mass Δm = ρΔV, where ρ is the density of the fluid. There are three major contributors:

• Pressure differences between different locations in the (microfluidic) system, leading to pressure-based forces: F_p = – grad p ΔV
• Gravity: F_g = Δm g = ρ g ΔV
• Frictional forces, F_ξ, between layers of the fluid flowing with different velocities v

Balancing over these three contributors yields Newton’s equation of motion for the mass element Δm = ρΔV:

(1.1)$F=F_p+F_{\mathrm{g}}+F_{\xi }=\mathrm{\Delta }m\mathit{a}=\rho \mathrm{\Delta }V\frac{\mathrm{d}\mathit{v}}{\mathrm{d}t}$

The forces involved in eq. 1.1 may have different magnitude and direction in each given experimental situation. Depending on that, the fluid flow can be dominated by just one of these contributors, whereas the others may be negligible. For example, if the frictional force F_ξ is small compared to the others, the fluid is named an ideal fluid; a typical example is the flow of air relative to a plane wing. By contrast, if F_ξ outweighs the other forces, the fluid is termed viscous fluid; typical examples are honey or syrup.

We first consider the case of an ideal fluid and focus on a fluid volume element ΔV that flows with speed v(r,t) at a spot r in our system at a point in time t. If there is no change of this velocity over time, the flow is named stationary. Even then, however, there might be variation of the flow speed in space, meaning that the volume element considered can have a different velocity once it has moved to a different location in our system. All the vectors v(r,t) in all locations r of our system constitute the flow field, which is stationary if all these vectors are time constant. The trajectory r(t) that our fluid volume element ΔV exhibits in the system is named streamline, as illustrated for a fluid flowing through a pipe with spatially different diameters in Figure 1.2. In a stationary flow field, the streamlines in the system coincide with the flow field lines, and each trajectory r(t) follows a corresponding curve v(r). In microfluidics, the most relevant type of flow is laminar flow. In this case, all streamlines are parallel without intermixing; this is the situation sketched in Figure 1.2. The counterpart to laminar flow is turbulent flow, which occurs if friction between the boundary layers of the fluid and the walls of the channel is strong, whereas friction within the fluid is small compared to the flow-accelerating forces. As to be seen at the end of Section 1.1.2, this type of flow is practically irrelevant in microfluidics, such that we can focus our discussion to the case of laminar flow.

Figure 1.2: Schematic of a circular cross-section microchannel that narrows down from cross-section A₁ at the left end to cross-section A₂ at the right end. A fluid that flows through this channel from th...

Table of contents

• Title Page
• Copyright
• Contents
• Preface
• Aim and approach of this book
• Abbreviations
• Volume conversion
• 1 Theoretical background
• 2 Segmented-flow or droplet-based microfluidics
• 3 Practical realization of microfluidics
• Appendix
• Index