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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Fully comprehensive introduction to the rapidly emerging area of micro systems technology
Transport Phenomena in Micro Systems explores the fundamentals of the new technologies related to Micro-Electro-Mechanical Systems (MEMS). It deals with the behavior, precise control and manipulation of fluids that are geometrically constrained to a small, typically sub-millimeter, scale, such as nl, pl, fl, small size, low energy consumption, effects of the micro domain and heat transfer in the related devices. The author describes in detail and with extensive illustration micro fabrication, channel flow, transport laws, magnetophoresis, micro scale convection and micro sensors and activators, among others. This book spans multidisciplinary fields such as material science and mechanical engineering, engineering, physics, chemistry, microtechnology and biotechnology.
- Brings together in one collection recent and emerging developments in this fast-growing area of micro systems
- Covers multidisciplinary fields such as materials science, mechanical engineering, microtechnology and biotechnology, et al
- Comprehensive coverage of analytical models in microfluidics and MEMS technology
- Introduces micro fluidics applications include the development of inkjet printheads, micro-propulsion, and micro thermal technologies
- Presented in a very logical format
- Supplies readers with problems and solutions
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Seitenzahl: 781
Veröffentlichungsjahr: 2015
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Table of Contents
Title Page
Copyright
About the Author
Preface
Acknowledgement
Chapter 1: Introduction
1.1 History
1.2 Definition
1.3 Analogy of Microfluidics with Computing Technology
1.4 Interdisciplinary Aspects of Microfluidics
1.5 Overall Benefits of Microdevices
1.6 Microscopic Scales for Liquids and Gases
1.7 Physics at Micrometric Scale
1.8 Scaling Laws
1.9 Shrinking of Human Beings
Problems
References
Supplemental Reading
Chapter 2: Channel Flow
2.1 Introduction
2.2 Hydraulic Resistance
2.3 Two Connected Straight Channels
2.4 Equivalent Circuit Theory
2.5 Reynolds Number
2.6 Governing Equation for Arbitrary-Shaped Channel
2.7 Summary of Hydraulic Resistance in Straight Channels
2.8 Viscous Dissipation of Energy
2.9 Compliance
Problems
Supplemental Reading
Chapter 3: Transport Laws
3.1 Introduction
3.2 Boundary Slip
3.3 Slip Flow Boundary Condition in Gases
3.4 Slip Flow Boundary Condition in Liquids
3.5 Physical Parameters Affecting Slip
3.6 Possible Liquid Slip Mechanism
3.7 Thermal Creep Phenomena
3.8 Couette Flow with Slip Flow Boundary Condition
3.9 Compressibility Effect in Microscale Flows
3.10 Slip Flow between Two Parallel Plates
3.11 Fluid Flow Modeling
Problems
References
Supplemental Reading
Chapter 4: Diffusion, Dispersion, and Mixing
4.1 Introduction
4.2 Random Walk Model of Diffusion
4.3 Stokes–Einstein Law
4.4 Fick's Law of Diffusion
4.5 Diffusivity and Mass Transport Nomenclature
4.6 Governing Equation for Multicomponent System
4.7 Characteristic Parameters
4.8 Diffusion Equation
4.9 Taylor Dispersion
4.10 Micromixer
4.11 Convective Diffusion
4.12 Detailed Analysis
4.13 Reverse Osmosis
Problems
Supplemental Reading
Chapter 5: Surface Tension-Dominated Flows
5.1 Surface Tension
5.2 Gibbs Free Energy and Surface Tension
5.3 Microscopic Model of Surface Tension
5.4 Young–Laplace Equation
5.5 Contact Angle
5.6 Dynamic Contact Angle
5.7 Superhydrophobicity and Superhydrophilicity
5.8 Microdrops
5.9 Capillary Rise and Dimensionless Numbers
5.10 Coating Flows
5.11 Enhanced Oil Recovery
5.12 Classification of Surface Tension Gradient-Driven Flow
5.13 Boundary Conditions
5.14 Thermocapillary Motion
5.15 Diffusocapillary Flow
5.16 Electrowetting
5.17 Marangoni Convection in Drops
5.18 Marangoni Instability
5.19 Micropropulsion System
5.20 Capillary Pump
5.21 Thermocapillary Motion of Droplets
5.22 Thermocapillary Pump
5.23 Taylor Flows
5.24 Two-Phase Liquid–Liquid Poiseuille Flow
5.25 Hydrodynamics of Taylor Flow
5.26 Plug Motion in Capillary
5.27 Clogging Pressure
5.28 Digital Microfluidics
Problems
References
Supplemental Reading
Chapter 6: Charged Species Flow
6.1 Introduction
6.2 Electrical Conductivity and Charge Transport
6.3 Electrohydrodynamic Transport Theory
6.4 Electrolytic Cell Example
6.5 The Electric Double Layer and Electrokinetic Phenomena
6.6 Debye Layer Potential Distribution
6.7 Electrokinetic Phenomena Classification
6.8 Electroosmosis
6.9 Exact Expression for Cylindrical Channel EO Flow
6.10 EO Pump
6.11 EO Flow in Parallel Plate Channel
6.12 Electroosmosis and Forced Convection
6.13 Electrophoresis
6.14 Dielectrophoresis
6.15 Polarization and Dipole Moments
6.16 Point Dipole in a Dielectric Fluid
6.17 Dielectric Sphere in a Dielectric Fluid: Induced Dipole
6.18 Dielectrophoretic Force on a Dielectric Sphere
6.19 Dielectrophoretic Trapping of Particles
6.20 AC Dielectrophoretic Force on a Dielectric Sphere
Problems
Supplemental Reading
Chapter 7: Magnetism and Microfluidics
7.1 Introduction
7.2 Magnetism Nomenclature
7.3 Magnetic Beads
7.4 Magnetic Bead Characterization
7.5 Magnetostatics
7.6 Magnetophoresis
7.7 Magnetic Force on Particles
7.8 Magnetic Particle Motion
7.9 Magnetic Field Flow Fractionation
7.10 Ferrofluidic Pumps
7.11 Magnetic Sorting and Separation
7.12 Magneto-Hydrodynamics
7.13 Governing Equations for MHD
Problems
Reference
Supplemental Reading
Chapter 8: Microscale Conduction
8.1 Introduction
8.2 Energy Carriers
8.3 Scattering Mechanism
8.4 Nonequilibrium Conditions
8.5 Time and Length Scales
8.6 Scale Effects
8.7 Fourier's Law
8.8 Hyperbolic Heat Conduction Equation
8.9 Kinetic Theory
8.10 Heat Capacity
8.11 Boltzmann Transport Theory
8.12 Microscale Two-Step Models
8.13 Thin Film Conduction
References
Chapter 9: Microscale Convection
9.1 Introduction
9.2 Scaling Analysis
9.3 Laminar Fully Developed Nusselt Number
9.4 Why Microchannel Heat Transfer
9.5 Gases versus Liquid Flow in Microchannels
9.6 Temperature Jump
9.7 Couette Flow with Viscous Dissipation
9.8 Isothermal Parallel Plate Channel Flow without Viscous Heating
9.9 Large Parallel Plate Flow without Viscous Heating: Uniform Surface Flux
9.10 Fully Developed Flow in Microtubes: Uniform Surface Flux
9.11 Convection in Isothermal Circular Tube with Viscous Heating
9.12 Flow Boiling Heat Transfer in Mini-/Microchannels
9.13 Condensation Heat Transfer in Mini-/Microchannel
Problems
References
Supplemental Reading
Chapter 10: Microfabrication
10.1 Introduction
10.2 Microfabrication Environment
10.3 Functional Materials
10.4 Surface Preparation
10.5 General Micromachining Procedure
10.6 Photolithography
10.7 Subtractive Techniques
10.8 Additive Techniques
10.9 Example of a Silicon Membrane Fabrication
10.10 PDMS-Based Molding
10.11 Sealing
10.12 Laser Microfabrication Techniques
Problems
Supplemental Reading
Chapter 11: Microscale Measurements
11.1 Introduction
11.2 Microscale Velocity Measurement
11.3 PIV Fundamentals
11.4 Micro-PIV System
11.5 Temperature Measurement
References
Supplemental Reading
Chapter 12: Microscale Sensors and Actuators
12.1 Introduction
12.2 Flow Control
12.3 Actuator Classification
12.4 Shear Stress Sensors
12.5 Classification of Shear Stress Sensors
12.6 Calibration of Shear Stress Sensors
12.7 Uncertainty and Noise
References
Supplemental Reading
Chapter 13: Heat Pipe
13.1 Introduction
13.2 Applications of Heat Pipe
13.3 Advantages of Heat Pipe
13.4 Heat Pipe Operation
13.5 Wick Structure
13.6 Working Fluids and Structural Material of Heat Pipe
13.7 Operating Temperature of Heat Pipe
13.8 Ideal Thermodynamic Cycle of Heat Pipe
13.9 Microheat Pipe
13.10 Effective Thermal Conductivity
13.11 Operating Limits
13.12 Cleaning and Charging
Reference
Supplemental Reading
Index
End User License Agreement
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Guide
Table of Contents
Begin Reading
List of Illustrations
Chapter 1: Introduction
Figure 1.1 (a) Size characteristics and (b) volume characteristics of different microsystems
Figure 1.2 (a) A banyan tree and (b) schematic of transport process inside the capillary network
Figure 1.3 A picture of spider web having more strength than that of steel
Figure 1.4 Three molecules of different sizes
Figure 1.5 A sketch showing the double helical structure of DNA
Figure 1.6 Electric field strength for dielectric breakdown of a parallel-plate capacitor in air
Chapter 2: Channel Flow
Figure 2.1 Flow patterns as a function of Reynolds number () of a backward facing step: (a) and (b) . The flow is analogous to two hydraulic resistors, and , connected in series for flow inside channel 1 and channel 2 of varying cross-sections
Figure 2.2 The series coupling of two channels (channel-1 and channel-2) with hydraulic resistances and
Figure 2.3 The parallel coupling of two channels (channel-1 and channel-2) with hydraulic resistances and
Figure 2.4 An equivalent circuit analysis of a cascade electro-osmotic micropump: (a) a sketch of the micropump, consisting of 10 narrow channels in parallel followed by a single wide channel in series, and (b) the equivalent circuit diagram for calculation of the hydraulic resistance of single stage of a micropump consisting of two wide channels and one multichannel combination of the micropump
Figure 2.5 A sketch of an infinite, parallel-plate channel of height in the – plane. The fluid is flowing in the -direction because of a pressure drop over the section of length
Figure 2.6 Fabrication of microchannels by laser ablation of polymer, PMMA: (a) schematic diagram of the laser beam, the laser ablated groove, including the molten PMMA and the vaporized hemispherical cloud of MMA leaving the cut-zone, (b) Scanning electron microscope (SEM) micrograph of the cross-section of an actual microchannel showing the resulting Gaussian-like profile
Figure 2.7 The Poiseuille flow problem in the -direction of a channel, which has an arbitrarily shaped cross-section in the –-plane. The boundary of is denoted by . The pressure at the left end, , is an amount higher than that at the right end,
Figure 2.8 The four specific cross-sectional shapes for the Poiseuille flow problem: (a) the ellipse with major axis and minor axis , (b) the circle with radius , (c) the equilateral triangle with side length , and (d) the rectangle with height and width
Figure 2.9 Schematic of transient fluid flow behavior inside a channel. For times the flow is in steady-state, due to the over-pressure applied to the left. The flow profile is a characteristic parabola. Suddenly, the pressure is turned off at . However, the inertia keeps up the flow. For the fluid velocity diminishes due to viscous friction, and in the limit the fluid comes to rest relative to the channel walls
Figure 2.10 A sketch of the geometry for calculating the viscous energy dissipation in a Poiseuille flow
Figure 2.11 Average temperature in the flow direction of a microtube at as a function of capillary diameter
Figure 2.12 (a) A volume of gas trapped in a closed channel wall partly filled with liquid, (b) equivalent hydraulic circuit, (c) a similar series circuit
Figure 2.13 The normalized pressure–time evolution of the trapped gas inside the closed channel
Figure 2.14 (a) Compliance due to a soft-walled channel filled with liquid, and (b) the equivalent circuit diagram corresponding to the soft-walled channel
Chapter 3: Transport Laws
Figure 3.1 Schematic representations of the (a) no-slip, (b) partial slip, and (c) perfect slip boundary conditions. Under no-slip boundary condition, the relative velocity between the fluid and the solid wall is zero at the wall. When slip occurs at the wall, is finite. The extent of the slip is characterized by the slip length
Figure 3.2 (a) Simplified view of gas–surface interaction, (b) specular reflection with incident angle same as reflected angle , (c) diffuse reflection where the gas molecules interact with the surface molecule multiple times as they are re-emitted to the gas
Figure 3.3 Momentum accommodation coefficient of nitrogen gas as a function of Knudsen number
Figure 3.4 A schematic showing gas molecule interaction with the wall
Figure 3.5 (a) The ratio of experiment flow rate () to theoretical flow rate () and (b) the slip length as a function of channel height for different fluids (water, silicone oil, decane, hexane, and hexadecane)
Figure 3.6 (a,b) Comparison of slip velocity and slip length between hydrophilic and hydrophobic surfaces as a function of shear rate
Figure 3.7 (a) Schematic of the arrangement for slip length characterization, (b) the normalized hydrodynamic force versus inverse of separation for fluid of different viscosities and comparison with no-slip flow calculation, and (c) slip length as a function of viscosity and driving rate
Figure 3.8 (a) Experimental arrangement for -PIV measurement and (b) velocity profile for hydrophilic and hydrophobic surfaces obtained from -PIV measurement
Figure 3.9 Velocity profile for (a) Couette and (b) Poiseuille flows. Comparison between molecular dynamics simulation, no-slip boundary condition, and partial slip boundary condition
Figure 3.10 A schematic of the thermal creep experiment
Figure 3.11 Schematic showing the thermal creep flow
Figure 3.12 Schematic of the Couette flow
Figure 3.13 Comparison of Couette flow velocity profile using the slip flow boundary condition with that of the no-slip flow boundary condition
Figure 3.14 Velocity profile in a Couette flow as a function of (a) Knudsen number with fixed and (b) tangential accommodation coefficient with fixed
Figure 3.15 A schematic of flow between two parallel plates
Figure 3.16 Poiseuille flow velocity profile inside two parallel plates of length m, height m, N–S/m by imposed pressure gradient N/m for (a) different Knudsen numbers with fixed and (b) different tangential accommodation coefficients with fixed
Figure 3.17 Variation of mass flow rate normalized with no-slip flow rate as a function of pressure ratio
Figure 3.18 Velocity slip variation on channel surface for different transverse dimensions of the channel
Figure 3.19 Operational range of various MEMS devices as a function of Knudsen number () and length scale
Figure 3.20 Different schemes for modeling of fluid flow
Figure 3.21 Validity range of different gas flow modeling approaches. Here, and are the mass density and the number density at standard condition of 1-atm pressure, is the mean molecular spacing, and is the mean molecular diameter
Figure 3.22 Schematic showing the representative control volume for the validity of continuum assumption
Figure 3.23 Schematic showing the domain for molecular dynamics simulation
Figure 3.24 Potential energy () with respect to the intermolecular distance based on the Lennard-Jones potential
Figure 3.25 Domain for MD-continuum coupling
Chapter 4: Diffusion, Dispersion, and Mixing
Figure 4.1 Random one-dimensional location of four particles with time starting from the same fixed location
Figure 4.2 An infinitely thin long microchannel filled with water and a fixed amount of source material introduced at time,
Figure 4.3 The concentration distribution for the point source 1-D diffusion, where is the length scale in the -direction and time scale, : (a) lengthwise dependence of concentration distribution at three time instants and (b) the time dependence of concentration at three streamwise positions
Figure 4.4 The concentration distribution in case of constant planar source diffusion, where concentration at remains constant at all later times: (a) the -dependence of concentration at three time instants and (b) the time dependence of concentration at four streamwise locations. Here, is the length scale and is the time scale
Figure 4.5 Example of Taylor dispersion in a microchannel with a steady Poiseuille flow: (a) initial flat concentration of the solute, (b) stretching of the solute to a paraboloid-shaped plug neglecting diffusion, and (c) solute plug with diffusion indicated by vertical arrows
Figure 4.6 The schematic for Taylor dispersion flow in a microchannel separated by distance, , between two planes
Figure 4.7 Schematic of an H-filter for separation of small-sized analytes from large-sized analytes
Figure 4.8 A circular micromixer operating on principle of Taylor dispersion
Figure 4.9 A micromixer with the principal channel divided into large number of smaller cross-sectional channels
Figure 4.10 Hydrodynamic focusing by a control flow
Figure 4.11 Evolution of two particles initially very close to each other in a chaotic system, which subsequently separate from each other
Figure 4.12 Different schemes for initiating chaotic advection in microscale flow: (a) slanted ribs/grooves, (b) herringbone grooves, (c) serpentine passage, and (d) posts or cylindrical obstacles on the channel
Figure 4.13 Schematic showing active mixing strategy: (a) pressure disturbance leading to segmentation and (b) dielectrophoretic, electrohydrodynamic, electrokinetic, and magnetohydrodynamic disturbance generated by the electrode
Figure 4.14 (a) Different flow patterns of microdroplet with an increase in capillary number, (b) droplet formation regime as function of capillary number, and (c) vortex structures inside droplet
Figure 4.15 The schematic showing the development of viscous and diffusion boundary layers over a reactive wall surface
Figure 4.16 Schematic of a developing velocity boundary layer in the internal flow situation
Figure 4.17 The schematic of a channel with soluble walls
Figure 4.18 Schematic of (a) asymmetric membrane and (b) thin-film composite membrane
Figure 4.19 A channel flow undergoing reverse osmosis process
Figure 4.20 Similarity solution for concentration defect in developing boundary layer at inlet region of a reverse osmosis channel flow
Figure 4.21 Concentration polarization development in downstream direction in a parallel membrane reverse osmosis channel with laminar flow and complete rejection
Chapter 5: Surface Tension-Dominated Flows
Figure 5.1 Schematic showing the origin of surface tension for a liquid–gas interface. (a) A molecule in the bulk of the liquid forms chemical bonds (arrows) with the neighboring molecules surrounding it. (b) A molecule at the surface of the liquid misses the chemical bonds in the direction of the surface (dashed lines). Consequently, the energy of surface molecules is higher than that of bulk molecules, and the formation of such an interface costs energy
Figure 5.2 Schematic of surfactant monolayer at the water–air interface
Figure 5.3 Schematic describing the pressure drop across a curved interface
Figure 5.4 (a) Definition of the contact angle and (b) the schematic of a liquid drop moving on an inclined plane
Figure 5.5 A sketch of the small displacement of the contact line away from the equilibrium position. The change of the interface areas is proportional to , , and for the solid–liquid, liquid–gas, and solid–gas interface, respectively
Figure 5.6 A liquid plug in a capillary tube with its advancing and receding contact angles
Figure 5.7 The dynamic contact angle data of silicon oil inside a 2 mm diameter capillary as a function of capillary number. The solid line represents the Tanner's law profile for different constants
Figure 5.8 Schematic of the advancing (), static (), and receding () contact angles
Figure 5.9 Schematic showing the microscopic view of droplet on the top of a lotus leaf
Figure 5.10 Sample SEM images of a lotus leaf surface with low resolution (a) and high resolution (b) demonstrating the nature of roughness
Figure 5.11 Microscopic view of a liquid drop on a rough solid surface
Figure 5.12 A schematic showing the superhydrophobic surface fabricated by etching microgrooves on a hydrophobic substrate
Figure 5.13 The displacement of the contact line of a drop on an inhomogeneous solid surface
Figure 5.14 (a) The schematic of the surfactant distribution in a liquid drop and (b) the influence of surfactant concentration on surface tension
Figure 5.15 The sequence of motion of a drop at the boundary of a step between hydrophilic (top) and hydrophobic (bottom) surface
Figure 5.16 The force distribution on a water droplet at the boundary between a hydrophilic/hydrophobic contact
Figure 5.17 Dispensing of microdrops to wells of a microplate of DNA microarray
Figure 5.18 Schematic showing partial and total wetting
Figure 5.19 Schematic showing the hydrophilic and hydrophobic contact of a droplet
Figure 5.20 Schematic view of forces at the hydrophilic and hydrophobic contact line
Figure 5.21 Schematic of a microdrop of oil on top of water layer
Figure 5.22 The schematic showing the capillary rise
Figure 5.23 Schematic of dip coating process
Figure 5.24 Formation of a liquid film in a circular capillary by blowing an air bubble
Figure 5.25 Schematic showing the thermocapillary motion
Figure 5.26 Marangoni effect in a microwell of a DNA array
Figure 5.27 Schematic of an (a) oil recovery system and (b) bubble shape inside the capillary due to accumulation of surfactant
Figure 5.28 The schematic showing the principle of electrowetting of a drop. The liquid is much better conductor than the insulating layer. The interface is polarized without generating any crossing current
Figure 5.29 Schematic cross-section of the electrowetting microactuator
Figure 5.30 Schematic of Marangoni-driven convection inside a droplet due to temperature difference
Figure 5.31 Schematic of Bénard cell seen from the top of the container, where a thin layer of liquid is heated below
Figure 5.32 Instability mechanism for Bénard cell formation
Figure 5.33 An object (bacteria) placed near an interface. Here, the paper is parallel to the interface
Figure 5.34 The surfactant is excreted at one end, and the net imbalance in surface tension force balances drag during motion
Figure 5.35 The movement of a small boat due to surface tension force
Figure 5.36 A lab-on-a-chip with capillary pump
Figure 5.37 Schematic showing the principle of a capillary pump. The curved meniscus results in an uncompensated Young–Laplace under pressure, . This pressure difference drives the liquid to the right in the microchannel
Figure 5.38 Schematic showing flow patterns inside a drop under horizontal thermal gradient
Figure 5.39 Schematic showing the thermocapillary pumping of a liquid drop on (a) hydrophilic surface and (b) hydrophobic surface
Figure 5.40 A schematic showing fluid plugs, that is, buffer fluid plugs and oil plugs
Figure 5.41 Synchronized fluid plugs moving in parallel capillaries
Figure 5.42 Various junction types for generation of two-phase flows in a microfluidic system: (a) T-junction and (b) cross-junction
Figure 5.43 Schematic showing the formation of droplets at different phases in a cross-junction microfluidic system
Figure 5.44 Schematic showing the formation of an air bubble
Figure 5.45 Schematic showing various gas–liquid flow patterns observed in capillary channels: (a) film flow, (b) bubbly flow, (c) segmented flow (Taylor flow), (d) churn flow, and (e) annular flow
Figure 5.46 Typical flow patterns as a function of representative dimensionless number
Figure 5.47 Schematic showing two-phase Poiseuille flow of fluid 1 (viscosity, ) and fluid 2 (viscosity, ) between two horizontally placed parallel infinite plates
Figure 5.48 Sample results from micro-PIV measurement inside the ethanol plug for 500 m capillary: (a) streamline patterns, (b) -velocity profile inside the ethanol plug, and (c) the -velocity profile inside the ethanol plug. Here, indicates the normalized distance from the interface normalized by the channel width
Figure 5.49 Comparison of film thickness () between theoretical prediction of Bertherton and experimental results of Taylor and Bretherton as a function of capillary number
Figure 5.50 Decomposition of plug flow into different lumped elements
Figure 5.51 Hysteresis of static contact angle
Figure 5.52 The plug moving inside a capillary and the pressure distribution (a) at low speed and (b) at high speed
Figure 5.53 A gas bubble surrounded by a liquid inside a hydrophilic axisymmetric channel with contraction
Figure 5.54 Different protocols for mixing of two fluids: (a) continuous flow, (b) plug flow, and (c) open-surface manipulation
Figure 5.55 Particle separation process based on digital microfluidics: (a) initial stage, (b) charge separation within the droplet, (c) splitting of droplet, and (d) transport of split daughter droplet
Chapter 6: Charged Species Flow
Figure 6.1 Schematic showing the influence of the electric field application on an ionized solution
Figure 6.2 A schematic showing electroplating, where the electrode-metal 1 is consumed and plated on the surface of electrode-metal 2
Figure 6.3 A schematic of an electrolytic cell
Figure 6.4 The current–voltage characteristic of the electrolytic cell
Figure 6.6 Concentration distribution inside a Debye layer
Figure 6.5 Schematic showing the electric double layer region
Figure 6.7 Detailed characterization of Debye layer
Figure 6.8 (a) An electrolyte occupying the space of width between two parallel plane electrodes. Application of a voltage difference between the two electrodes develops a Debye layer of width on each of them. (b) The equivalent circuit diagram of panel (a) consisting of one capacitor for each Debye layer and one resistor for the bulk electrolyte
Figure 6.9 Electroosmotic flow of water in a porous charged medium
Figure 6.10 The velocity profile, , and the negative Debye layer charge density profile, , in an ideal electroosmotic (EO) flow inside a channel. The EO flow is induced by the external potential difference , resulting in the homogeneous electric field . The velocity profile reaches the constant value at a distance of a few times the Debye length from the walls
Figure 6.11 Dimensionless potential distribution across a cylindrical capillary obtained by the numerical solution of the potential distribution equation
Figure 6.12 Sketch showing capillary with a different Debye length
Figure 6.13 The normalized EO flow profile for a cylindrical channel of radius , with three different values of the Debye length
Figure 6.14 The velocity profile and the Debye layer charge density profile in an ideal electroosmotic (EO) flow with back pressure, , inside a cylindrical channel of radius, . The EO flow is induced by the external potential difference, . It may be noted that the flat EO flow profile in Figure 6.10 now has a parabolic dent due to the superimposed back-pressure-driven Poiseuille flow profile
Figure 6.15 (a) The flow rate–pressure characteristic for an ideal EO flow with back pressure . (b) The flow profile in a cylindrical microchannel at the electroosmotic pressure , where the net flow rate is zero ()
Figure 6.16 A frit-based electoosmotic micropump, where the glass frit (gray hatched square) is situated in the central layer between polymer sheets. The platinum electrodes, where gas bubbles are generated by electrolysis, are separated from the liquid flow by anion exchange membranes, which only allow the passage of ions
Figure 6.17 (a) The cascade EO pump with three identical stages. Each stage consists of 10 narrow channels in series with one wide channel, and the total voltage drop per stage is zero. (b) The schematic of a single stage of the cascade EO pump, which yields a finite EO flow with the total voltage drop along the channel equal to zero
Figure 6.18 Schematic for electroosmotic flow inside parallel plate channel geometry
Figure 6.19 Distribution of electric potential inside the double layer
Figure 6.20 Velocity distribution as a function of Debye number () inside parallel plate channel geometry
Figure 6.21 Fully developed liquid flow forced with convection in microchannel
Figure 6.22 Microchannel heat transfer with EDL effect
Figure 6.23 The principle of electrophoresis. A spherical particle of charge and radius moves in a low-conductivity liquid with viscosity under the influence of an applied electrical field
Figure 6.24 A negatively charged particle placed in an electrolyte forming a diffuse layer, which tends to screen the electric field produced by the particle
Figure 6.25 (a) A simple capillary electrophoresis system and (b) an example of temporal reading of species
Figure 6.26 The schematic showing the positive and negative dielectrophoresis
Figure 6.27 (a) The simple point dipole consisting of a charge separated from a charge by the distance . (b) The dipole moments and external charges inside a body. Polarization charge is left behind in the body when the dipole moments stick out at the surface of the body
Figure 6.28 Sketch showing the direction of the electric dipole moment induced in a dielectric sphere with dielectric constant inside a dielectric fluid having dielectric constant by the inhomogeneous electrical field . (a) The particle is more polarizable than the fluid, that is, . (b) The particle is less polarizable than the fluid, that is, . (c) and (d) The effective charges and directions of and corresponding to (a) and (b), respectively
Figure 6.29 (a) A dielectric fluid with a dielectric constant penetrated by an unperturbed homogeneous electric field . (b) A dielectric sphere of radius and dielectric constant placed in the dielectric fluid. The electric field polarizes the sphere, resulting in a perturbed electric field,
Figure 6.30 (a) An example of DEP trap in a rectangular microfluidic channel of dimensions to catch dielectric particle suspended in a liquid flow with velocity profile . (b) Schematic showing the inhomogeneous electric field created by applying a voltage difference between the semispherical electrode at the floor of the microchannel and the planar electrode covering the ceiling
Figure 6.31 Real part of the Clausius–Mossoti factor as a function of frequency, where is the crossover frequency
Figure 6.32 Crossover frequency of polystyrene bead in water as function of the radius. The symbols are expt-data
Chapter 7: Magnetism and Microfluidics
Figure 7.1 (a) Schematic of the magnetic field lines around a bar magnet. (b) Illustration of magnetic permeable material (soft iron) influence on the magnetic field lines
Figure 7.2 (a) Homogeneous magnetic field along the surface of a large NdFeB magnet and (b) inhomogeneous field above the surface of a tapered magnet
Figure 7.3 Molecular magnets alignment of a (a) unmagnetized substance and (b) magnetized substance
Figure 7.4 Hysteresis loops for soft and hard magnetic materials
Figure 7.5 Magnetic field lines distribution inside (a) a diamagnetic material and (b) a paramagnetic material
Figure 7.6 The relationship between magnetization and the external magnetic field for different types of particles
Figure 7.7 Schematic showing the magnetophoresis for the separation of the target molecule
Figure 7.8 A schematic of the microbead for magnetic separation in a lab-on-a-chip (LOC) system
Figure 7.9 The principle of magnetic separation of biomolecules. (a) Flow carrying magnetic microbeads, (b) immobilization of the magnetic microbeads, (c) introduction of samples containing antigens, (d) capture of antigen by the immobilized antibody beads, (e) rinsing of the microchannel, and (f) release of the target sample by deactivating the magnets
Figure 7.10 A schematic sketch of the magnetic field flow fractionation (MFFF)
Figure 7.11 A schematic view of magnetic field flow fractionation (MFFF)
Figure 7.12 Two different trajectories followed by two different types of beads
Figure 7.13 The principle of a circular ferrofluidic pump. Two magnets (M) are employed to manipulate ferrofluid plugs in a circular microchannel. One magnet is moving and another is stationary
Figure 7.14 Principles of H-shaped separators: (a) from suspension of particles and (b) for continuous flow separation
Figure 7.15 Schematic showing the magnetic force acting on a current-carrying conductor in a magnetic field
Figure 7.16 A schematic diagram of the MHD pump. Two electrodes with a potential difference are deposited along the opposing walls of the conduit. The right Figure depicts a cross section of the conduit. The conduit is filled with an electrolyte solution and exposed to a uniform magnetic field of intensity
Chapter 8: Microscale Conduction
Figure 8.1 Temperature–time trace from oscilloscope during the experiment of Bertman and Sandiford (1970). Note that no temperature and time scale was given
Figure 8.2 Different scattering mechanisms of free electrons within a metal
Figure 8.3 Range of applicability for different heat transfer modeling approach of silicon at ambient temperature as a function of the system length
Figure 8.4 A schematic of semi-infinite solid exposed to a constant temperature at one end
Figure 8.5 The comparison of temperature distribution in a semi-infinite solid based on Fourier's conduction and hyperbolic conduction approach
Figure 8.6 Schematic showing the traveling of thermal wave
Figure 8.7 The schematic showing the transport phenomena based on kinetic theory
Figure 8.9 Thermal conductivity of Cu, Al, and W plotted as function of temperature
Figure 8.8 Molar specific heat of Au compared to the Debye model using 170 K for the Debye temperature (Weast
et al.
, 1985)
Figure 8.10 Thermal conductivity of three elements having diamond structure as a function of temperature
Figure 8.11 Schematic of electron and phonon trajectories in (a) relatively thick film and (b) relatively thin film
Figure 8.12 Measured thermal conductivity of yttria-stabilized zirconia as a function of temperature and mean grain size (Yang
et al.
, 2002).
Figure 8.13 Nondimensional unsteady temperature distribution inside a thin film () as a function of nondimensional time, , and nondimensional distance,
Figure 8.14 Nondimensional temperature distribution in a thick film () as a function of nondimensional distance, , and nondimensional time,
Chapter 9: Microscale Convection
Figure 9.1 A schematic showing microchip heat transfer using heat sink with microchannels and microfins
Figure 9.2 Different flow regimes of microscale convection
Figure 9.3 Representation of velocity slip condition
Figure 9.4 Temperature jump boundary condition near a boundary
Figure 9.5 Schematic of Couette flow between two large parallel plates
Figure 9.6 The schematic of the parallel plate channel flow
Figure 9.7 The limiting Nusselt number as a function of velocity slip and temperature jump of a microchannel
Figure 9.8 Schematic for heat transfer in fully developed parallel plate flow
Figure 9.9 Differential element for application of conservation of energy equation
Figure 9.10 Schematic of the microtube flow with uniform surface heat condition and slip flow velocity profile
Figure 9.11 Schematic for the application of energy equation to a small element
Figure 9.12 Effect of viscous heating on heat transfer at the microtube entrance for uniform heat flux at the wall (, )
Figure 9.13 Variation of the fully developed as a function of , for uniform heat flux at the microtube wall
Figure 9.14 Effect of viscous heating for microtube with uniform wall temperature case (, )
Figure 9.15 Mechanisms of flow boiling in uniformly heated channel: (a) saturated flow boiling and (b) subcooled flow boiling
Figure 9.16 Schematic of boiling flow regimes: (a) nucleate boiling dominant heat transfer and (b) convective boiling dominant heat transfer
Figure 9.17 Boiling curve for (a) water for = 341 , G = 228 kg/, = 30 (Qu and Mudawar, 2004) and (b) R134a for = 349 , G = 270 kg/, = 0.07
Figure 9.18 Schematics of flow regimes during condensation of FC72 in 1 mm 1 mm square channel at mass flow rate of 6 g/s (Kim and Mudawar, 2012)
Chapter 10: Microfabrication
Figure 10.1 (a) Comparison of different scales for adopting general fabrication strategies and (b) different types of microtechnologies
Figure 10.2 Different crystal planes in the cubic lattice of monocrystalline silicon
Figure 10.3 Schematic showing the definition of Miller index
Figure 10.4 Schematic showing polycrystalline silicon
Figure 10.5 An image of an oxidation furnace. (Courtesy of Micro Fabrication Laboratory, ME Department, IIT Kanpur)
Figure 10.6 The image of a fume hood system for wet etching and surface treatment. (Courtesy of Micro Fabrication Laboratory, ME Department, IIT Kanpur)
Figure 10.7 Various processing steps during standard micromachining procedure of silicon-based material
Figure 10.8 The decomposition of microfabrication procedure to three primary steps, that is, addition, multiplication, and subtraction of thin solid film
Figure 10.9 An image of a photolithography system. (Courtesy of Micro Fabrication Laboratory, ME Department, IIT Kanpur)
Figure 10.10 An image of a spin coater. (Courtesy of Micro Fabrication Laboratory, ME Department, IIT Kanpur)
Figure 10.11 Schematic showing the spin coating process
Figure 10.12 Schematic showing half-light effect, that is, zone with light and dark region
Figure 10.13 The schematic showing pattern transfer using both positive and negative resists: (a) coating of resist, (b) photolithography, and (c) development
Figure 10.14 (a) Isotropic etching of Si with EDP and (b) anisotropic etching of Si with KOH
Figure 10.15 Etching profiles during wet etching due to influence of stirring: (a) well stirred and (b) not stirred
Figure 10.16 Bubble formation during Si etching in KOH solution as a function of temperature and concentration
Figure 10.17 Formation of a V-shaped groove in (100) silicon by using a KOH solution
Figure 10.18 Schematic of different shapes resulting from anisotropic etching of Si as a function of crystallographic orientation
Figure 10.19 (a) The schematic of a physical dry etching process and (b) a setup to sustain plasma for etching
Figure 10.20 Schematic showing the physicochemical process during etching
Figure 10.21 Schematic showing the schematic of sputtering procedure
Figure 10.22 An image of a dual PECVD-sputtering system. (Courtesy of Micro Fabrication Laboratory, ME Department, IIT Kanpur)
Figure 10.23 Schematic showing the principle of PECVD process
Figure 10.24 (a) Conformal deposition, where the deposited film takes form of the substrate, and (b) nonconformal deposition, where the deposited film has different forms/shape than those of the substrate
Figure 10.25 Photolithography and etching steps carried out for fabrication of a silicon membrane
Figure 10.26 Semistructural formula of PDMS
Figure 10.27 The schematic procedure showing the molding procedure of PDMS structure
Figure 10.28 Fabrication of Y-channel using soft lithography: (a) SU-8 master fabrication, (b) PDMS pouring and lift-off, and (c) surface treatment by plasma and bonding by glass
Figure 10.29 (a) PDMS master fabrication and (b) micromolding for microchannel fabrication
Figure 10.30 (a) Schematic showing the anodic bonding process and (b) principle of anodic bonding
Figure 10.31 An image of a laser micromachining center (CHE/ME Department, IIT Kanpur)
Figure 10.32 (a) Propagation of Gaussian laser beam and (b) its intensity profile
Figure 10.33 Laser pulse interaction with the workpiece material
Chapter 11: Microscale Measurements
Figure 11.1 (a) PIV image pair and interrogation zones and (b) the computation scheme for cross-correlation analysis
Figure 11.2 Processing of PIV images
Figure 11.3 Schematic representation of PIV data quality as a function of pulse delay time
Figure 11.4 Schematic showing the deformation of the interrogation window in the second exposure image
Figure 11.5 A schematic illustration of -PIV system setup
Figure 11.6 Difference between light sheet and volume illumination
Figure 11.7 Principle of fluorescence: (1) a fluorochrome is excited by a photon to an energy level higher than the ground state (excited state 1); (2) the excited electron loses energy due to interactions with the environment, thereby falling to a relaxed excited state (excited state 2); and (3) the electron collapses back to its ground state emitting a photon with energy corresponding to the difference between excited state 2 and ground state
Figure 11.8 Image overlapping. Left: individual -PIV recordings, right: result of overlapping of 16 images (background noise subtracted)
Figure 11.9 Sample geometry (metal film heater mounted on the sample) for the implementation of the 3 method
Figure 11.10 Temperature oscillation measurement of at K measured by the method
Figure 11.11 Schematic of a typical measurement apparatus
Figure 11.12 Schematic diagram of the Wheatstone bridge common-mode cancellation method. is the heater, is the variable resistor, is the fundamental signal from the function generation, and is the differential output voltage sent to the lock-in amplifier
Figure 11.13 Schematic of scanning thermal microscope based on AFM
Figure 11.14 Schematic of a (a) thermocouple tip and (b) passive thermoresistive probe used with a AFM tip for scanning thermal microscopy
Figure 11.15 Electrical circuit for measurement by thermoresistive probe
Figure 11.16 Different mode of heat transfer between the tip and the sample of scanning thermal microscope
Figure 11.17 Schematic showing the heating and probing spot of a laser interacting on a sample
Figure 11.18 Schematic showing the interaction of laser pulse with layered material
Figure 11.19 Schematic of a typical transient thermoreflectance setup
Figure 11.20 Experimental results (symbols) from thermoreflectance measurement of 30 nm Cr film on Si along with the model fit (solid line)
Figure 11.21 Fluorescence intensity versus temperature of Rhodamine B dye at different dye concentrations
Chapter 12: Microscale Sensors and Actuators
Figure 12.1 A schematic of flow control arrangement
Figure 12.2 A schematic of synthetic jet actuator
Figure 12.3 A possible fabrication procedure of synthetic jet actuator
Figure 12.4 (a) Vorticity plots for synthetic jet during no-jet formation (top) and jet formation (bottom) cases. (b) Reynolds number () versus Stokes number () of synthetic jet for no-jet and jet formation cases
Figure 12.5 (a) Schematic of a balloon actuator and (b) the picture of a deformed balloon actuator at two different pressure levels
Figure 12.6 Fabrication procedure of microballoon actuator
Figure 12.7 Typical deflection versus actuation pressure plot of a balloon actuator
Figure 12.8 Schematic of a magnetic flap actuator
Figure 12.9 Fabrication procedure of a magnetic flap actuator
Figure 12.10 Angular displacement versus magnetic field strength of flap actuator
Figure 12.11 (a) The schematic of a hot-wire sensor connected to the Wheatstone bridge circuit and (b) the schematic of a flush-mounted thermal shear stress sensor
Figure 12.12 The flow and heat transfer mechanism of a flush-mounted thermal shear stress sensor
Figure 12.13 The schematic of a floating element shear stress sensor: (a) top view and (b) cross-sectional view
Figure 12.14 The schematic of (a) MEMS skin friction fence and (b) its calibration curve between the bridge voltage () and the shear stress ()
Figure 12.15 The schematic showing (a) the fringe formation for oil height measurement and (b) an experimental setup using oil-film interferometry
Figure 12.16 The schematic showing (a) the principle of shear-sensitive liquid crystal and (b) the experimental setup for shear stress measurement using shear-sensitive liquid crystal
Figure 12.17 (a) The relative hue () versus the shear stress angle () for different shear stress magnitude () and (b) the relative hue () versus the shear stress angle () for two cameras (left, ; right, ) at a particular shear stress magnitude
Figure 12.18 Schematic of static calibration apparatus: (a) using disk and (b) long, high aspect ratio smooth channel flow
Figure 12.19 Static calibration curve: (a) the bridge output () versus shear stress () and (b) the input power versus (shear stress) of thermal shear stress sensor
Figure 12.20 The schematic of a dynamic calibration apparatus for shear sensor
Chapter 13: Heat Pipe
Figure 13.1 A schematic showing the structure and operation of a conventional heat pipe
Figure 13.2 (a) Liquid and vapor flow, (b) wall and vapor temperature, (c) vapor and liquid pressure distribution, and (d) vapor and liquid flow rates
Figure 13.3 Some common wick structures used in traditional heat pipe
Figure 13.4 Pressure–temperature diagram of a pure substance
Figure 13.5 Temperature entropy diagram showing the operation of a heat pipe
Figure 13.6 Schematic of the microheat pipe showing its operational principle
Figure 13.7 Various microheat pipe profiles (square, rectangular, modified rectangular, circular outer and triangular inner, circular outer and square inner, tapered)
Figure 13.8 Possible limiting range of a heat pipe as a function of operating temperature
Figure 13.9 Schematic showing the nomenclature of the triangular groove for calculation of capillary pressure
Figure 13.10 Compressible flow characteristic in a converging–diverging nozzle
Figure 13.11 Temperature–axial location plot of a typical sodium heat pipe to explain the sonic limit
List of Tables
Chapter 1: Introduction
Table 1.1 Unit system used to describe microsystems
Table 1.2 Typical values of mean free path of different gases at normal conditions
Table 1.3 Comparison of contour length and radius of gyration for two different molecules (see Figure 1.5)
Chapter 2: Channel Flow
Table 2.3 The hydraulic resistance for straight channels with different cross-sectional shapes
Table 2.1 The friction factor of an elliptic tube for different cross-sections ( ratios)
Table 2.2 as a function of for a rectangular cross-section channel
Chapter 3: Transport Laws
Table 3.1 The accommodation coefficient for different gas–surface combinations
Chapter 4: Diffusion, Dispersion, and Mixing
Table 4.1 The osmotic pressure of NaCl at different concentrations
Chapter 5: Surface Tension-Dominated Flows
Table 5.1 Measured values of the surface tension, , at liquid–vapor interfaces and the contact angle, , at liquid–solid–air contact lines
Chapter 6: Charged Species Flow
Table 6.1 Normalized molar conductivity of some ions in dilute solutions of water
Table 6.2 Experimental values for ionic mobility and diffusivity for small ions in aqueous solutions at small concentrations
Chapter 7: Magnetism and Microfluidics
Table 7.1 Magnetic susceptibilities of some materials at C
Chapter 8: Microscale Conduction
Table 8.1 Mean free path and critical film thickness for various materials at
Chapter 9: Microscale Convection
Table 9.1 Nusselt number for laminar fully developed flow in microchannels for various channel cross-sections
Table 9.2 Nusselt number variation as a function of the Knudsen number for air ( = 1.4 and = 0.7)
Table 9.3 Fluid properties and hydraulic diameter corresponding to transition from macro- to microchannel flow at 1 bar
Table 9.4 Fluid properties and hydraulic diameter corresponding to transition from macro- to microchannel flow for water and HFE 7100 at 1 bar
Table 9.5 The thermophysical properties of FC72 at .
Chapter 10: Microfabrication
Table 10.1 Properties of monocrystalline silicon
Table 10.2 Mechanical properties of silicon by principal planes
Table 10.3 Mechanical properties of some common functional materials
Table 10.4 Common properties of some polymers
Table 10.5 Film thickness at a spin speed of 1000 rpm for different SU-8 photoresists
Table 10.6 Examples of wet etchants for some common materials
Table 10.7 Etch rate of silicon as a function of crystallographic orientation in KOH at temperature of 70 C for different KOH concentrations
Table 10.8 Effect of composition and temperature on the etch rate of silicon by KOH
Table 10.9 Some representative materials with their chemical reactions and CVD techniques
Table 10.10 Representative properties of PDMS
Chapter 11: Microscale Measurements
Table 11.1 Field of view for various microscope objectives (Model: Leica DMI 5000M) used in -PIV applications
Table 11.2 Absorbing and emitting wavelength frequency of different fluorescent media
Chapter 13: Heat Pipe
Table 13.1 Working fluids and operating temperatures of heat pipe
Table 13.2 Experimental compatibility tests
Transport Phenomena in Microfluidic Systems
Pradipta Kumar Panigrahi
Indian Institute of Technology, Kanpur, India
This edition first published 2016
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About the Author
Dr Pradipta Kumar Panigrahi is the N.C. Nigam Chair Professor and Head of the Mechanical Engineering Department at IIT Kanpur, India. He was previously the Head of Photonics Science and Engineering Program and Center for Lasers and Photonics at IIT Kanpur. Dr Panigrahi received an MS in Mechanical Engineering, MS in System Science, and PhD in Mechanical Engineering from Louisiana State University, USA. His research focuses on optical methods in thermal sciences at both the macro and micro scales, microfluidics, heat transfer, and flow control. He has authored over 65 refereed journal papers, 62 conference papers, 3 popular articles, 6 book chapters, 2 Springer conference proceedings, and 2 Springer monographs. He received the Humboldt Research Fellowship, Germany; BOYSCAST Fellowship, Japan; and AICTE Career Award and Swarnajayanti Fellowship, India.
Preface
Several advances on microscale devices and systems have taken place in the past few decades. These devices have taken advantage of low cost and superior performance for the augmentation in transport processes because of their small scale. However, there is a limited understanding of physical processes in these devices. More experimental and simulation studies are essential for further improvement and development of these microsystems. Therefore, I decided to pursue research on the emerging field of microfluidics and heat transfer. My first interest was to extend my prior expertise on experimental techniques for macroscale systems to microsystems. While initiating research on this topic, I also proposed an optional course at IIT Kanpur to expose the students to this new exciting research area. I searched for a textbook on this topic but could not find a single book that satisfies all the requirements of my course proposal. Therefore, I had to refer to many reference books for the preparation of my class notes. This book is the result of several revisions of my class notes.
This book is intended as an optional course for senior undergraduate and graduate level students of various engineering and science disciplines owing to the interdisciplinary nature of the subject. It introduces different transport processes related to microdevices. The purpose of this book is to prepare students with the fundamentals and tools needed to model and analyze different microsystems. It may also serve as a reference book for microsystem designers and researchers.
The primary objective of this book is to provide a detailed overview of this subject. All aspects of transport processes relevant to microsystems, that is, mass transfer, momentum transfer, energy transfer, charge transfer, surface tension-driven flow, magnetofluidics, microscale conduction, and microscale convection, have been discussed. It is also felt that a student needs to be exposed to various microfabrication capabilities in order to appreciate the scope and significance of microscale transport phenomena. Therefore, a brief introduction to microfabrication technology has also been included in one of the chapters. Characterization of microscale transport processes is essential for validation of different simulation models and for testing of prototypes. Therefore, experimental techniques for the characterization of microscale transport processes have also been included as a separate chapter. Sensors and actuators form an integral part of both macrosystems and microsystems for the optimization of their performance. Therefore, different microsensors and actuators are also included as a chapter for highlighting the potential applications of microsystems. A micro heat pipe involving several complexities of microscale transport processes is discussed at the end of the book as one of the practical examples. Several other examples of microscale devices and systems are also included in this book depending on the importance of the specific transport process for that device.
Rapid development in microsystem technology has taken place in the past few years. It is not possible to include all the developments in an introductory textbook. Online or ancillary teaching materials need to be used by the instructor for exposing the students to several recent developments in this field.
This work owes a great deal to several published literature on microfluidics and heat transfer. I have used examples and problems from these published works while developing my course notes for the class. As I did not keep the record of all references in my early years of teaching, I have tried to eliminate most of these materials as much as I knew. However, I would like to express regret if few of them have been unintentionally included. Finally, I would appreciate receiving suggestions from readers in improving the contents of the book and the online supplementary/ancillary material.
Pradipta Kumar Panigrahi
IIT Kanpur, India
Acknowledgement
I would like to acknowledge with gratitude the initial support by the Centre for Development of Technical Education (CDTE) of IIT Kanpur for initiation of the book writing proposal. I also thank the Ph.D. students, Tapan, Balakrishna and Archana for offering miscellaneous help during final preparation of the text book. A special note of appreciation is due to Alok for preparation of Figures and Manoj for handling many of the secretarial details.
