NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 4-1, p15
Lecture 4-1 Microfluidic Devices I
-- Fundamentals and flow channels
ð Fundamentals
u Micromachining has numerous applications in fluidics. For examples: chemical analysis, biological and chemical sensing, drug delivery, molecular separation, amplification, sequencing or synthesis of DNA, environmental monitoring, etc.
u Some components are mature, and system integration is highly desired but still under development. Packaging, interfaces, compatibility, and testing issues need to be addressed.
u Materials in wide varieties, including glasses, plastics/polymers, metals, ceramics, and semiconductors.
u Benefits: reduced size, improved performance, reduced power consumption, disposability, integration of control electronics, and lower cost. (may be not all true!!)
u Comparison between macro and micro fluidic system
Note: performance considerations in micro fluidic systems: minimal dead volume, low leakage or gas permeation, good flow/volume control accuracy, rapid mechanical/diffusion mixing times, appropriate chemically/biologically compatible surfaces, etc.
1. Basic fluid properties and equations
Density:
Ideal gas law:
Pascal's principle: pressure applied to an enclosed fluid is transmitted to every portion of the fluid.
Archimedes' principle: buoyant force action on an immersed body is equal to the force of gravity on the displaced fluid.
Viscosity: how resistance of a fluid is to flow. Dynamic viscosity-- m, kinematic viscosity-- n. increases with pressure. Decreases rapidly with temperature for liquid, increases with temperature for low pressure gas.
Gas Viscosity (Sutherland's formula):
Liquid Viscosity:
Volume flow rate:
Continuity equation (steady state):
Bernoulli's equation (steady state, inviscid, incompressible):
Newtonian fluids--shear stress is linearly proportional to shear rate:
Non-Newtonian fluids—
a. Time-independent fluids with yield stress (need force to initiate flow, ketchup)
b. Time-dependent fluids with shear rates that are both function of magnitude of deformation and time history
c. Viscoelastic fluids: permit some energy of deformation to be recovered (polymer gels)
Note: most body fluids containing high molecular weight solutes are non-Newtonian fluids!! Shear thinning for blood—apparent viscosity at high shear rates is smaller in tiny tubes than in large ones.
2. Types of flow
u Reynolds number: , inertial force to viscous force.
u In large circular ducts:
Re> 2300, Laminar flow=> turbulent flow
u Non circular ducts:
Transition Re is between 2000~3000.
Note: a. for gas flow, flow rate can approach sound velocity when still in laminar range (low Re)
b. Slip flow may occur for gas flow in small channel when dimension is close to the free path of gas molecules, allowing higher flow rate.
d. Liquid viscosity becomes higher in small channel, which may be related to the polar nature of some fluids.
3. Bubbles and particles
u If buoyancy force is smaller than surface tension (< mm size), bubble will stay in place.
u Pressure drop will be large due to surface tension force.
u Bubble valve can be employed according to the above reason.
u To solve bubble problem, using soluble gas for priming, like CO2
u Particle: Stoke law of the force exerted by fluid
4. Capillary forces
u Very important force in micro scale
5. Fluidic resistance
Circular pipe, from Hagen-Poiseuille equation (Newtonian fluid):
=>
ð Flow channels
u Fundamental building blocks
u Can be fabricated by bulk, surface micromachine, and molding, etc.
u Important factors:
a. available channel cross-section areas
b. channel interior surface materials
c. complexity of fabrication
d. Optical accessibility
e. Wall roughness
f. Hermeticity
g. Burst pressure
1. Bulk micromachined channels
a. Bonding of two fused silica at 1000 °C(for cytometry)
b. EDP monolithic silicon substrate (for neural probe, inkjet head)
c. Combining wet and dry bulk micromachine:
d. Buried channels
2. Surface micromachined channels
a. Silicon nitride/silicon substrate (needle, droplet injection for spectroscopy)
b. Low temperature channel (Poyimide+parylene, SU-8, plated metal, LIGA, etc)
3. Other types
u Mechanically fabricated fluidic channels in acrylic, diamond fly cut to obtain smooth surface, and thermally bonded under pressure.
u Integrating flow channel: sensor on silicon, flow channel on glass substrate, polymer gasket, conductive epoxy bumps for electrical connection.
u Combine discrete silicon based fluidic devices on a silicon/glass substrate or mold plastic. Hybrid assembly is more practical than monolithic fluidic system in current stage.
ð Applications of flow channels
u Provide functions of mixing, amplification, separation, switching, and logic operations.
1. Mixers
u Controlling of mixing is important in chemical analysis/synthesis, drug dosing, compound labeling, cell lysis, etc.
u Fick's law:
J: Particle/molecule/ion flux, 1/m2s
D: diffusion coefficient, m2/s
C: concentration, 1/m3
Diffusion time:
u Maximize contact area, and complete by diffusion.
u No turbulent flow to help the above in micro scale. (mixing volume from pl to ml)
u Modes to enhance mixing:
a. sharp corners encourage turbulence (in macro scale)
b. flow around a sharp turn—cause secondary flow
u Laminating mixers
Fold or laminate fluids together to increase the contact area. For flow rate 0.5-12 ml/min, mixing time on the order of 100-300 ms.
u Plume mixers
400 nozzles, 15 mm on a side. For flow at 45 ml/min (total volume 0.5 ml), it takes 1.2 seconds to mix.
u Active mixers
Addition of external energy, i.e., ultrasonic traveling wave, thermal generated vapor bubbles. The later one use chaotic advection, in which initially neighboring particles become widely spread in a chaotic flow field.
2. Diffusion-based extractors
Extraction of molecules can be accomplished on the basis of diffusion coefficient differences.
3. Fluidic amplifiers and logic
Fluidic rectifier (Tesla, 1920)
Coanda effect (1934): flow emerging from a free jet opening will tend to followed nearby angled or curved surfaces and attach to it.—low pressure region forms from the closer side which provide less entrainment molecules.
Temperature, shock, and radiation resistance control and computational systems.—Logic and analog fluidic components:
Fluidic oscillators( LIGA, 500 mm height and 100 mm nozzle width, frequencies of 250-390 Hz from water pressure 0.6-2.4 atm):
Vortex amplification device: use a control stream to deflect a normally straight stream into a spiral path, thereby greatly increasing its path length and pressure drop.—flow and power gains are on 200 and 3000, respectively. This can be also used as a accelerometer.
Thermal bimorph Coanda effect flow director: at 2-7 bar and flow rates of 100-150 ml/min, deflection can be on 1 ms. ~1 W power consumption. Used to control a micromachined valve.