CET2011_NanoPaper-v3

7/31/2019 CET2011_NanoPaper-v3

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Modelling of Nanoparticle Diffusion in the Paranasal

Sinuses

Qinjiang Ge, Kiao Inthavong, Jiyuan Tu

School of Aerospace Mechanical Manufacturing Engineering, RMIT University

Bundoora, Australia

Abstract A nasal-sinus cavity model was created in order to

determine if any nanoparticles (NPs) would deposit within themaxillary sinuses at a steady inhalation flow rate of 10L/min. The

computational model was simulated in Fluent v12.1using the

Brownian diffusion model. Airflow contour patterns and

streamlines showed very low flow (


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The nasal-sinus cavity dimensions and its comparison withother models in the literature are given in Table 1. The meshingscheme used a hybrid mesh that included six-prismatic layerswith an inner tetrahedral core. Grid independence based onvelocity profiles at the outlet was performed and the final meshsize for the nasal-sinus model was 3.2million cells.

TABLE I. NASAL CAVITY GEOMETRY COMPARISONS

Doorly et al. [5]

Model 1 Model 2 Model 3 Xiong [4] CurrentOverall length (cm) 10.5 10.6 11 9.1 9.7

Overall width (cm) - - - 6.6 7.3

Surface area (cm2) 106* 107* 109* - 290

Volume (cm3) 13.8 14.2 22.4 - -

*right nasal cavity only

B. Numerical modellingThe commercial CFD code, Fluent v12.1 was used to solve

the governing equations for fluid flow under steady flow rate of10 L/min. The inspiratory flow rates for adults can rangebetween 5-12L/min for light breathing and 12-40L/min fornon-normal conditions such as during exertion and physicalexercise. Up to a flow rate of 15L/min the flow regime in therespiratory airways has been determined as dominantlylaminar, although traces of turbulent flow structures may exist[6]. In this study a laminar flow model is used to focus on thediffusion process of the NPs and because of the low flow rates.

The steady-state continuity and momentum equations forthe gas phase (air) in Cartesian tensor notation can be cast as:

( ) 0=

gig

i

ux

(1)

+

=

j

g

ig

ji

g

j

g

ig

jx

u

xx

p

x

uu

1 (2)

The equations were discretised with the QUICK schemewhile the pressure-velocity coupling was resolved through theSIMPLE method.

For a low volume fraction of dispersed phase (particles),the Lagrangian approach with one-way coupling is used, i.e.the airflow transports the particles, but the effect of particlemovements on the flow is neglected. In this approach, theairflow field is first simulated, and then the trajectories ofindividual particles are tracked by integrating a force balanceequation on the particle which can be written as:

p

iD g B L T

duF F F F F

dt= + + + + (3)

FD is the drag force per unit particle mass taking the formof Stokes' drag law [7], Fg is the gravity term, FB is theBrownian force [8], is Saffman's lift force due to shear, and FTis the thermophoretic force. Particle rebounding from thesurfaces was ignored and particle deposition was determined

when the distance between the particle centre and a surface wasless than or equal to the particle radius. The particle tracking isthen terminated.

Inhalation through the nasal cavity is induced through apressure difference between the nostril inlets (Pin = 0Pa) andthe nasopharynx outlet (Pout) that is set to a negative pressure

relative to atmospheric pressure that is caused by themovement of the diaphragm. Boundary conditions for theparticles are set up as a circular particle release entrained in theflow field. Particles were released from 0.01m from the inlet toprevent any spurious data exiting the inlet upon immediaterelease. Furthermore, a particle was located at no less than0.1mm away from the wall to eliminate artificial immediatedeposition on the walls due to the stochastic nature of theBrownian motion model. A near wall interpolation scheme [1]

is applied onto wall adjacent cells to allow the particle velocityto vary as it approaches zero rather than be a uniform velocitythroughout the cell.

III. RESULTS

A. Brownian diffusion modelling validationThe number of particles tracked was checked for statistical

independence since modelling Brownian motion is inherentlyof a stochastic nature. Independence was achieved for 70000particles, since an increase of particles to 100,000 particlesyielded a difference of less than 1% in the depositionefficiency. Deposition of NPs in the range of 5-12nm particleswas tested for a 90

obend pipe (Figure 2). The applicability of

the Gaussian white noise Brownian diffusion model used

within Fluent-v12.1 (BMv12)needs to be verified given that thesame model in Fluent-v6.3 failed to predict nanoparticledeposition [1, 2]. The results show that the model in Fluent-v6.3 under predicts the deposition of the NPs especially for11nm. The results show up to two orders of magnitude belowthe experimental data. The results for Fluent-v12 show betteragreement with the experimental data. It must be noted that themodels for Brownian motion that are available in Fluent v6.3and v12.1 is the same model based on a Gaussian white noiseprocess.

90o Bend Pipe

5 7 9 1110

-5

10-4

10-3

10-1

10-2

100

Particle Diameter (nm)

DepositionEfficiency

(%)

Wang (2002)

FLUENT v6.3

FLUENT v12.1

Figure 2. Comparison of deposition efficiency results using Brownian

models from Fluent 6.3, and Fluent 12.1 in (a) straight pipe 1L/min, (b)straight pipe 10L/min, and a (c) 90o bend pipe.

B. Flow patterns and streamlinesContours of velocity magnitude at slice a-e (as defined in

Figure 1) are shown below in Figure 3. Flow acceleration isfound in slice-a with a peak velocity of 1.8m/s while pockets oflow velocity are found at the top and bottom of the slice. As theflow travels downstream the peak velocity decreases and in


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slice-c and slice-d, the peak velocity reaches only 1.3m/s. Thisis due to the airway passage expanding in cross-sectional arearesulting in lower velocities. The contours show that the bulkflow regions occur mainly through the mid-height region andclose to the nasal septum which separates the two cavities. Thecontour at slice-e shows a well mixed pattern which is causedby the airflow from the left and right sides of the nasal cavitymerging together. Very low flows at < 0.1m/s are found in thesinus regions.

a b c

d e

Figure 3. Velocity magnitude contours at 10L/min for Slices a-e. Colour

scale is given in [m/s].

Flow streamlines were released from the left and rightnostrils in order to trace the flow patterns (Figure 4).

(a) (b)

(c) (d)

Figure 4. Streamlines passing through the nasal cavity that originates from

the (a) left and (b) right nostrils at 10L/min. Colour scale represents thevelocity magnitude in [m/s].

In both instances the streamlines initially accelerate nearthe nostril opening before passing mainly through the mainnasal passage at mid-height. Some streamlines travel along thefloor of the nasal cavity, while some reach the olfactoryregions, but these streamlines are highlighted with blue colour,which denotes a low velocity 0.01m/s. Streamlines also passinto the maxillary sinus, squeezing through the narrow ostium(Figures 4c and 4d). These streamlines are very low velocitythat recirculates inside the maxillary sinus. CFD analysis

showed that the minimum ostium diameter is 3.03mm and3.78mm, and the pressure difference between the ostiumentrance and inside the maxillary sinus are 0.056Pa and0.0026Pa for the left and right sides respectively. The massflow rate through the left and right ostium is 11.4e-9 kg/s and6.77e-9 kg/s which are < 0.006% of the total inhalation flowrate. This small percentage of flow is not conducive to particledeposition and that the only mode of deposition in theparanasal sinus will be due to the particle Brownian diffusion.

C. Nanoparticle depositionThe number of particles tracked was checked for statistical

independence because the BM is inherently of a stochasticnature. Particle number independence was achieved for 70,000particles, because an increase of particles to 100,000 particles

yielded a difference of less than 1% in the depositionefficiency. Deposition patterns for 1nm and 10nm particles areshown in Figure 5 which shows that early deposition occurs for1nm with nearly all particles depositing in the anterior half ofthe nasal cavity with a large proportion of the particlespersisting for less than 0.022secs in the nasal cavity domain.

(a)

(b)

Figure 5. NP deposition pattern in the nasal-sinus cavity for (a) 1nm -

resulting in 98% deposition and (b)10nm - resulting in 29.8% deposition.Particles are coloured by trajectory time within the nasal cavity before

impacting onto the surfaces at 10L/min..


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This deposition pattern is indicative of the highly diffusivenature of NPs that become as small as 1nm. The strength orinfluence of the Brownian diffusion decreases as the particlesize increases from 1nm upwards, since the molecularcollisions with the particle become less significant. This isevident in the deposition pattern of 10nm which shows morerandom and evenly distributed deposition sites. For 10nmparticles, the time scale is 10x as great as that for 1nm whichsuggests that the particles are not as diffusive and are

transported with the inhaled flow field for longer and hence theability to travel deeper into the nasal cavity. This particletrajectory time is particularly important for NP depositionstudies as it gives an indication of the likelihood of depositionin different regions of the nasal cavity. For example the shorterresidence time of 1nm means that deposition occurs nearlyimmediately and the deposition zone is restricted to the nasalcavity and further deposition downstream is unlikely. Thisprotects the sensitive lung airways from those NPs that exhibitdangerous properties for respiratory health. Conversely theability to deposit particles in the middle regions of the nasalcavity or even deeper into the lung airways with highdeposition, can be important for therapeutic drug delivery.

Since the diffusion property of NPs provides maximumdeposition for 1nm and decreases rapidly as the particle size

increases, a number of different sized NPs were released fromthe nostril inlets to determine if any would deposit within themaxillary sinuses. The particles that reach the ostium isexpected to deposit due to diffusion only and that the inertialmomentum from the inhaled air has insignificant effect becauseof the low percentage of flow passing through the ostium.Figure 6a shows that in the right maxillary sinus, inclusive ofthe ostium, a small percentage of particles

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