Utilizing APTV to investigate the dynamics of polydisperse suspension flows beyond the dilute regime
Authors: Brockmann Philipp , Symanczyk Christoph , Ennayar Hatim , Hussong Jeanette 
Published: August 2022

Abstract
We present a methodology that allows to measure the dynamics of polydisperse suspension flows by means of Astigmatism Particle Tracking Velocimetry (APTV). Measurements are successfully performed with tridisperse suspensions flows in a square duct of up to $$\varPhi =9.1\%$$

Φ
=
9.1
%

particle volume fraction. Using a refractive index matching technique, a small amount of the particles ($$\varPhi =0.08\%$$

Φ
=
0.08
%

) is labeled with fluorescent dye to be visible to the camera during the particle tracking procedure. Calibration measurements are performed for ten different particles diameters $$d_p$$

d
p

ranging from $$d_p= {15}\upmu \mathrm{m}$$

d
p

=
15
μ
m

to $$d_p= {260}\,\upmu \mathrm{m}$$

d
p

=
260

μ
m

. It is shown that Euclidean calibration curves of different $$d_p$$

d
p

overlap outside the focal planes, which induces ambiguities in a polydisperse APTV measurement. In the present approach, this ambiguity can be overcome utilizing the light intensity of a particle image which increases sharply with $$d_p$$

d
p

. In this way, extended Euclidean calibration curves can be generated for each particle group which are spatially separated through the light intensity which serves as an additional calibration parameter (Brockmann et al. in Exp Fluids 61(2):67, 2020). The extended Euclidean calibration allows to simultaneously differentiate particles of different sizes and determine their 3D location. This facilitates to investigate the migration behavior of mono- and tridisperse suspension flows which we demonstrate here for square duct flows with cross-sectional areas of $$0.6\times 0.6\,\mathrm{mm}^2$$

0.6
×
0.6

mm

2

and $$0.4\times 0.4\,\mathrm{mm}^2$$

0.4
×
0.4

mm

2

at bulk Reynolds numbers of $$\mathrm{Re}_b \approx 20$$

Re
b

≈
20

and $$\mathrm{Re}_b \approx 40$$

Re
b

≈
40

for particle volume fractions of $$\varPhi =0.08\%$$

Φ
=
0.08
%

and $$\varPhi =9.1\%$$

Φ
=
9.1
%

. At $$\varPhi =0.08\%$$

Φ
=
0.08
%

and $$\mathrm{Re}_b=20$$

Re
b

=
20

, we observe particles to arrange themselves in a ring-like formation inside the capillary, henceforth referred to as Pseudo Segré Silberberg Annulus (PSSA), with no significant differences between mono- and polydisperse suspension particle distributions. At $$\varPhi =9.1\%$$

Φ
=
9.1
%

, particles in monodisperse suspensions scatter around the PSSA. This scattering decreases when $$d_p$$

d
p

increases or $$Re_b$$

R

e
b

increases from 20 to 40. Striking differences are observed in polydisperse suspensions. Large particles ($${60}\,\upmu \mathrm{m}$$

60

μ
m

) scatter significantly less around the PSSA in the polydisperse case compared to a monodisperse suspension of the same overall volume fraction. In contrast, small and intermediate particles ( $${30}\,\upmu \mathrm{m}$$

30

μ
m

, $${40}\,\upmu \mathrm{m}$$

40

μ
m

) are repelled by larger particles resulting in regions of high concentration close to the channel walls which can be only observed in the polydisperse case.

Graphical abstract