Size distribution dynamics of a hygroscopic aerosol flowing through an isothermal wall tube
with coupled heat and mass transfer: modeling and experimental validation
Alan Shihadeh and Rawad Saleh
Aerosol Research Laboratory, Mechanical Engineering Dept, American University of Beirut, Lebanon
Experimental
Key contributions
Key issues
· generate a quasi-plug flow via turbulent mixing
· particle stopping distance << Kolmogorov scale to ensure locally quiescent particles
· negligible deposition and coagulation
· how to measure changes in particle size distribution for a volatile aerosol?
Approach
· use residual method to determine tube inlet particle size distribution
· can be shown that bulk temperature and particle size are uniquely relatedmeasure variation of bulk
phase temperature rather than PSD with axial distance
· Demonstrate the use of temperature as a diagnostic when volatility and high number density make direct
measurement of particle size difficult
· No previous published data on a hygroscopic aerosol flowing through heated or cooled tube where 2-way
coupling is important
· Experimentally validate a methodology used to predict particle growth in inhaled pharmaceutical aerosols
Background
This research was prompted by our ongoing investigation of tobacco smoke
aerosols generated in the “narghile” waterpipe, a traditional smoking device which
is currently experiencing a popular revival in many parts of the world. While
investigating changes in aerosol concentration and size distribution as the smoke
travels through the waterpipe, we found it necessary to develop a computational
model to predict particle growth and evaporation due to heat and mass transfer
at the flow boundaries. Using an approach found in the literature on hygroscopic
growth of inhaled pharmaceutical aerosols (Finlay and Stapleton, 1995), we
implemented a plug-flow code with boundary layer-driven heat and mass transfer
dynamics. Because of the high mass concentration of waterpipe smoke and
pharmaceutical aerosols, phase change to/from the particle phase affects the bulk
flow, and vice-versa. Thus a “two-way coupled” model was necessary in which
the relevant conservation and rate equations between the particle and bulk
phases, and bulk phases and flow boundaries were solved simultaneously. Having
implemented such a model and validated it against analytical solutions for particle
size distribution in simplified cases, we were unable to find any experimental data
in the aerosol literature in which two-way coupling was important. Thus we
directed our efforts toward developing an experimental apparatus for validating
the 2-way plug flow model.
Tw
Td
Tw
Tb
Qw
The droplets are initially at
thermal and phase equilibrium
with the bulk phase, (Td=Tb,
cd=cb). The aerosol enters the
heated pipe and heat (Qw)
transfers from the wall to the
bulk, elevating Tb.
Td
Tw
Tb
Qd
With Tb>Td, heat (Qd) transfers
from the bulk to the droplets,
elevating Td.
Tb
Td
Model
Major assumptions
· particles quiescent in surrounding bulk  transport by diffusion alone
· negligible diffusion in flow direction
· 1-D plug flow  heat and mass transferred at wall instantaneously distributed
radially
Resulting equations (applied to n particle size bins each with N particles)
· particle phase
dmd
 md
dmd
M P
P
 2 Cmdd D v ( vd  vb )
dt
dt
Ru Td Tb
dT
dm
md cd d  Qd  d hfg
Qd  2 dd k (Tb  Td )
dt
dt
conservation equations
diffusion rate equations
· bulk phase
Qw  hA(Tb  Tw )
n
dmvb
dmd
  ( Ni
)  mw
dt
dt
i 1
mw  hm A(cb  cw )
n
dTb
dm
(macpa  mvbcpv )
 [ Ni (Qd  d c pv (Td  Tb ))]  Qw  mwcpv (Tb  Tw )
dt
dt
i 1
wall heat/mass transfer
conservation equations
Implementation
· explicit finite difference solution
· Lagrangian tracking of aerosol volume (moves by its length each time step)
· full-moving particle bin structure
m
As Td increases, cd increases
as well, so cd > cb. The droplets
evaporate which causes the
vapor concentration in the bulk
to increase and the temperature
of the whole aerosol to
decrease.
Comparison to analytical solutions for simplified cases
a) atmospheric aerosol—no coupling [2]
b) condensing flow in a pipe–no aerosol [3]
Results
Measured and predicted bulk phase
temperature for two different flow
rates, inlet temperatures, and mass
concentrations are shown. Heat
transfer coefficient used in
predictions was determined for each
flow rate using dry air only. Excellent
agreement is shown.
Schematic of two-way coupled heat and mass transfer
Conclusions
· the use of temperature as a diagnostic where high volatility and particle number density render size
measurements difficult has been demonstrated
Cited literature
[1] W. H. Finlay and K. W. Stapleton. 1995. The Effect of Regional Lung Deposition of Coupled Heat
and Mass Transfer Between Hygroscopic Droplets and Their Surrounding Phase. Journal of Aerosol
Science, 26, 655.
[2] John H. Seinfeld and Spyros N. Pandis. 1997. Atmospheric Chemistry and Physics. New York:
Wiley.
[3] H.J.H. Brouwers. 1990. Film Models for Transport Phenomena with Fog Formation: the Classical
Film Model. International Journal of Heat and Mass Transfer, 35, 1.
· satisfactory predictions of hygroscopic growth/evaporation can be achieved using a plug-flow model
with boundary layer heat/mass transfer at the wall for aqueous NaCl flowing through a tube at near
body-temperature
For further info
http://webfea.fea.aub.edu.lb/aerosol/index.html