Index
Note: Page number followed by f indicate figures and t indicate tables.
A
Adams-Moulton formula
500
Advancing contact angle
430,
431
Amine-based cationic surfactants
436
Amphoteric surfactants.
See Zwitterionic surfactants
Artificial compressibility method
702–703
Axisymmetric drop shape analysis (ADSA)
493
B
Balanced rectangular function
411
Balancing viscous dissipation
358
Bashforth–Adams schemes
499
Bashforth and Adams curvature method
480–481
Bilayer and micelle formation
432–434
Biochemical passivation
441
Blast furnace process
111
finite difference method in Microsoft Excel
627–629
one-dimensional heat equation
645
Brien, Ben, and van den Brule curvature method.
See Sessile drops
C
denominators containing sums
48
infinitesimal changes
49–50
variable and derivative
48
negative capillary pressure
447
Cartesian/cylindrical coordinates conversion
148–150
coordinate system transformation
148–150
Cartesian/polar coordinates conversion
150
coordinate system transformation
150
Cartesian/spherical coordinates conversion
151–154
coordinate system transformation
151–154
Central finite difference
59,
712
Central finite distance scheme
561–562
Central processing unit (CPU)
CFD.
See Computational fluid dynamics (CFD)
Characteristic polynomial
Chebyshev differential equation
620
momentum conservation
310
Classical LU-decomposition
525
Colebrook-White equation
335
Compressible continuity equation
303–306
Computational fluid dynamics (CFD)
609
Conservative notation, integral form of
volume-averaged conservative form
636
Convection constant, pressure for
717
Cartesian coordinates
303
Cartesian/cylindrical coordinates conversion
148–150
Cartesian/polar coordinates conversion
150
Cartesian/spherical coordinates conversion
151–154
circular cross-sections
362,
365
planar infinitesimally extended cross-sections
362,
365
square cross-sections
363,
366
Critical micelle concentration (CMC)
432,
438
Critical micelle temperature (CMT)
432
Critical surface tension
463
Cross-section hydraulic resistance
361–362
Curl-free vector fields
140
D
Damped harmonic oscillation
576,
576f
Darcy-Weisbach equation
334
Debye and Keesom interaction
463
Decelerating Poiseuille flow
372
del Río and Neumann curvature method.
See Pendant drops
Fourier transformation of
43
mathematical treatment
40–41
Differential equation
22–24
for Hagen-Poiseuille flow
615f
harmonic oscillation ODE, Laplace transform for
200–204
linear differential equations with nonconstant coefficients
198–200
ordinary differential equations, solutions to
194–198
partial differential equations, solutions to
205–213
time-dependent diffusion equation, in three dimensions
238–240
two-dimensional partial differential equations
235–238
variables approaches, substitution and separation of
214–219
Differentiation property
82
Digital diffusion experiment
130,
131f
Digital microfluidics
441
for diffusion and convection
289
dimensionless Navier-Stokes equation
284–285
Dimensionless analysis
405
Dimensionless convection-diffusion equation
289
Dimensionless Navier-Stokes equation
284–285
Dimensionless volume forces
288
Dissipation coefficient
300
Divergence-free vector fields
140
Divergence theorem.
See Gauss's theorem
Divergent Navier-Stokes equation
705–707
Droplet microfluidics
441
Dynamically linked library (DLL)
20
Dynamic contact angle measurement
430–431
Dynamic surface tension
457
E
Elementary
Maple commands
vectors and matrices
10–11
Elliptical and circular profiles
flow rate for circular cross-sections
325
flow rate for elliptical cross-sections
324–325
velocity profile for circular cross-sections
325
velocity profile for elliptical cross-sections
324
state, thermodynamic equation of
300–301
denominators containing sums
48
infinitesimal changes
49–50
variable and derivative
48
boundary conditions (BC)
29–30
differential calculus, important rules in
27–28
differential equations, systems of
30
homogeneous and inhomogeneous
24
ordinary and partial
24–25
trigonometric equivalences
conversion from cosine
34
conversion from cotangent
34
conversion from tangent
34
conversions for half-angles
34
ENO reconstruction.
See Essentially non-oscillatory (ENO) reconstruction
Equivalent molar concentration
98
Essentially non-oscillatory (ENO) reconstruction
640
Extended Fowkes model
462
F
Falling ball viscosimeter
252f
,
253
Fast radial diffusion
407
FDM.
See Finite difference method (FDM)
FEM.
See Finite element method (FEM)
alternative use of the spreadsheet
629–631
numerical scheme implementation
626–627
Finite-difference scheme
663
approximation functions in
659f
Finite element method (FEM)-Galerkin method
659–660
Fluid effects, at interfaces
temperature dependency
424
characteristic breakup time
476
Fluid mechanical effects
445,
446
critical shear stress
243
Fluorinated anionic surfactants
435
Fluorinated surfactants
435
Flux theorem.
See Stoke's theorem
Formula translating system (FORTRAN)
492
Forward finite distance approximation
60
nonperiodic functions
68–77
Fourier's law, heat conduction
heat flows, balance of
127
instationary heat conduction
128
stationary heat conduction
127
one-dimensional diffusion equation
224–230
Free surface boundary condition
256
Free-surface condition
29
extended Fowkes model
462
Fully developed flow profile
266
Function approximation methods
590–593
determining the constants
c
i
638
piecewise-parabolic profile
641–642
Fused deposition modeling (FDM)
624
FVM.
See Finite volume method (FVM)
G
algorithmic implementation
619
multiple independent variables
615–618
systems of differential equations
618–619
Geometric hydraulic resistance
361
for electrochemical reactions
118
Gibbs-Helmholtz equation
122
Global positioning system (GPS)
538
Global truncation error
564
H
Hagen-Poiseuille flow
78,
320,
329–335,
329f
,
371,
372f
,
402,
409,
414,
605,
606f
,
612,
615f
,
629,
687
Heat conduction equation
190
Fourier transformation
46
High free surface energy
422,
442
Homogeneous differential equations
24
H ×
W Meshes, general rule for
597
Hyperbolic cosine function
32,
337
Hyperbolic sine function
32
Hyperbolic tangent function
32
I
one-dimensional velocity probability distribution
104–106
Idealized thermodynamic processes
108
Incompressible continuity equation
303–306
Incompressible Newtonian fluids
280–282
Independent variable
21–22
Infinitesimal negative change
59
Infinitesimal positive change
59
Inhomogeneous differential equations
24
Inhomogeneous partial differential equations
239
Inhomogeneous solution
196
Initial boundary value problem (IBVP)
30
Initial value problem (IVP)
30
Initiating Poiseuille flows
372
Integrated circuit technology
Integrated development environment (IDE)
20
Integrated gas chromatography
Interface stabilization
441
J
Cartesian/cylindrical coordinates conversion
157–159
Cartesian/polar coordinates conversion
159
Cartesian/spherical coordinates conversion
159–160
Jurin height.
See Capillary heights
K
Kinematic boundary condition
473
L
Laminar Hagen-Poiseuille flow
334
Langmuir–Blodgett film
433
Laplace constant, for velocities
717
for harmonic oscillation ODE
200–204
Lifshitz/Van der Waals contribution
463
Linear differential equations
Linear systems, of equations
500,
537
sequential dense LU-decomposition
525–530
tridiagonal matrix algorithm (Thomas algorithm)
531–534
Liquids, surface tension measurement of
capillarity measurement
459
Localized support function
659,
660
Local truncation error
564
Low free surface energy
422
M
elementary
Maple commands
9–13
matrix/vector multiplication
542–543
Mass concentration function
402–403
Mass, conservation of
309,
701
convection-diffusion equation
270–271
flowrate, integral representation
269
Maximum bubble pressure method
456–457
Maxwell speed distribution
reaction compartments
441
Microelectromechanical system (MEMS)
analytical applications
4–5
integrated circuit technology
Microoptoelectromechanical system (MOEMS)
Microsoft Excel, finite difference method (FDM) in
624–631
Miniaturized total analysis systems (μTAS)
Modified Bessel functions
38–39
Momentum, conservation of
control volume, transfer into and out of
273
pseudo-plastic fluids
251
time-dependent viscosity
251
N
Navier-Stokes equation
24,
303–308,
310,
312,
338–339,
352,
371,
373,
379–380,
471,
498,
609,
679–680,
693–694,
701,
705–707
Navier-Stokes equation, for incompressible newtonian fluids
Lagrangian frame of reference
282
Nonperiodic boundary condition
619–620
Nonzero Dirichlet boundary conditions
628
Normalized capillary heights
446–447
Normalized hydraulic resistance
359–361
Numerical methods, for solving differential equations
central finite distance scheme
561–562
coupled ordinary differential equations
575–585
forward and backward finite distance
559–560
function approximation methods
590–593
higher-order ordinary differential equations
575–585
infinitesimal changes
549
ordinary differential equations with boundary conditions
585–590
advantages and disadvantages
497–498
nonlinear systems, of equations
537,
539f
O
OCG model.
See van Oss, Chaudhury, and Good (OCG) model
ODE.
See Ordinary differential equation (ODE)
One-dimensional diffusion
190
One-dimensional example, flow in infinitesimally extended channels
One-dimensional heat conduction
190
One-dimensional velocity probability distribution
104–106
vector field potentials
142
vector multiplication
140
Ordinary differential equation (ODE)
24,
85,
601
linear differential equations
variables and partial integration, separation of
194–195
Oscillating piston viscosimeter
252f
,
253
Ostwald approximation
250
Owens, Wendt, Rabel, and Kaelble (OWRK) model
462
P
PDE.
See Partial differential equation (PDE)
Pendant drop analysis
465
Periodic boundary condition
619
Permutating LU-decomposition (PLU)
523
Physical drop contour vs. derived drop contours
491–492,
492f
Planar infinitesimally extended channel cross-sections
Plateau-Rayleigh instability
characteristic breakup time
476
stability considerations
467
elliptical and circular profiles
323–326
planar infinitesimally extended channel cross-sections
326–329
sequential dense LU-decomposition
596–598
calling SolvePoissonSOR from Maple
603–604
Polysorbate surfactants
440
convection constant for
717
volume force constant for
717
Pressure constant, for pressure
717
artificial compressibility method
702–703
divergent Navier-Stokes equation
705–707
problem with incompressible fluids
702
Pseudo-plastic fluids
251
Pyranoside surfactant
440
Q
R
Radial average mass concentration
403
Reconstruction stencil
640
substitution and separation of variables
336
Reynolds' dye flow experiment
286,
287f
Reynolds' transport theorem
145–146
Rolling ball viscosimeter
252f
,
253
Rotating piston viscosimeter
252f
,
253
S
cylindrical coordinates
166
spherical coordinates
181
Semiimplicit method for pressure-linked equations (SIMPLE) algorithm
610,
703–705
Shear-thickening fluids.
See Dilatant fluids
Shear-thinning fluids.
See Pseudo-plastic fluids
SIMPLE algorithm.
See Semiimplicit method for pressure-linked equations (SIMPLE) algorithm
Sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE)
435
Solving for
p, Taylor-Aris dispersion
coordinate system transformation
405
fast radial diffusion assumption
407
gradients along
z-axis
405
SOR.
See Successive over-relaxation (SOR)
Source-free vector fields
140
nonperiodic boundary condition
619–620
periodic boundary condition
619
Spherical coordinate system
147
Square wave function
63–65
Stabilization, of suspensions
440
Standard formation enthalpy
111
Static contact angle measurement
430
Stationary flow numerical solver implementation boundary values
Successive over-relaxation (SOR)
513–517
Successive over-relaxation (SOR) implementation
Surface active agent.
See Surfactant
Surface free energy.
See Free surface energy
fluid effects, at interfaces
421–430
Surface tension measurement
capillarity measurement
459
maximum bubble pressure method
456–457
T
convection-diffusion equation
401–405
mass concentration function
402–403
exponential function
54–56
central finite difference
59
forward and backward finite difference
60
infinitesimal negative change
59
infinitesimal positive change
59
Taylor series expansion
54–56
Temperature dependency
111
Tensiometer.
See Liquids, surface tension measurement of
Thermodynamic potential
120
one-dimensional velocity probability distribution
104–106
idealized thermodynamic processes
108
weights and concentrations
96–98
Thermodynamics state variables
99–100
Thomas algorithm.
See Tridiagonal matrix algorithm
Three-dimensional flow problems
stationary flow numerical solver implementation
715–725
Three-dimensional grids
658
Three-dimensional numerical solver
725–743
Three-dimensional point source diffusion
236
Time and space, two-dimensional problems of first order in
648–652
Time-dependent Couette flow
373–379
dimensionless velocity profiles
377–379
Time-dependent diffusion equation, in three dimensions
238–240
Time-dependent Hagen-Poiseuille flow
379–385
transient and steady-state solutions
380–381
Time-dependent transient effects
371–373
Navier-Stokes equation
371
Time-dependent transient flows
679
Time-dependent transient solution
372
Time-dependent viscosity
251
Time-independent steady-state solution
402
Transient and steady-state solutions
380–381
time-dependent Couette flow
373–379
time-dependent Hagen-Poiseuille flow
379–385
time-dependent transient effects
371–373
Transient flow, time-dependent
679
Triangular-like function
65–66
Tridiagonal matrix algorithm
Trigonometric equivalences
conversion from cosine
34
conversion from cotangent
34
conversion from tangent
34
conversions for half-angles
34
Truncation error function
54
Two-dimensional entrance flow problems
687–699
space-dependent transient flows in circular channel profiles
695,
696f-698f
Two-dimensional example, flow in rectangular channels
using the worksheet to solve the Poisson equation
677–678
Two-dimensional partial differential equations
235–238
Two-dimensional point source diffusion
236
Two-dimensional problems of first order, in time and second order in space
652–654
regular axes-incident grid
653
Two-dimensional problems of first order, in time and space
648–652
regular axes-incident grid
651
Two-dimensional time-dependent flow problems
680–687
Backward Euler scheme
681
time-dependent transient flows in circular channel profiles
685–687
time-dependent transient flows in rectangular channel profiles
684–685
U
Unbalanced intermolecular forces
421
Uncharged surfactants
431
V
van Oss, Chaudhury, and Good (OCG) model
463
coordinate system transformation
147–154
scalar multiplication
138
in microfluidic channel
356
Navier-Stokes equation
352
Visualization, Taylor-Aris dispersion
414
W
Newton's second law of motion
191–192
variables, substitution and separation of
219–224
Weighted essentially nonoscillatory (WENO)
Weighted residual methods
approximation function
611
differential operator
610
linear independent functions
610
WENO.
See Weighted essentially nonoscillatory (WENO)
Y
Young-Laplace pressure
448
Z
Zonyl FSA fluorosurfactants
435
Zonyl FSO surfactants
440
Zwitterionic surfactants
431