Deposition fraction of ellipsoidal fibers in the human nasal cavity- Influence of non-creeping formulation of hydrodynamic forces and torques

doi:10.1016/j.ijmultiphaseflow.2020.103238

International Journal of Multiphase Flow

Volume 126, May 2020, 103238

https://doi.org/10.1016/j.ijmultiphaseflow.2020.103238 Get rights and content

Highlights

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Dispersion and deposition of ellipsoidal fibers in a model of nasal cavity are evaluated using non-creeping formulations for hydrodynamic forces and torques.
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For laminar flows, lower deposition fractions are obtained with non-creeping formulations compared to the creeping formulation.
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For turbulent flows in the nasal cavity lower deposition fraction of fibers is observed with non-creeping formulation rather than creeping formulation and the difference is more than laminar flows.
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Recommendations are presented for numerical simulations with non-creeping formulations considering the fiber size and air flow rate in the nasal cavity.

Abstract

In this study, the deposition of fibrous particles in a realistic 3D model of the right nasal cavity of a 24-years-old woman was simulated using the non-creeping formulations for hydrodynamic forces and torques. The Lagrangian trajectory analysis approach within the Ansys-Fluent software was used for these simulations. Several user-defined functions (UDFs) for solving the coupled translational and rotational motion of an ellipsoidal fiber and for evaluation of non-creeping forces and torques were developed and were incorporated in the Ansys-Fluent DPM. The passage included the main nasal cavity from the nostril to the beginning of the nasopharynx. Both laminar and turbulent steady inhalation breathing conditions were assumed, and for turbulence modeling, the Realizable k-ε model was employed. It was assumed that the airflow was incompressible. The breathing rates of 2.5, 5.0, 7.5, and 10 lit/min per nostril were considered for laminar airflow corresponding to the rest or light physical activity conditions. For turbulent airflow, the breathing rates of 15, 20, and 30 lit/min were assumed for high physical activities. The transport and deposition of fibers of different sizes and aspect ratios in the nasal cavity under laminar and turbulent airflow regimes were investigated.

The simulation results showed that the increase of air flow rate, fiber diameter, and aspect ratio led to the increase of deposition in the human nasal cavity. In addition, the use of forces and torques estimated from the more accurate non-creeping flow estimation led to somewhat lower particle deposition in the nasal cavity compared to those obtained from the simplified creeping flow assumption.

Introduction

The use of inhalation medical drug delivery for the treatment of pulmonary and other diseases is becoming increasingly prevalent in comparison with the more common methods, such as interveinal injection and/or taking medication orally. Therefore, research on targeted drug delivery has attracted attention as an advanced method for treating pulmonary diseases. Most drug particles, however, were found to deposit in upper respiratory passages, and the efficiency of drug delivery to deep lung airways and alveoli region is low.

The deposition efficiency of drug particles in the human respiratory tract is affected by several important parameters, including the geometry of the airways, particle size, and aspect ratio (for elongated particles), and the airflow regime. In the last three decades, many experimental and numerical studies on dispersion and deposition of particles in various parts of the human respiratory system were performed. The majority of these studies were concerned with the deposition of spherical particles with very few dealing with non-spherical (elongated) particles. Almost all available studies on computational modeling of fibrous particles in the human respiratory system used the creeping estimation for hydrodynamics forces and torques acting on the particle. This has been the case even for larger fibers and higher airflow velocity, where the flow around the particle may be beyond the creeping flow condition.

Reviews of literature on dispersion and deposition of particles in the human respiratory system were reported by Tu et al. (2013) and Ahmadi and Abouali (2017), among others. Inthavong et al. (2008) employed the equivalent diameter method and investigated the deposition of fibers in the right and left nasal cavities of an adult person. Tian and Ahmadi (2013) performed numerical simulations of ellipsoidal fiber dispersion and deposition in the human tracheobronchial airways. They solved the coupled translational and rotational equation of fiber motion and found that the fiber deposition in the airway is enhanced by their rotational motions. In a related study, Feng and Kleinstreuer (2013) simulated the deposition of ellipsoidal fibers in a model of the human respiratory system from the oral cavity to the 4th generation of lung airways. They reported the total and regional deposition of ellipsoidal fibers and compared their results with those obtained for the equivalent sphere particles.

Dastan et al. (2014) performed a series of numerical simulations investigating the deposition of ellipsoidal fibers in three human nasal cavity models under laminar breathing conditions. They solved the coupled translational and rotational equations of motion for ellipsoidal fibers and reported the total fiber deposition in different nasal passages. They also showed that using the impaction parameter, the fiber deposition fraction in the various nasal cavity models collapsed to a single curve. Tian and Ahmadi (2016) numerically simulated the effect of Brownian motion on dispersion and deposition of nano-fibers in the human upper tracheobronchial airways. They concluded that while the Brownian motion enhances the nano-fiber deposition, it has a negligible impact on the deposition of micro-fibers. Tavakol et al. (2017) evaluated the deposition fraction of ellipsoidal fibers in a human nasal cavity model for both laminar and turbulent breathing conditions. They employed the Lagrangian particle tracking in their analysis and included the effects of turbulence velocity and velocity gradient fluctuations on transport and deposition of various ellipsoidal micro-fibers. They highlighted the importance of proper modeling of turbulence fluctuations on deposition fraction of fibers. In addition, their results showed that the fiber aspect ratio significantly affects the fiber deposition rate. In particular, for fibers with high aspect ratios, the simulated deposition fractions were higher than those reported for the equivalent spheres.

Jia et al. (2017) reported the deposition pattern of micro-particles in a realistic model of the human upper respiratory tract. For non-spherical particles, the drag coefficient was estimated using a non-linear correlation based on particle Reynolds number and an orientation parameter. They reported that the deposition fraction of particles was a function of the particle shape factor. As noted before, almost all earlier studies regarding dispersion and deposition of elongated particles used the creeping flow formulation for hydrodynamic forces and torques. In a previous study, Tavakol et al., 2015a evaluated the dispersion and deposition of fibrous particles in fully developed laminar pipe flows using the non-creeping flow formulations of Zastawny et al. (2012) for hydrodynamic forces and torques. They also presented a new empirical expression for the deposition efficiency of fibers in fully developed laminar pipe flow that is valid for both creeping and non-creeping flow conditions.

In a recent study, Arcen et al. (2017) examined the motion of ellipsoidal particles in a vertical turbulent channel flow using the direct numerical simulation (DNS). They used a new set of non-creeping formulation for hydrodynamic forces and toques to assess the influence of inertia, shape, and gravity on the dynamics of fibrous particles. Their results demonstrated that in the presence of gravity the dynamics of ellipsoids are different from spheres and shape effect becomes important; however, in the absence of gravity, the dynamics of ellipsoids become close to spheres. Zarghami and Padding (2018) performed a series of Lattice Boltzmann simulations (LBM) and investigated the drag, lift and torques acting on a non-spherical particle moving near a wall. They then evaluated the motion of a single 2D elliptical particle and assessed the influence of particle Reynolds number, distance to the wall, orientation angle and aspect ratio on hydrodynamic forces and torques. In another study, Sanjeevi et al. (2018) used the LBM to determine the drag, lift and torque coefficients acting on non-spherical particles. They performed a series of numerical simulations for a wide range of particle Reynolds number, 0.1<Re_p<2000 and different incidence angles. Based on their numerical simulations, they proposed new correlations for drag, lift and torque coefficients.

In the present study, the transport and deposition of ellipsoidal particles in a model of the human nasal cavity was simulated using CFD and Lagrangian particle tracking. Several UDFs were developed to track the motion of elongated particles and account for the non-creeping expressions for hydrodynamic forces and torques and were coupled to the Ansys-Fluent DPM. Simulation results for dispersion and deposition of fibrous particles in the nasal passage were evaluated and compared with those obtained with the creeping flow formulation. The results showed that using the non-creeping formulations for hydrodynamic forces and torques led to lower deposition fractions in the nasal cavity. The differences between creeping and non-creeping simulations also increased at higher breathing rates under the turbulent flow regime.

Section snippets

Carrier flow

For a steady-state and incompressible airflow with constant properties, the continuity and the Navier-Stokes equations are given as: $\frac{\partial u_{i}}{\partial x_{i}} = 0$ $ρ u_{j} \frac{\partial u_{i}}{\partial x_{j}} = - \frac{\partial P}{\partial x_{i}} + μ \frac{\partial^{2} u_{i}}{\partial x_{j} \partial x_{j}}$ where u_i and x_i are the components of velocity and position vectors, ρ is the fluid density, P is the pressure and µ denotes the fluid viscosity.

For turbulent airflow field, averaging Eqs. (1) and (2), the mean continuity and the Reynolds averaged Navier-Stokes (RANS) equations are obtained as: $\frac{\partial {\bar{u}}_{i}}{\partial x_{i}} = 0$ $ρ {\bar{u}}_{j} \frac{\partial {\bar{u}}_{i}}{\partial x_{j}} = - \frac{\partial \bar{P}}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} (μ \partial u$

Numerical simulation

In the present study, the dispersion and deposition of non-spherical particles in a realistic model of the human nasal cavity are simulated using the non-creeping formulations for hydrodynamic forces and toques, and the results are compared with the experimental data and the creeping flow simulations. For this purpose, different inhalation flow rates, representing the rest condition to severe physical activity, are considered. In this section, geometry of studied airway passage is described and

Results

In this section, the results for fiber deposition in a nasal cavity with the use of the developed UDF for non-creeping flow are described. Evaluation of hydrodynamic forces and torques for laminar and turbulent flow regime is first presented by comparing the simulation results with the experimental data. Then, the simulation results of the developed non-creeping flow UDF for fibrous particle deposition in the nasal cavity are presented and results are compared with simulations using the

Conclusions

In this study, dispersion and deposition of fibrous particles in a realistic model of the human nasal cavity were investigated by the Lagrangian particle tracking method using the discrete phase model (DPM) of the Ansys-Fluent code. Several user-defined functions (UDFs) were developed that incorporate the non-creeping formulation for hydrodynamic forces and torques acting on an ellipsoid, and they were used for predicting the deposition fraction of ellipsoidal fibers in the nasal passage under

CRediT authorship contribution statement

M. Abolhassantash: Investigation, Data curation, Software, Validation. M.M. Tavakol: Conceptualization, Methodology, Software, Writing - original draft. O. Abouali: Conceptualization, Writing - review & editing. M. Yaghoubi: Conceptualization, Writing - review & editing. G. Ahmadi: Supervision, Writing - review & editing.

Declaration of competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The second author acknowledged the support from the Islamic Azad University, Shiraz Branch, Iran.

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Deposition fraction of ellipsoidal fibers in the human nasal cavity- Influence of non-creeping formulation of hydrodynamic forces and torques

Highlights

Abstract

Introduction

Section snippets

Carrier flow

Numerical simulation

Results

Conclusions

CRediT authorship contribution statement

Declaration of competing interests

Acknowledgments

J. Aerosol Sci.

Comput. Biol. Med.

J. Aerosol. Sci.

Comput. Fluids

J. Aerosol Sci.

Int. J. Multiphase Flow

J. Aerosol Sci.

J Comput Phys

Int. J. Multiphase Flow

J. Aerosol. Sci.

J. Aerosol. Sci.

J. Aerosol. Sci.

Comput. Fluids

Int. J. Multiphase Flow

J. Aerosol. Sci.

J. Aerosol. Sci.

J. Aerosol. Sci.