SUPPLEMENTAL INFORMATION
“Assessment of a Cylindrical and a Rectangular Plate Differential Mobility Analyzer for Size
Fractionation of Nanoparticles at High Aerosol Flow Rates”
by Esther Hontañón, Marcel Rouenhoff, Alfredo Azabal, Emilio Ramiro, Frank Einar Kruis
Esther Hontañón (), Marcel Rouenhoff, Frank Einar Kruis
Institute of Technology for Nanostructures (NST) and Centre for Nanointegration Duisburg-Essen
(CENIDE), University of Duisburg-Essen, Bismarckstr. 81, Duisburg, 47057 Germany
 Esther Hontañón
E-mail: esther.hontanon@uni-due.de
Telephone: +49 (0) 203 379 1047
Fax: +49 (0) 203 379 3268
Alfredo Azabal, Emilio Ramiro
RAMEM S.A., Sambara 33, 28027 Madrid, Spain
1
High Flow DMAs
Table S1. Parameters of the high flow DMAs relevant to particle size fractionation.
High Flow
DMAs
Outer radius
(mm)
120
a)
b)
c)
Column
length
(mm)
Aerosol /
sheath
nominal
flow rates
(slm)
Minimum
particle
mobility a)
(cm2V-1s-1)
Flow
Reynolds
number b)
Particle
Peclet
number c)
42
100
100
1000
3.27x10-3
(26 nm)
2027
5.1x104
25
230
200
2000
1.88x10-3
(35 nm)
4444
1.1x105
Inner radius
(nm) (mm)
Cylindrical
Rectangular
plate
Electrode
separation
distance
(mm)
78
Classification zone width
(mm)
550
Minimum particle mobility based on the sheath nominal flow rate and a maximum attainable voltage of 35 kV; the
mobility equivalent diameter for singly charged spheres is given between parentheses.
Reynolds number based on the total (aerosol+sheath) nominal flow rate, the electrode distance and the kinematic viscosity
of air 1.5x10-5 m2s-1 at 20°C and 1 atm.
Peclet number based on the flow Reynolds number and the Schmidt number for spheres of a diameter of 3 nm with a
diffusion coefficient of 6x10-7 m2s-1 in air at 20°C and 1 atm.
Table S2. Laminarization screens used in the high flow DMAs.
High Flow
DMA
Manufacturer
Material
Model
Wire
diameter
(µm)
Mesh
Opening
(µm)
Open
Area
(%)
Cylindrical
HF-DMA
SEFAR®
PET 1000
54-70W PW
70
109
34.8
Rectangular
plate DMA
SEFAR®
PET 1000
27-120W PW
120
249
45.3
NYTAL
PA-12 XXX-112
70
112
38
2
Experimental Facility
A facility called Big Monodisperse Aerosol Generator (BigMAG) has been designed and built
to enhance the yield of monodisperse nanoparticles in gas phase by means of Differential Mobility
Analyzer (DMA). Fig. S1 shows a layout of the facility. The aerosol carrier gas and the sheath gas
which is required for operating the DMA circulate in two closed loops driven by roots pumps (Ruvac
WS, Oerlikon Leybold Vacuum GmbH, Germany) with maximum pumping speeds of 251 m3h-1 and
2100 m3h-1, respectively. In each loop the gas flow rate is determined by measuring the pressure drop
of the flow through a laminar flow element (FCO96-2000L and 10000L, Furness Controls Ltd., UK)
with the help of a differential pressure transmitter (FCO318, Furness Controls Ltd., UK). The flow
rate is then maintained by a PID controller (T16/P16, Red Lion Controls Inc., USA) acting on a
frequency converter (Ruvatronic RT5, KEB GmbH, Germany) that regulates the pump rotational
speed. Two homemade bypass valves are installed nearby the pumps in parallel to the flow
recirculation lines for coarse adjustment of the flow rates. Also, the valves allow determining the
optimal working point of the roots pumps for fine adjustment of the flow rates by the PID controller,
as well as keeping a pressure balance condition between the inlet and the outlet of the pumps. The
pressure in the facility is monitored by a pressure transmitter (Baratron 626B with display unit
PR400B, MKS Instruments GmbH, Germany). A muffler and a water cooling unit are installed
downstream of the roots pump in the sheath gas loop to reduce vibrations and noise and to cool down
the sheath gas to room temperature. The particle laden gas flows are cleaned upstream and
downstream of the pumps by using HEPA filters (MFCA H13, TROX Technik GmbH, Germany). The
BigMAG facility is vacuum tight. All connections between the pipes and with the equipment and the
instrumentation are sealed by means of standard vacuum flanges (ISO K 63, 100 and 160, Trinos
Vacuum Systems Inc., USA).
3
N2
sheath gas loop
aerosol loop
MFC
SMPS
HF
VV
RP
LFE
aerosol
f low control
DMA
BPV
BV
FC
BV
VV
HF
DPT
PID
RP
BPV
FC
PID
muf f ler
HV
sheath gas
f low control
CV
water
f low
control
cooling
unit
DPT
aerosol
generator
HF
capacitor
charger
PID
HV
PT
TC
VV
LFE
HF
SMPS
BV
BPV
CV
VV
TC
PT
Ball valve
Bypass valve
Control valve
Vacuum valve
Thermocouple
Pressure transducer
DPT Dif f erential pressure transmitter
LFE Laminar f low element
MFC Mass f low controller
RP
Roots pump
FC
Frequency converter
PID
Proportional-integral-derivative controller
HV
High voltage supply
DMA
Dif f erential mobility analyzer
SMPS Scanning mobility particle sizer
HF
HEPA f ilter
FIG. S1 Layout of the BigMAG facility with the aerosol and sheath gas recirculation loops.
4
Analytical Work
The particle number mobility distribution dN/dZ of an aerosol is derived from the particle
number size distribution dN/d(log dp) measured by the SMPS as follows
d(log d )
1
p
dN
dN



dZ ln 10  Z d(log Z) d(log d )
p
. [S1]
To evaluate the term d(log dp)/d(log Z), the relationship between the mobility Z and the diameter
dp for singly charged spheres is recalled
d
p

C(d )
p
Z
;
[S2]
with K = e/(3πµ) = 9.28x10-3, Z (cm2.V-1.s-1) and dp (nm); e is the elementary charge (1.6021x10-19 C);
µ is the gas viscosity (1.83x10-5 Pas for air at 23 ºC and 1 bar). The Cunningham slip factor C(dp) is
given by C (d )  (1  Kn)   1.142  0.558 exp  0.999 Kn   ; where Kn is the particle Knudsen number
p
Kn  2 λ d
p
, and λ is the gas mean free path (67.3 nm for air at 23 ºC and 1 bar). Then, log dp is
expressed as log d
p
 log Κ  log Z  log C(d
p
) and, for nanoparticles, this expression is fairly well
matched by a linear function y=a+bx with coefficients a = 0.13739 and b = -0.5183. Hereinafter, the
following relationship between the particle diameter dp and the particle mobility Z is used
d  10 a  Z b
p
.
[S3]
The exact expression Eq. [S2] and the approximate expression Eq. [S3] are compared to each
other in Fig. S2. Therefore, d(logdp)/d(logZ)=b and by substituting this and the particle number size
distribution dN/d(log dp) given by the SMPS in Eq. [S1], the particle number mobility distribution
dN/dZ of the polydisperse aerosol is finally obtained, which is well fitted by a log-normal function.
5
FIG. S2 Relationship between diameter dp and electrical mobility Z for spheres (solid line) and
approximate expression (dashed line).
The transfer function of the ideal DMA operating with balanced flow has a triangular form and
is given by the expression (Knutson and Whitby, 1975)

 Z Z*   1 1    Z Z*  


Ω(Z, Z* )  max  0, min  1,
,
  ; [S4]



 



where Z* is the central mobility of the particles classified by the DMA and  is the aerosol to sheath
flow ratio (q/Q). The log-normal particle number mobility distribution dN/dZ of a polydisperse aerosol
calculated by using Eq. [S1] and the transfer function of an ideal DMA given by Eq. [S4] are plotted
in Fig. S3a. It is assumed that the voltage applied to the DMA matches the voltage required to classify
particles of a mobility Z* equal to the point of maximum (mode) of the log-normal function,
Z* = 1.223x10-2 cm2.V-1.s-1, and that the DMA operates with  = 0.5.
The particle number mobility distribution dN/dZ of the particles selected by the DMA is
calculated as the product of the two functions in Fig. S3a, with the result shown in Fig. S3b. A
Gaussian function with a central mobility Zc of 1.24x10-2 cm2.V-1.s-1 and a relative full width at half
height FWHH/Zc of 0.5 fits closely the calculated particle number mobility distribution, consistently
with the values of Z* and  of the transfer function of the DMA.
6
a)
b)
FIG. S3 a) Log-normal particle number mobility distribution (solid line) of a polydisperse aerosol and
transfer function of an ideal DMA operating with balanced flow and a sheath to aerosol flow ratio of 2
(dashed line). b) Calculated number mobility distribution (solid line) of the particles classified by the
DMA and Gaussian fit (dashed line).
Then, the particle number size distribution dN/ddp of the particles selected by the DMA can be
derived from dN/dZ and Eq. [S3], as follows
dN
1 Z dN


dd
b d dZ
p
p
7
.
[S5]
By replacing dN/dZ by the Gaussian fit in Fig. S3b, dN/ddp is obtained, as displayed in Fig. S4.
A log-normal function with a geometric mean diameter dg of 13.32 nm and a geometric standard
deviation g of 1.10 matches well the calculated particle number size distribution of the aerosol
leaving the DMA.
FIG. S4 Calculated particle number distribution of the aerosol selected by an ideal DMA operating
with balanced flow and a sheath to aerosol flow ratio of 2 (solid line) and log-normal fit (dashed line).
8