1. MODELLING OF THERMOPHORESIS IN
MULTIPHASE FLOWS
Master's Thesis
Student: Andrés Gude Lustres
Study Program: Master of Industrial Engineering
Mentor: assoc. Prof. Dr. Jure Ravnik
Maribor 07.07.2016

2. CONTENTS
INTRODUCTION
MODELS
NUMERICAL SIMULATIONS
RESULTS
CONCLUSIONS

3. OVERVIEW OF THE PROBLEM
• Researches into micro and nanoparticles.
• Significant progress in all branches of science.
• Thermophoresis one of most studied phenomena.
• Concern about climate change and pollution.
• Importance in numerous industrial processes.
• Examples: air cleaning, coal combustion, chemical
vapor deposition and microcontamination.

4. GOALS AND AIMS
• Analyze the behavior of thermophoresis on
microparticles and nanoparticles.
• Analyze multiphase fluids with the presence of
Brownian motion and thermophoresis.
• Analyze multiphase fluids only with the
presence of thermophoresis.
• Understand the relationship between the two
phenomena.

5. BROWNIAN MOTION
• Brownian motion is the random motion of
particles suspended in a fluid (liquid or gas)
resulting from their collision with the quick
atoms or molecules in the gas or liquid.
• Statistically independent successive
displacements.
• May be described by a force with random
components

6. Why the motion is caused?
• Small particles disperse faster in hotter
regions and slower in colder regions.
• The particle velocity in the hotter regions is
higher than in the colder regions.
• Particles collide and move toward the colder
region.
• The force that push them is the
thermophoretic force.

7. THERMOPHORESIS
• Consequence of the Brownian movement of
particles in fluids with an externally sustained and
constant temperature gradient.
• Is the migration of a particle away from the
higher-temperature region and toward the lower-
temperature region in large particles.
• Is the migration of a particle away from the
lower-temperature region and toward the higher-
temperature region in small particles.
• Is the average motion of the particles.

8. THERMOPHORESIS MODELS
• MODEL 1: Kn<2.
• MODEL 2: transition regime (0.2 < Kn < 10).
• MODEL 3: Kn>>1. For monoatomic gases.
• MODEL 4: entire range of small and larger Kn.
• MODEL 5: entire range of small and larger Kn.
• MODEL 6: entire range of small and larger Kn.
• MODEL 1,4,5: Dioctyl phthalate (DOP) droplets in
air, silicone oil in argon, tricresylphosphate in air.
• MODELS 2,3,6: for monatomic gases.

9. CHOSEN MODEL
• The mean free path of water is 2.5 angstrom.
• The characteristic length scale is 1 cm.
• Kn << 1.
• Continuum regime.
• Particles massless (as they are very small and
their Stokes number are very small, thus they
follow the fluid.)
• Drag, lift and gravity forces are neglected
• Particles have the same velocity as the fluid plus
Browninan and thermophoretic velocities.

10. BROWNIAN MOTION EQUATIONS
• STOKES-EINSTEN EQUATION
• DISPLAZAMENT
N : is the random vector. (-1,1)

11. THERMOPHORESIS EQUATIONS
• PARTICLE VELOCITY
• THERMOPHORETIC VELOCITY

12. THERMOPHORESIS EQUATIONS
• VELOCITY-VORTICITY. NAVIER -STOKES.
• VORTICITY TRANSPORT
• ENERGY TRANSPORT

13. DESCRIPTION OF THE MODEL
• A cubic cavity is filled with fluid and subjected to a
temperature difference on two opposite vertical sides.
• Constant temperature on two vertical walls.
• Zero heat flux on other four wall (adiabatic).
• Zero velocity on all walls (no-slip boundary condition).

14. DESCRIPTION OF THE MODEL
• In-houde CFD code, which uses Euler-Lagnrange
method to simulate flow and movement of
particles.
• 100.000 particles.
• 100 time steps .
• Ra = 1000, Ra = 10000, Ra = 100000; Ra =
1000000.
• 1º case: with thermophoresis.
• 2º case: with thermophoresis and Brownian
motion.

15. MATERIAL PROPERTIES

16. MATERIAL PROPERTIES

17. FLUID TEMPERATURE
Ra = 1000 Ra = 10000
Ra = 100000 Ra = 1000000

18. FLUID VELOCITY
• Cut our cubic cavity into slices, by
perpendicular planes to the normal unitary
vectors.

19. FLUID VELOCITY
Ra = 1000 Ra = 100000

20. POSITION AND NUMBER OF PARTICLES
• For each Rayleigh number.
• The YZ plane is analyzed.
• X axis is analyzed.
• The X axis scale is from 0 [cm] to 1 [cm].
• The position 0 is the coldest side.
• The position 1 is the hottest side.
• Time steps intervals analyzed: 1st to the 10th, from
the 31st to the 40th, from the 61st to 70th, from the
91st to 100th.

21. POSITION AND NUMBER OF PARTICLES
• XZ plane and time step 50.
Ra = 1000 Ra = 10000

22. POSITION AND NUMBER OF PARTICLES
• XZ plane and time step 50.
Ra = 100000 Ra = 1000000

23. POSITION AND NUMBER OF PARTICLES
0
500
1000
1500
2000
2500
3000
0 0.05 0.1 0.15 0.2
N
X axis [cm]
t: 1-10 (Th)
t: 31-40 (Th)
t: 61-70 (Th)
t: 91-100 (Th)
0
500
1000
1500
2000
2500
3000
0.6 0.7 0.8 0.9 1
N
X axis [cm]
t: 1-10 (Th)
t: 31-40 (Th)
t: 61-70 (Th)
t: 91-100 (Th)
0
5
10
15
20
25
30
0 0.05 0.1 0.15 0.2
N
X axis [cm]
t: 1-10 (Th)
t: 31-40 (Th)
t: 61-70 (Th)
t: 91-100 (Th)
0
5000
10000
15000
20000
25000
30000
35000
40000
0.6 0.7 0.8 0.9 1
N
X axis [cm]
t: 1-10 (Th)
t: 31-40 (Th)
t: 61-70 (Th)
t: 91-100 (Th)
Ra=1.000Ra=1.000.000

24. POSITION AND NUMBER OF PARTICLES
0
500
1000
1500
2000
2500
3000
0 0.05 0.1 0.15 0.2
N
X axis [cm]
t: 1-10 (Th+Bw)
t: 31-40 (Th+Bw)
t: 61-70 (Th+Bw)
t: 91-100 (Th+Bw)
0
500
1000
1500
2000
2500
3000
0.6 0.7 0.8 0.9 1
N
X axis [cm]
t: 1-10 (Th+Bw)
t: 31-40 (Th+Bw)
t: 61-70 (Th+Bw)
t: 91-100 (Th+Bw)
0
1
2
3
4
5
0 0.05 0.1 0.15 0.2
N
X axis [cm]
t: 1-10 (Th+Bw)
t: 31-40 (Th+Bw)
t: 61-70 (Th+Bw)
t: 91-100 (Th+Bw)
0
5000
10000
15000
20000
25000
30000
35000
0.6 0.7 0.8 0.9 1
N
X axis [cm]
t: 1-10 (Th+Bw)
t: 31-40 (Th+Bw)
t: 61-70 (Th+Bw)
t: 91-100 (Th+Bw)
Ra=1.000Ra=1.000.000

25. HEAT FLUX
• Heat transfer though a vertical wall expressed
as Nusselt number versus time.
• For four different Rayleigh numbers.
• Thermophoresis (Th) case and
thermophoresis and Brownian motion
(Th+Bw) case are analyzed.

26. HEAT FLUX
1.345
1.34505
1.3451
1.34515
1.3452
1.34525
1.3453
1.34535
1.3454
1.34545
1.3455
50 100 150 200 250 300 350 400 450 500
Nusseltnumber[-]
time [-]
Ra = 10^3 (Th)
Ra = 10^3 (Th+Bw)
2.178
2.1785
2.179
2.1795
2.18
2.1805
2.181
2.1815
2.182
2.1825
50 100 150 200 250 300 350 400 450 500
Nusseltnumber[-]
time [-]
Ra = 10^4 (Th)
Ra = 10^4 (Th+Bw)

27. HEAT FLUX
4.9
4.902
4.904
4.906
4.908
4.91
4.912
50 100 150 200 250 300 350 400 450 500
Nusseltnumber[-]
time [-]
Ra = 10^5 (Th)
Ra = 10^5 (Th+Bw)
9.9
9.95
10
10.05
10.1
10.15
10.2
10.25
10.3
50 100 150 200 250 300 350 400 450 500
Nusseltnumber[-]
time [-]
Ra = 10^6 (Th)
Ra = 10^6 (Th+Bw)

28. CONCLUSIONS
• Fluid temperature is the same in both cases.
• Fluid velocity: the flow is stronger and this is
moved over the external faces of the XY plane
due to vorticity.
• Fluid velocity: the effect of Brownian motion is
irrelevant.
• Position and number of particles: the effect of
Brownian motion is irrelevant.
• Heat flux: the effect of Brownian motion is
irrelevant.