Aerosol Science 39 (2008) 113–126www.elsevier.com/locate/jaerosci

Turbulent flow energy for aerosolization of powder particles

Jakub Gac1, Tomasz R. Sosnowski, Leon Gradon∗

Faculty of Chemical and Process Engineering, Warsaw University of Technology, Waryñskiego 1, 00-645 Warsaw, Poland

Received 23 January 2007; received in revised form 11 October 2007; accepted 16 October 2007

Abstract

The process of re-entrainment and re-dispersion of powder particles is studied both theoretically and experimentally in orderto discuss the possibilities of improvement of the quality of aerosol emitted from dry powder inhalers (DPI). The eddy fluidparticle model (EFPM) is employed to solve turbulent flow structure in the microscale in a channel with various types of turbulencepromoters. The resuspension process caused by the gas shearing forces is modeled with the Verlet algorithm taking into accountthe inter-particle cohesive interactions. Nondimensional numbers are introduced to define the domains of powder aerosolization.Computational results indicate the importance of the geometry of turbulence promoters for powder re-entrainment (fluidization) andde-aggregation of particle clusters. The theoretical findings, are supported by experimental results obtained in a model resuspensionchamber with a pharmaceutical powder (disodium cromoglycate). A noticeable increase of emission and re-dispersion was obtainedat low airflow rates due to the use of turbulence promoters mounted in the vicinity of the powder layer. The corresponding increaseof flow resistance is acceptable in respect to the practical application in DPIs.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Modeling; Re-entrainment; Eddy fluid particle; Resuspension; Turbulence promoters; DPI

1. Introduction

Aerosolization of particles which initially form a powder structure is a key effect for many processes in chemicalengineering, environmental protection, toxicology, medicine and others. Removal of dust particles from solid surfacesin clean technologies is one of the example. Another important process, where the re-entrainment of solid particles intothe flowing gas plays a principal role, is drug inhalation from a DPI (dry powder inhaler, Borgström, O’Callaghan, &Pedersen, 2002). This type of inhalers is currently used by almost 40% of European patients with asthma and COPD,(Atkins, 2005). Aerosol is typically created via dispersing by air inhaled through an aliquot of possibly loose powder.The amount of respirable particles depends on the primary size of the micronized powder grains, the cohesive forcesacting among particles in the powder, and on the energy of the flowing air required to re-entrain the particles into theair stream and to break apart particle clusters (Telko & Hickey, 2005). Some of these contributions have been studiedin recent theoretical and experimental works by Grzybowski and Gradon (2005, 2007).

∗ Corresponding author. Fax: +48 22 825 91 80.E-mail address: gradon@ichip.pw.edu.pl (L. Gradon).

1 Present affiliation: Faculty of Physics, Warsaw University of Technology.

0021-8502/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.jaerosci.2007.10.006

114 J. Gac et al. / Aerosol Science 39 (2008) 113–126

The fine particle fraction (FPF), i.e. the relative mass of aerosolized drug particles within the size range of 1.5 �m, istypically below 40% in virtually all DPIs available in the market today (Frijlink & de Boer, 2007; Smith & Parry-Billings,2003). This suggests that the process of powder resuspension in such devices still needs optimization.

Many pharmaceutical formulations contain blends of micrometer-sized drug particles with larger (20 �m and above)carrier particles are used to facilitate powder de-aggregation and to increase the FPF. Large particles are efficientlyeliminated from the aerosol stream in the oral cavity and throat, but since the de-aggregation is not complete, a certainamount of active substance is also deposited there. For the formulations composed solely of micronized or spray-drieddrug particles (e.g., budesonide in Turbuhaler or insulin in Exubera inhaler), the efficient de-aggregation process is evenmore important to avoid producing an aerosol with a broad size distribution, composed mainly of clusters of primaryparticles, which are too big to penetrate to the lungs.

The major function of a DPI as a device is to redirect kinetic energy of the gas to promote the disaggregation ofparticle clusters and release of primary particles. The question arises, whether the kinetic energy of flowing air ishigh enough for breaking up particles agglomerates being already re-entrained. We want to focus our attention on thisproblem by a simultaneous theoretical and experimental approach.

The paper is constructed as follows: The aim of the first part is to answer, how the intensity of turbulence influencesthe re-entrainment of particles and what happens to the clusters of particles when they interact with turbulent eddiesof the flowing gas. This part contains both the formulation and solution of a model of turbulent gas flow through thepowder sample. The intensification of the turbulent energy during a gas flow through an object can be realized byintroducing the turbulence promoters into the object. Due to limited computational possibilities, we will reduce thecalculation to a small scale of observation in order to obtain mainly a qualitative description of behavior of the systemunder consideration. In the second, experimental part of the paper we examine the effect of re-entrainment for thetypical scale of processes occurring in DPI inhalers, using basic suggestions that had arisen from the analysis done intheoretical part of the paper.

2. Modeling of the re-entrainment of particles

2.1. Model of re-entrainment

The ensemble of solid particles deposited on a support surface is exposed to the flowing gas. The interactions betweenparticles in a powder agglomerate structure and between particles and the support surface, reduced to the microscale,are described by short-range effects such as van der Waals forces, electrostatic forces or capillary effects induced bythe presence of condensed fluid between particles. One of the models of particle agglomerate behavior, which refersto this scale of observation, is an oscillatory model of solid–solid interactions. First, models proposed by Reeks andHall (1988), Vainsthein, Ziskind, Fichman, and Gutfinger (1997), and Ziskind, Fichman, and Gutfinger (2000) wereextended by Grzybowski and Gradon (2005) to an “oscillatory” model describing large clusters of particles for whichthe oscillation damping and the external forces acting on the agglomerate of particles are incorporated.

The equation of particle oscillation in an agglomerate used in this paper has the following form:

md2 �xdt2

+ bd�xdt

+ k�x + �Fext = 0, (1)

where m is the particle mass, x the position of particle center in the system, b the damping coefficient, k the stiffnesscoefficient of elastic interaction between particles, and Fext denotes external forces exerted on the particles. In our case,Fext includes mean shearing forces of the fluid flow and gravity.

Values of the coefficients incorporated in the model depend on the particle material properties, such as Poisson ratio,Young’s modulus and adhesion energy. The damping coefficient includes two effects—oscillation damping in solidsand in a fluid. Modeling of the particles agglomerate behavior, using the proposed description requires the observationof particles or clusters during the action of external forces. The connection between single particles or their clusters isassumed to be broken if the distance,yb, between their surfaces at a given moment of time is estimated according tothe formula proposed by Vainsthein et al. (1997).

For the problem considered in this paper, we will focus our attention on determining of the gas velocity field forcalculation of temporal and local values of the velocity in turbulent flow.

J. Gac et al. / Aerosol Science 39 (2008) 113–126 115

The principal entity of the flowing gas which influences the process of re-entrainment, is the energy which can existin various forms, and its distribution. For our analysis we will consider kinetic, turbulent and thermal energy. Thekinetic energy is carried by the mean flow, while the heat is the kinetic energy of molecular fluctuations. The turbulentenergy is the kinetic energy of fluctuations that are large in comparison to the molecular scale but small compared to themean-flow scale. The transitions between these three forms of energy are observed during a gas flow. The mean-flowkinetic energy of a moving fluid degrades to thermal energy, but frequently part of it is first transformed to kinetic energyof turbulence. For the case of transfer of mean-flow kinetic energy to turbulence, the turbulence viscosity producesdrag, i.e. it induces a fluid shear stress, which is independent of the molecular viscosity of the fluid. We would like toincorporate such behavior of the fluid into the description of the process of re-entrainment of particles exposed to thegas flow. One of the sources of the turbulence in the flowing fluid is shear instability (Kelvin–Helmholtz instability),which occurs, for example, when a fluid is moving rapidly past a fixed boundary. It is one of the main effects, whichare considered further in this paper.

The local interactions between powder particles and flowing gas depend on local and temporal distributions of the gasvelocities at the gas-particle boundary. The Navier–Stokes (N–S) equation is a source of such information. There areseveral methods of solving the N–S equation. Unfortunately, the best known of them, i.e. the method of computationalfluid dynamics (CFD) is effective for obtaining the mean velocity field of the fluid stream only. This information isinsufficient for solving of our problem. Hence, we will use here the “Eddy Fluid Particle Model” (EFPM) describedby Potter (1973).

2.2. The eddy fluid particle model (EFPM)

Let us consider the N–S equation for an incompressible fluid, in the form:

��u�t

+ (u · ∇)�u = �f − 1

�∇p + � · ∇2 · �u, (2)

where: u is the fluid velocity, � is the fluid density, � is the fluid kinematic viscosity, p is the pressure in a fluid, f isthe body force acting on the fluid element. Taking into account conditions of the process considered in the paper, theassumption of incompressibility of the fluid is justified.

Now we introduce the operator of velocity rotation � into the N–S equation which is defined as

�� = ∇ × �u. (3)

Utilizing properties of this operator, we can rewrite the Eq. (2) in the form:

����t

+ (u · ∇) · �� = � · ∇2 · ��. (4)

The viscous term in Eq. (4) can be omitted when kinetic energy is mainly dissipated into its turbulent form. Finally theequation of motion we will work with has the form:

����t

+ (u · ∇) · �� = 0. (5)

The structure of Eq. (3) is general and has a form similar to many equations, which express the laws of conservationwithout internal sources.

The EFPM method is used to describe the behavior of a fluid which consists of many “fluid particles” possessingthe elementary rotation of the velocity; one can say the “quantum of rotation”.

The domain of our interest is divided into elementary cells, each consisting of so many “eddy fluid particles” definedabove, that the total rotation in the cell is equal to the sum of elementary rotations of these particles. Taking into accountthe clarity of presentation of the calculation results, we will reduce our consideration to the case of two-dimensional(2D) fluid flow. For this, we can treat the velocity rotation as a scalar (in fact for 3D it is an axial vector). We expectthat limiting the analysis to a 2D domain will give at least a qualitative explanation of the process, which is the goal ofthis part of our investigation.

116 J. Gac et al. / Aerosol Science 39 (2008) 113–126

According to Eq. (5), the eddy particle moves in the field of fluid velocity and, at the given point, has a linear velocityequal to the velocity of the fluid at this point. When all eddy particles move in the given step, we obtain a new field ofvelocities for the next step of calculation. We will now introduce the concept of stream function �, defined as:

�u = (∇ × ��). (6)

Introducing Eq. (6) into Eq. (3) we obtain:

�� = ∇ × (∇ × ��) (7)

and after simple transformation using properties of vector analysis we have:

∇2 �� = −��. (8)

Using one of the well known methods of solving the Laplace Eq. (8) we are able to find a new field of the streamfunction �, provided the field of rotation is known from the previous step of calculations. In other words, from thepositions of eddy particles and the velocity field of the fluid at time t , we can calculate their positions at time t + �t .After that we calculate the field of rotation of the velocity, the field of the stream function and a new field of the velocityat this time, using Eq. (5).

The accuracy of calculation and time of calculation is influenced by the choice of time step �t . It is determined bythe condition that during a time step �t the eddy particle moves no more than the distance between mesh nodes. If wedefine this distance as d, and the average fluid velocity as u, the time step value should satisfy the inequality �t �d/u.

The knowledge of the flow structure within a domain gives us information about the forces of interaction betweenthe fluid and solid particles immersed in the fluid. For the description of solid particle displacement as a result ofinteraction with the fluid, the Verlet algorithm is used.

2.3. The Verlet algorithm

The model of particle resuspension proposed above was realized using methods of molecular dynamics calculations,(Allen & Tildesley, 1987). It is based on a single iteration step, in which the average acting force is calculated for everyagglomerate particle. Using this information we can calculate body acceleration, velocity and position according to theVerlet algorithm (Sadus, 1999; Heermann, 1986).

The form of the algorithm arises from the expansion in series of two expressions:

�x(t + �t) = �x(t) + d�x(t)

dt�t + 1

2

d2 �x(t)

dt2(�t)2 + 1

6

d3 �x(t)

dt3(�t)3 + 0[(�t)4],

�x(t − �t) = �x(t) − d�x(t)

dt�t + 1

2

d2 �x(t)

dt2(�t)2 − 1

6

d3 �x(t)

dt3(�t)3 + 0[(�t)4]. (9)

Summation of both sides of the system of Eqs. (9) gives

�x(t + �t) = 2�x(t) − �x(t − �t) + d2 �x(t)

dt2(�t)2 + 0[(�t)4] (10)

or, if we take into account the second law of dynamics:

�x(t + �t) = 2�x(t) − �x(t − �t) + �Ft(t)

m(�t)2 + 0[(�t)4], (11)

where Ft means the vector sum of forces acting on the particle.Using Eq. (11) we can calculate the position of a particle at the moment of time (t + �t), if its positions at time t

and (t − �t), and the values of forces acting on the particle at time t are known.The particle velocity Vp at time t is calculated from the equation:

�Vp(t) = �x(t + �t) − �x(t − �t)

2�t. (12)

J. Gac et al. / Aerosol Science 39 (2008) 113–126 117

Calculation of the particle position at the starting point t = 0, for which �x(−�t)should be known (position at the timeless than zero) is based on the Euler algorithm.

For the purpose of our model we have modified the original Verlet algorithm by extending it to the case when damping(or any friction) forces are taken into account. Because the friction force depends on the particle velocity, we excludethat force �F ′from the sum of forces �Ft:

�Ft = �F + �F ′, (13)

where F means the resulting force acting of the particle as a result of the gas flow, gravity and interaction with theneighboring particles.

Now the expression (11) obtains the form:

�x(t + �t) = 2�x(t) − �x(t − �t) + �F [�x(t), t]m

(�t)2 −�F ′[ �Vp(t)]

m(�t)2. (14)

As mentioned F is the sum of the following forces:

• The fluid-particle shear force, which for fully developed turbulent flow has the form:

�Ff = 0.44�d2

p

4· �( �Vp − �u)2

2, (15)

where dp is the particle diameter and � the gas density.• Gravitional force:

�Fg = −m�g. (16)

• The force of interaction between neighboring particles, which is assumed to be a harmonic force:

�Fpp = −k|�rp1 − �rp2 − �rn| · �n, (17)

where k is the coefficient of stiffness, rp1 and rp2 are the respective positions of particles 1 and 2 in the structure,rn is the distance between particles for which their mutual interaction disappears, and �n is an unit vector parallel tothe line connecting the centers of these two particles.

The model of adhesive interaction is simple but sufficient for the analysis of the problem proposed above.The damping term in the oscillatory model of particle interaction, which represents the force �F ′ in Eq. (13), has the

form:

�F ′ = −b · d�xdt

, (18)

where b is the damping coefficient.Taking all this into account, the final form of the modified Verlet algorithm has the form:

�x(t + �t) = 2�x(t) − (1 − (b · �t/2m))�x(t − �t) + �F(�x(t), t)/m(�t2)

1 + (b · �t/2m), (19)

where: �F = �Ff + �Fg + �Fpp.This algorithm together with the procedure of gas velocity calculation presented in the previous section was used

for the calculation of the effectiveness of the transition of particles from the powder layer into the flowing gas and thebreaking of particles clusters as a secondary effect of the re-entrainment.

2.4. Results of calculation of the model of particle re-entrainment

Our analysis of the process of particles re-entrainment was focused on the chosen geometry of the channel flowat the presence of selected geometrical shapes of the turbulence promoters shown in Fig. 1. The model of particle

118 J. Gac et al. / Aerosol Science 39 (2008) 113–126

Fig. 1. Three types (a, b, c) of turbulence promoters considered in simulations.

re-entrainment described above was used to calculate of the displacement of particles originally placed between twoplates (2D) in a form of hexagonal structure, see Fig. 2. This structure consisted of 93 particles exposed to the airflow.The airflow was made turbulent by the presence of turbulence promoters of different shapes.

We have calculated the efficiency of particle re-entrainment at the defined exposure time, t. The following pro-cess parameters taken for the model calculations were used, at this stage, as an example for the analysis of thephenomenon:

• particle diameter dp = 20 �m,• particle density �s = 800 kg m−3,• air density � = 1 kg m−3,• stiffness coefficient for particle–particle interaction k1 = 0.15 kg s−2,• stiffness coefficient for particle–wall interaction k2 = 0.19 kg s−2,• damping coefficient b = 0.19 kg s−1,• critical distance between solid bodies yb = 0.5 �m,• air face velocity V = 0.29 m s−1.

Similar calculations were extended to various sets of the process parameters, including a wide range of particlesdiameters, in the following simulations.

“Snap-shots” of the rearrangement of particle positions during destruction of the powder structure caused by turbulentflow of the gas, created by the presence of the promoter of rectangular cross-section, are shown in Fig. 2. The primarystructure initially becomes loose, and then particles or their clusters are transferred into the gas stream. Some of theclusters, when interacting with eddies of high energy, are broken with the release of single primary particles into theair. The effectiveness of clusters break-up depends on the intensity of turbulence.

The destruction of the powder structure for two different turbulence promoters is shown in Fig. 3. This figure showsthat the number of re-entrained single particles into the air stream increases with the turbulence intensity. High energyof turbulent flow causes the secondary break-up of particle clusters already present in the air stream due to the primaryre-entrainment process.

The turbulence promoters can intensify the turbulent energy of the flowing air, but because of their geometry theycan also influence the direction of the main stream of the air to create a stronger interaction with powder. This results inan increased effectiveness of the re-entrainment. The influence of the promoter’s shape on re-entrainment of particles isshown in Fig. 4. A significant increase in efficiency is observed for the rhombic cross section, which directs the airflowtowards the powder and simultaneously is a source of turbulence.

The collected results of our calculations, obtained for various sets of process parameters, show that the total efficiencyof the re-entrainment of particles of different morphology (clusters) and the break-up of clusters with formation of

J. Gac et al. / Aerosol Science 39 (2008) 113–126 119

Fig. 2. Displacement of the particles due to interactions with the turbulent gas flow (turbulence promoter ‘a’).

singlets is a function of two characteristic dimensionless numbers, defined as:

NL = � · u2R2

k · yb,

NJ = � · u2

�s · g · R, (20)

where R is the radius of primary particle and �s is the particle material density.The physical meaning of NL is the ratio of the fluid shear force exerted on the particle to the cohesive forces between

interacting particles. NJ characterizes the ratio of the shear force to the gravitational force holding particles on thesurface of the support.

120 J. Gac et al. / Aerosol Science 39 (2008) 113–126

Fig. 3. Number of re-entrained single particles for promoters ‘a’ and ‘b’ (see Fig. 1).

Fig. 4. Total number of re-entrained particles for promoters ‘a’, ‘b’ and ‘c’ (see Fig. 1).

Our simulations show that for values of NL and NJ larger than 10, the efficiency of re-entrainment is highand agglomerates of particles are quickly destroyed in the gas stream. When NL �NJ (the cohesive forces dom-inates), the efficiency of re-entrainment is low and only single particles are removed from the powder structure.When NJ is only slightly larger than NL, and both numbers are less than 1, particles are removed mainly in aform of big clusters, and when NL is larger than NJ (gravity force dominates), the re-entrainment practicallydisappears.

J. Gac et al. / Aerosol Science 39 (2008) 113–126 121

3. Experimental studies of powder re-entrainment

The theoretical part of the paper demonstrated the mechanisms of break-up of powder particle clusters resulting inthe emission of finer aggregates or even single primary particles. Some suggestions arising from these findings areused in the following experimental studies related to powder re-entrainment on the realistic, larger scale of observation.We want to stress that although no geometry analyzed numerically is replicated in the experimental part, we used thetheoretical analysis to test specific airflow arrangements for intensification the turbulence in the powder resuspensionzone.

3.1. Materials and methods

The experimental set-up, Fig. 5, consists of a resuspension channel (1) connected to a buffer chamber (2), from whichthe aerosol is sampled (via probe 3) for size analysis in the range of 0.6.30 �m (light-scattering technique—WELASspectrometer, Palas), 6–7. Air was drawn to the chamber by pump 4 (Vacuubrand) via the calibrated flowmeter and filter5. Flow calibration was done with a BIOS DC-1 flow calibrator (USA). The resuspension channel (1) had the shape of a200 millimeter-long duct with square cross-section (10×10 mm), Fig. 6a. Exchangeable inserts (I, II and III in Fig. 6b)were used to investigate different airflow arrangements in the vicinity of the powder layer. Insert I was constructed asan empty channel, while inserts II and III contained additional elements used to redirect and disorder the airflow. InsertII was equipped with a wedge-shaped element used to promote flow acceleration towards the powder layer located atthe bottom surface. Insert III contained, in addition to the wedge-shaped element present in the insert II, two needlesbeyond the re-entrainment zone, which were mounted perpendicularly to the flow direction. This configuration wasintended to disturb the flow structure of the aerosol formed in the re-entrainment process. According to the simulationresults, promoting a locally strongly turbulent flow field was expected to improve de-aggregation of particle clusterssignificantly. Each insert, acting as a separate powder resuspension chamber, was equipped with an opening for loadingan aliquot of powder (approximately 30 mg).

Pure micronized disodium cromoglycate (GlaxoSmithKline Pharmaceuticals) was used as a pharmaceutical testpowder in all experiments. The SEM photograph of the powder shown in Fig. 7 indicates that primary particles aresmaller than 10 �m and that their surface is smooth. After the powder had been loaded at the bottom of the chamber,the upper opening was sealed tight with the screw and the whole insert was weighed with the accuracy 0.1 mg. Thenthe insert was mounted in the channel and the powder layer was exposed to the airflow. The aerosol spectrometer wasactivated simultaneously with the air pump. After the powder was aerosolized completely the airflow was stopped,while the aerosol sampling and counting by WELAS spectrometer were continued for the half a minute. Then the insert

1

2

3

4

56 7

Fig. 5. Experimental set-up: 1—resuspension channel, 2—aerosol holding chamber, 3—sampling probe, 4—pump, 5—filter, 6—WELAS spectrom-eter: optical chamber, 7—WELAS spectrometer: main unit.

122 J. Gac et al. / Aerosol Science 39 (2008) 113–126

Fig. 6. Geometry of resuspension channel (a), and details of inserts I, II and III (b).

Fig. 7. SEM image of disodium cromoglycate powder used in the resuspension experiments.

was weighed again to find the mass of aerosolized powder. The resuspension process was studied by this technique forseveral values of airflow rate in the range of 1.90 dm3/ min.

3.2. Results of experiments and discussion

The re-entrainment efficiency, calculated as ME/ML (where: ME is the mass of powder emitted from the chamber, andML is the mass of powder initially loaded to the resuspension chamber), is illustrated in Fig. 8 for each flow configuration(I, II and III shown in Fig. 6b) as a function of the volumetric airflow rate. At flow rates below 8 dm3/ min, no emissionis observed in any configuration since the airflow energy is too weak to break-up inter-particle forces within the powderstructure and fluidize particles. This situation corresponds to the condition NJ < NL < 1, where both dimensionlessnumbers NJ, NL are defined by Eq. (20). For increasing—but still low—airflow rates below 30 dm3/ min, the re-direction and acceleration of flow by the wedge-shaped element (insert II) increases the re-entrainment efficiencysignificantly. The same effect is observed for insert III, but, interestingly, the presence of needles in this configurationdoes not improve the re-entrainment efficiency. However, at increasing airflow rates in configuration III, the localfluid velocities are high enough so that both numbers NL and NJ are larger than 10, which leads to the effectivebreak-up of particle aggregates. For the specific configuration described in the experiments, the critical domains ofthe numbers NL and NJ were calculated for the following values of parameters: � = 1 kg m−3, �s = 1600 kg m−3,k (estimated)= 0.1 kg s−2, R = 4 · 10−6 m, and yb = 0.2 · 10−6 m. The average air velocity u was calculated from CFDdata, using the k-� model of turbulence for each geometrical data configuration (Fig. 6b).

J. Gac et al. / Aerosol Science 39 (2008) 113–126 123

0102030405060708090

100

1 10 100

Res

uspe

nsio

n ef

fici

ency

[%

]

I II III

Volumetric airflow rate [dm3/min]

Fig. 8. Aerosol emission efficiency powder particles in chambers with inserts I, II and III.

5

10

15

20

0 10 20 30 40 50 60 70 80 90

MM

D [

µm]

I II III

Airflow rate [dm3/min]

Fig. 9. Mass median diameter of aerosol emitted from chambers with inserts I, II, and III.

Further information on the de-aggregation process can be obtained from Fig. 9, which shows the relationship betweenairflow rate and the mass median diameter (MMD) of particles emitted from the resuspension chamber. Particle de-aggregation is facilitated by higher flow rates, however no clear difference for inserts I and II can be observed. On thecontrary, the effect of needles present in configuration III on the break-up of re-entrained particle clusters is evident.Aerosol emitted at the given airflow rate from the chamber with insert III was always characterized by the lower MMDthan aerosol emitted from the chamber with inserts I or II. This observation suggests that powder re-entrainment andparticle de-aggregation do not necessarily take place simultaneously. Results obtained for configurations II and IIIindicate that the resuspension process occurs in two steps: particles are fluidized by flowing air as clusters (in our case,often larger than 10 �m), and then they are broken apart by the stresses generated when the flowing aerosol becomesturbulent. In such a way, the interactions of needles with the flowing aerosol (configuration III) induce the aerodynamicconditions, which at flow rates above 30 dm3/ min lead to reduction of the aerosol MMD to approximately 8 �m. Suchlow MMD values could not be obtained for two other flow configurations. These results agree with the conclusionsof our theoretical analysis presented in the previous part of the paper, which predicted an important role of localpromoters of turbulence on breaking the clusters of powder particles. An MMD at the level of 8 �m may seem to belarge; nevertheless it also indicates that the FPF of the aerosol is in the range of 20–30%, which is comparable to thevalue found in commercial DPIs, (Smith & Parry-Billings, 2003).

CFD simulations done previously for the tested configurations (Sosnowski, 2007), indicate that regions beneath theedge-shaped element and near the needles are characterized by extremely high values of shear rate what is responsiblefor efficient powder re-entrainment and de-aggregation of aerosolized particles.

It should be noticed that the introduction of additional elements, which act as local flow turbulizers and cause amore efficient transfer of gas kinetic energy to aggregated powder particles, always results in an increased pressuredrop during flow of air through the channel. This is an extremely important issue for DPIs, since powder resuspensionin the majority of inhalers of that type is driven solely by the energy of air inhaled by a patient. As the capabilities ofproducing a vigorous airflow by persons with lung diseases can be considerably limited, the arrangement of the inhaler

124 J. Gac et al. / Aerosol Science 39 (2008) 113–126

resuspension chamber should be carefully designed. Strong airflow obstructions must be avoided, even though theymight promote excellent resuspension at high values of the flow rate. Such flow rate values, however, might never beattained in reality during the use of the inhaler by a patient.

A good measure of usefulness for a given geometrical configuration of powder resuspension chamber is the valueof its specific resistance to airflow, RD, which is defined as

RD =√

�P

Q, (21)

where �P is the pressure drop in the system, Q is the volumetric airflow rate (Clark & Hollinhgworth, 1993). TheRD values of DPIs which are currently on the market remain in the range of 0.05.0.2 hPa0.5 dm−3 min. For airflowconfigurations I, II and III tested in this work, the coefficient RD was equal to 0.019, 0.034 and 0.04 hPa0.5 dm−3 min,respectively. This suggests that the proposed flow arrangements can be considered potentially applicable to powderinhaler designs.

4. Conclusions

Efficient aerosolization of particles from a powder sample to the form suitable for inhalation requires a considerableamount of energy input for fluidization and break-up of particle aggregates. The latter process is more energy-demandingbecause inter-particle cohesive forces have to be overcome by the stresses of the interactions between the flowing airand the aerosolized aggregates. The problem of the optimal use of flow energy is especially important in the caseof passive (i.e. driven solely by inhalation) dry powder inhalers, where sufficient airflow rates required for particleresuspension often cannot be achieved due to restriction in patient breathing functions.

The eddy fluid particle model (EFPM) used for description of the flow structure and Verlet algorithm used forcalculation of particle resuspension are efficient methods for modeling of the analyzed phenomenon because of their highrate of calculations and easy numerical implementation in comparison to other (e.g., SIMPLE) algorithms, (Anderson,1995). As demonstrated by the results of computations for a small geometrical scale and simplified geometries, theeffect of particle fluidization and de-aggregation can be achieved by focusing the kinetic energy of airflow to createlocal turbulence, which is characterized by steep velocity gradients and high shear stresses within the fluid. In this wayan aerosol with a higher fraction of fine particles can be produced. It was shown that application of a general fluidflow analysis combined with a model of adhesive and cohesive interactions allow to predict the qualitative behavior ofpowder particles in the fluid. Two dimensionless numbers: NL and NJ, defined by Eq. (20), indicate the importance offluid shear, adhesion and gravity, balance of which determines the dynamics of aerosol particle clusters.

Some suggestions from theoretical part of this work were incorporated into experiments in the macroscopic (natural)scale described in the second part of the paper. Their results unambiguously demonstrated the benefits for the powderaerosolization process resulting from a suitable arrangement of the airflow in the channel. It was shown that the effectiveresuspension takes place in two steps. Local flow acceleration is required for efficient powder fluidization, i.e. formationof aerosol, however it may be not sufficient to break-up the particle clusters. De-aggregation step can be achieved, ifthe aerosol is forced to flow in a turbulent regime.

Concepts presented in the paper may be considered as applicable in dry powder inhalers, however optimization ofthe geometry of DPI resuspension chambers is an engineering challenge. Since the energy required for overcomingadhesive and cohesive interactions is transferred directly from the flowing gas drawn by an inhaling person, it is essentialto design the flow structure in a way which minimizes energy dissipation and does not lead to significant increase of flowresistance. In addition to some concepts proposed recently by Sosnowski, Bernatek, and Gradon (2006) and Gradon,Sosnowski, and Moskal (2006), the ideas presented in this paper also satisfy these restrictions, and may be consideredas guidelines in designing of novel resuspension chambers of DPIs.

Notation

b damping coefficientdp particle diameterf body force

J. Gac et al. / Aerosol Science 39 (2008) 113–126 125

F ′ friction forceFext external forcesFpp interparticle interaction forceFt sum of forces acting ion the particleg acceleration due to gravityk stiffness coefficientm particle massME mass of emitted powderML mass of loaded powderNJ dimensionless numberNL dimensionless numberp pressure�P pressure dropQ volumetric airflow raterpi position of particle i in the structureR radius of primary particleRD specific aerodynamic resistancet time�t time stepu gas velocityV air face velocityVp particle velocityx particle positionyb distance between solid bodies

Greek letters

� gas kinematic viscosity� gas density�s particle density� stream function� velocity rotation

Acknowledgment

Work supported by the budget funds for science in the years 2005–2008 (Project no. 3T09C 028 29).

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