Contents
1. Introduction
9. Liquid Handling
2. Fluids
10.Microarrays
3. Physics of Microfluidic
Systems
11.Microreactors
12.Analytical Chips
4. Microfabrication Technologies
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
13.Particle-Laden Fluids
5. Flow Control
a. Measurement Techniques
6. Micropumps
7. Sensors
b. Fundamentals of
Biotechnology
8. Ink-Jet Technology
c. High-Throughput Screening
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
1
2. Fluids
1. General Characteristics
2. Dispersions
3. Thermodynamics
4. Transport Phenomena
5. Solutions
6. Surface Tension
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
7. Electrical Properties
8. Optical Properties
9. Biological Fluids
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
2
2.3. Thermodynamics
1. Heat and Temperature
2. Heat Capacity
3. Chemical Potentials
4. Kinetic Theory of Gases
5. Compressibility
6. Thermal Expansion
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
7. Real Gases
8. Vapor Pressure
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
3
2.3.1. Heat and Temperature
 Thermal energy per molecule




In thermal equilibrium
Number of degrees of freedom f
Boltzmann constant
Heating 1 mole of ideal gas by 1 K consumes 4.16 J per DoF
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Three translational DoFs
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
4
2.3.1. Heat and Temperature
 Mean kinetic energy
 Combination yields for mean (random, thermal) velocity
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
5
2.3. Thermodynamics
1. Heat and Temperature
2. Heat Capacity
3. Chemical Potentials
4. Kinetic Theory of Gases
5. Compressibility
6. Thermal Expansion
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
7. Real Gases
8. Vapor Pressure
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
6
2.3.2. Heat Capacity
 Raising temperature of N particles by T takes energy
 Heat capacity
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Specific heat capacity
 Molar heat capacity
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
7
2.3. Thermodynamics
1. Heat and Temperature
2. Heat Capacity
3. Chemical Potentials
4. Kinetic Theory of Gases
5. Compressibility
6. Thermal Expansion
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
7. Real Gases
8. Vapor Pressure
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
8
2.3.3. Internal Energy
 Internal energy U
 State property
 Conservation of energy
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Amount of transferred heat Q
- Q > 0: heat absorbed by system
 (Expansion) work W = p V
- W > 0: system delivers work, i.e. system spends energy
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
9
2.3.3. Enthalpy
 Enthalpy (state property)
 Chemical reactions normally at constant p
 Heat energy absorbed or released to system at constant p
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Transferred heat Qp= change in enthalpy
 No volumetric expansion
- Transferred heat = change in internal energy
 Example:
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
10
2.3.3. Entropy
 Entropy
 Probability Wprob of finding system in given state
 Entropy of „universe“
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Entropy of environment Senv
 Entropy of system under investigation S
 Stot constantly grows
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
11
2.3.3. Gibbs Free Enthalpy
 Processes at constant T and p
 Typical for chemical reactions
 Can process occur spontaneously?
 Gibbs free enthalpy G = H - TS
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 G < 0 for spontaneous process
 Decrease in enthalpy H
 Increase in entropy S
 High temperature T
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
12
2.3. Thermodynamics
1. Heat and Temperature
2. Heat Capacity
3. Chemical Potentials
4. Kinetic Theory of Gases
5. Compressibility
6. Thermal Expansion
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
7. Real Gases
8. Vapor Pressure
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
13
2.3.4. Kinetic Theory of Gases
 Gas Pressure
 Force perpendicular to surface A
 Scalar
 Isotropic
 Units




Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
1 Pa = 1 N m-2
1 Torr (= mm Hg) = 133.4 Pa
1 mbar = 1 hPa
1 psi = 6897 Pa
 Standard pressure
 1 atm = 1013 hPa = 1013 mbar =
=760 Torr = 14.7 psi
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
14
2.3.4. Kinetic Theory of Gases
 Molecular picture
 Particle density: N / V
 Only particles in defined sub-volume (A x v x t ) have chance to hit
wall within given time t
 1/3 of velocity vectors statistically perpendicular to surface A
 1/2 of them pointing towards wall
 Number of collisions (N / V ) x ( A x v x t ) / 6
 Each particle transfers twice its momentum: 2 x mv = F t
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
v t
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
15
2.3.4. Kinetic Theory of Gases
 Bernoulli equation
 By replacing v² with v² (mean square velocity)
 Substitute v² by thermal velocity
 Equation of state for ideal gas
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
particles
moles
 # molecules N
 # moles n
 Gas constant Rg = 8.31 J K-1 mol-1
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
16
2.3.4. Kinetic Theory of Gases
 (Trivial) conclusions from equation of state
 Law of Boyle-Mariotte
 Law of Gay-Lussac
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Law of Charles
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
17
2.3.4. CV and Cp for Gases
 Heat capacity of gases
 At constant volume
-
CV = ½ f N kB
 At constant pressure
- Volumetric expansion associated with mechanical work
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
heat
mech. work
 Equivalence of thermal and mechanical energy
 1 cal = 4.18 J
 1842: Robert Mayer and J. P. Joule
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
18
2.3.4. Adiabatic Change of Condition
 Adiabatic process
 No exchange of thermal energy Q = 0
 E.g., under thermal insulation  U = – W
 Complete conversion (internal) heat  pneumatic work
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Insertion of equation of state and CV
CV = ½ f N kB
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
19
2.3.4. Adiabatic Change of Condition
 Relationship for adiabatic process
„non-adiabatic“ gas laws
 Adiabatic coefficient
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Poisson equations
 Compare to „non-adiabatic“ gas laws
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
20
2.3.4. Mean Free Path
 Collisional cross section for given gas
 Mean free path scales with
 Inverse of particle density
 Inverse of collisional cross-section of particles
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
thermal motion of targets
 Example: H2 at p = 1013 hPa
 lmfp = 270 nm
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
21
2.3. Thermodynamics
2.3.1. Heat and Temperature
2.3.2. Heat Capacity
2.3.3. Chemical Potentials
2.3.4. Kinetic Theory of Gases
2.3.5. Compressibility
2.3.6. Thermal Expansion
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
2.3.7. Real Gases
2.3.8. Vapor Pressure
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
22
2.3.5. Compressibility
 Compressibility of fluids
 Isothermal compressibility for ideal gas
 Bulk modulus
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
p V = const.
 Differentiation of modified (adiabatic) law of Boyle-Mariotte
 Adiabatic compressibility
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
23
2.3.5. Compressibility
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
24
2.3. Thermodynamics
2.3.1. Heat and Temperature
2.3.2. Heat Capacity
2.3.3. Chemical Potentials
2.3.4. Kinetic Theory of Gases
2.3.5. Compressibility
2.3.6. Thermal Expansion
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
2.3.7. Real Gases
2.3.8. Vapor Pressure
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
25
2.3.6. Thermal Expansion
 Thermal expansion coefficient
 Derivation from equation of state for (ideal) gases
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Expansion of cube
 Linear approximation
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
26
2.3.6. Thermal Expansion
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
27
2.3. Thermodynamics
2.3.1. Heat and Temperature
2.3.2. Heat Capacity
2.3.3. Chemical Potentials
2.3.4. Kinetic Theory of Gases
2.3.5. Compressibility
2.3.6. Thermal Expansion
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
2.3.7. Real Gases
2.3.8. Vapor Pressure
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
28
2.3.7. Real Gases
 Van-der-Waals equation
 Volume per mole Vn
 „Internal pressure“ a/Vn²
- Attractive forces between molecules
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Parameter for strength of interaction a
 Covolume b
- Spatial extension of molecules subtracted from overall volume
- At low pressures negligible due to large volume per mole Vn
 Joule-Thomson effect
 Change in temperature during rapid expansion
 Work against intermolecular forces
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
29
2.3. Thermodynamics
2.3.1. Heat and Temperature
2.3.2. Heat Capacity
2.3.3. Chemical Potentials
2.3.4. Kinetic Theory of Gases
2.3.5. Compressibility
2.3.6. Thermal Expansion
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
2.3.7. Real Gases
2.3.8. Vapor Pressure
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
30
2.3.8. Vapor Pressure
 Coexistence of liquid and gaseous state




Closed vessel
Vapor forms above liquid
Saturated vapor pressure
Boiling
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
Standard
Pressure
 Temperature dependence
Boiling
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
31
2.3.8. Vapor Pressure
 Vapor pressure curve
 Coexistence of liquid and vapor
 Restricted to 1-dimensional curve
- Above only vapor
- Below only liquid
 Critical point
 Phases „converge“
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
32
2.3.8. Vapor Pressure
 Absolute humidity abs
 Concentration of mass, measured in g / m3
 Relation to partial pressure of water pwater
- Mass of water molecule mwater
 Relative humidity
 rel referred to abs at saturation
Pr isbexa ispel: Ausar beitun gspha
Au tsarbei ungde rStand ard-Ze el
 Heat of vaporization 
 E per mass to „escape“ liquid phase
 Equation of Clausius and Clapeyron
 Temperature T
 Derivative of vapor pressure curve dp / dT
 Difference between specific volumes Vm
Microfluidics - Jens Ducrée
Fluids: Thermodynamics
33