Contents. 2. Fluids. 1. Introduction
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1 Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors 12.Analytical Chips 13.Particle-Laden Fluids a. Measurement Techniques b. Fundamentals of Biotechnology c. High-Throughput Screening Microfluidics - Jens Ducrée Fluids: Electrical Properties 1
2 2. Fluids 2.1. General Characteristics 2.2. Dispersions 2.3. Thermodynamics 2.4. Transport Phenomena 2.5. Solutions 2.6. Surface Tension 2.7. Electrical Properties 2.8. Optical Properties 2.9. Biological Fluids Microfluidics - Jens Ducrée Fluids: Electrical Properties 2
3 2.7. Electrical Properties Distinction Gases Liquids (Direct) current Electric field E = U / L Response: motion of free charge carriers - Ions - Electrons Gases Plasma-like state Liquids Electrolytes containing solvated ions Microfluidics - Jens Ducrée Fluids: Electrical Properties 3
4 2.7. Electrical Properties Gas Discharges Conductivity in Liquids and Solutions Electrochemical Cells Dielectric Properties Microfluidics - Jens Ducrée Fluids: Electrical Properties 4
5 Gas Discharges Constant generation of charge carriers Equal number N of positive and negative charge carriers Charge generation rate αq Recombination rate Constant of recombination β Stationary concentration Natural sources αq = 10 6 m -3 s -1 Recombination β = m 3 s -1 Charge carrier density ρ N = 10 9 m -3 very small Microfluidics - Jens Ducrée Fluids: Electrical Properties 5
6 Gas Discharges Ionization chamber Measuring electrical properties of gas - Ionic mobility µ - I(U) Microfluidics - Jens Ducrée Fluids: Electrical Properties 6
7 Stationary drift velocity Gas Discharges Collisions with neutral atoms Superimposed upon thermal velocity v T >> v Time between collisions τ = lmfp / v T Acceleration a = q E / m Mean velocity - Assuming total loss of kinetic energy upon collision v = µ E - Comparison of factors yields (with q = e) ionic mobility Microfluidics - Jens Ducrée Fluids: Electrical Properties 7
8 Gas Discharges Proportional counter tube (low U) Stationary charge carrier density Current density scales in Ohmic fashion with electric field strength Region of saturation All ions generated in active region reach electrode Region of impact ionization High field strength in vicinity of wire anode in Geiger-Müller tube Charge amplified in avalanche of electron impact ionizations Additional electrons ionize atoms while proceeding to anode Microfluidics - Jens Ducrée Fluids: Electrical Properties 8
9 Gas Discharges Paschen curve Break through voltage U break Product pd - Electrode spacing d - Pressure p Example Standard pressure 1013 hpa Microscopic distances µm pd = mm hpa Part below minimum At fixed d, U break sharply decreases with pressure p Microfluidics - Jens Ducrée Fluids: Electrical Properties 9
10 2.7. Electrical Properties Gas Discharges Conductivity in Liquids and Solutions Electrochemical Cells Dielectric Properties Microfluidics - Jens Ducrée Fluids: Electrical Properties 10
11 Conductivity in Liquids and Solutions Velocities of anions and cations Limit of high dilution: independent migration of ions Stationary case - Equal electrical and frictional forces: Fυ = - FE Microfluidics - Jens Ducrée Fluids: Electrical Properties 11
12 Conductivity in Liquids and Solutions Current densities Law of Kohlrausch - High dilution limit Charge carrier concentrations ci Relative charge zi Both carrier types contribute constructively Electrolytic conductivity Measured at AC (polarization) Microfluidics - Jens Ducrée Fluids: Electrical Properties 12
13 Conductivity in Liquids and Solutions Overall electric neutrality Electrolyte always neutral on macroscale Valid down to Debye radius - Distance where thermal energy roughly equals Coulomb energy Ionic strength Coulomb coupling capability per unit volume Microfluidics - Jens Ducrée Fluids: Electrical Properties 13
14 2.7. Electrical Properties Gas Discharges Conductivity in Liquids and Solutions Electrochemical Cells Dielectric Properties Microfluidics - Jens Ducrée Fluids: Electrical Properties 14
15 Electrochemical Cells Galvanic Cell Chemical energy converted into voltage difference U Example: Daniell cell - Zn-electrode in ZnSO4 solution - Cu-electrode in CuSO4 solution - Semipermeable membrane or KCl salt bridge Blocks metal ions Zn 2+ and Cu 2+, SO4 2- passes membrane Prevents direct e-exchange between Cu 2+ and Zn - Overall redox reaction Microfluidics - Jens Ducrée Fluids: Electrical Properties 15
16 Electrochemical Cells Electromotive force (EMF) Voltage produced by galvanic cell Often specified for standard conditions - a= 1 (activity, effective concentration) - c= 1 mol l C - p= 1013 hpa Daniell element at standard conditions U0 = 1.10 V Reference: standard hydrogen electrode Microfluidics - Jens Ducrée Fluids: Electrical Properties 16
17 Electrochemical Cells Maximum energy Galvanic cell operating at U EMF Moles of redox pair n Electrons produced per reaction z Faraday constant - Relates moles to charge Change in Gibbs enthalpy - U EMF > 0 for spontaneous process G < 0 Microfluidics - Jens Ducrée Fluids: Electrical Properties 17
18 Electrochemical Cells Nernst equation Potential under non-standard conditions k c constant of mass action law Dependency on molar concentration c - Galvanic cells with equal parameters - Except concentration of solvated ions Microfluidics - Jens Ducrée Fluids: Electrical Properties 18
19 Electrochemical Cells Electrolytic cells Reversal of spontaneous redox reaction Voltage source U > -U EMF Electrolysis Electrical energy chemical energy E.g. rechargeable batteries Electrolysis of water Protons reduced to H2 gas at cathode Hydroxide ions oxidized at anode Faraday s Law Microfluidics - Jens Ducrée Fluids: Electrical Properties 19
20 2.7. Electrical Properties Gas Discharges Conductivity in Liquids and Solutions Electrochemical Cells Dielectric Properties Microfluidics - Jens Ducrée Fluids: Electrical Properties 20
21 Dielectric Properties Poisson equation Vacuum conditions ε 0 = x C V -1 m -1 Capacity Parallel plate capacitor in vacuum Cross sectional area A Distance between plates d Microfluidics - Jens Ducrée Fluids: Electrical Properties 21
22 Dielectric Properties Dielectric permittivity Dielectric medium between plates Capacity enhanced by factor of ε = Cq/Cq,0 > 1 Relative permittivity ε Absolute permittivity εε 0 Molecular dipole moments Charge q, spaced by vector dêr Density of molecular dipole moments Dielectric susceptibility Microfluidics - Jens Ducrée Fluids: Electrical Properties 22
23 Dielectric Properties Microfluidics - Jens Ducrée Fluids: Electrical Properties 23
24 Dielectric Properties Mechanisms of dielectric polarization Dipole moment induced by external field E Elastic constant k elast (d / dr) F Coul Polarizability αε 2πε 0 r 3 Atomic radius r Relation between microscopic and macroscopic quantities Law of Clausius-Mosotti (for liquids and solids) Takes non-negligible dipole-dipole interactions into account Microfluidics - Jens Ducrée Fluids: Electrical Properties 24
25 Dielectric Properties Dielectric relaxation Response time for adjustment of dipole moments to E-field Approx s for induced dipole moments Frequency-dependency negligible even for visible light Field oscillation at approx s Permanent dipoles much slower - E.g., water s for complete reversal - Response time even slower for solids ε=ε(ν) for ν >10 10 Hz Phase shift δ with respect to E-field Complex dielectric permittivity microwave heater (GHz) Microfluidics - Jens Ducrée Fluids: Electrical Properties 25
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