Class 2 Principles of Microfluid Mechanics Jack Merrin Institute of Science and Technology Austria May 8, 2017

What is microfluidics? Consequences of miniaturization of fluids in physics, mathematical physics, chemistry, biology, and engineering Physics – Description of flow through micro pipes, effects of viscosity, diffusion, heat transfer, simulations of velocity fields Chemistry – Mini chemical reactions, catalysis, single molecule Biology – Manipulation of single cells, environment of cells, assays, screening, physical limitations of living matter Engineering – Automation, parallelization, elimination of pipetting, lab on a chip, microfabrication of devices that solve science problems Approach of Course: Start with basic engineering and physics then apply what we know to biology and biochemistry

Engineering Point of View A channel with an inlet and an outlet is the simplest microfluidic device. Most devices are some variation of this, with more channels and more ports. We will build up to understanding the flow through a circular pipe while it is actually easy to make rectangular pipes In future classes, we will discuss various methods to produce master molds depending on the length scale you are trying to construct at.

Experimental Physics Point of View Linear Phenomenon Time Independent Laminar Nonlinear Turbulent Complicated Time Dependence

Theoretical Physics Point of View Navier-Stokes Equation – Everything you want to describe fluids Nonlinear equation – velocity repeats twice in one term Describes time dependent spatial flows like turbulence Great unsolved problem of classical physics – Millennium Prize PHYSICS GOAL – Understand all symbols in the NS equation and resulting simplifications for microfluidics What you really need to know for microfluidics is much easier

Non calculus symbols Density Pressure Viscosity – Fluids that drag and dissipate energy like honey Velocity of the fluid at each point

Differential Calculus Regular Derivative Partial Derivatives Chain Rule for Composition of Multiple Variable Functions

Vector Calculus – Understanding the Symbols A vector has a magnitude and direction Dot product Del operator and Gradient Chain Rule Laplacian

Viscosity Newton defined dynamic viscosity as Kinematic viscosity You can hear viscosity, cold or boiling water pouring Velocity is zero on the boundaries

Comparison of NS with Newton’s Law Newton’s Second Law Transition to liquids uses density not particles Liquids are incompressible Just add the other types of forces, pressure, viscous forces or external

Reynolds Number by Dimensional Analysis Inertial Forces Pressure, viscous, and external forces If Re is small then the terms on the left are negligible. Ratio of inertial to viscous forces. Removes the time dependence Turbulence not possible Result is called laminar flow L is the conventional length scale V is the average velocity Also depends on density and viscosity

Scaling Laws Work with models in a wind tunnel

Now We Can Solve the Microflow Through a Pipe! Integrate twice and apply the boundary conditions

Flow rate through the pipe Hagen-Poiseuille Flow at Low Reynolds Number Working this out for a rectangular channel is much more complicated, but qualitatively similar

Electronics Analogy Microfluidic Resistance Electrical Resistance of a wire Channels in Series Channels in Parallel Capacitance Example Microballoon

Resistance in series can be effectively the smallest constriction

Taylor Dispersion and Qualitative Limitations of Laminar Pipe Flow If you reverse the flow the green dye goes back and spreads to the left

Plug Flow

Diffusion of chemicals and heat in fluids Mixing in microfluidics occurs primarily by diffusion Transporting temperature is analogous to diffusion Brownian motion and random walks

Gradient by flow or diffusion

Chaotic Micromixer

Hydrodynamic Focusing

Christmas Tree Device

H Filter

Surface Tension

Contact Angle

Capillary Action

Hydrophobic and Hydrophilic Inside Channel

Spin Coating General formula for an ideal fluid Power laws for photoresist that evaporates

Effect of Pressure on Protein Function At the bottom of the ocean P = 110 MPa High pressure tends to force water into hydrophobic core of proteins Life at the bottom of the ocean near thermal vents is adapted to high pressures and high temperatures

Experimental setup for temperature-regulated fluorescence anisotropy measurements at high pressures. Jack Merrin et al. PNAS 2011;108:19913-19918 ©2011 by National Academy of Sciences

Fluorescence Anisotropy of RecA with ssDNA Thermus thermophilus E. coli

Effect of temperature on RecA DNA binding Denaturation Aggregation Without RecA

Effect of T and P on RecA function

Theoretical Fit Hyperbola or Ellipse

E. coli vs T. thermophillus Bottom Ocean P