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Markl, Daniel; Wang, Parry; Ridgway, Cathy; Karttunen, Anssi Pekka; Bawuah, Prince;Ketolainen, Jarkko; Gane, Patrick; Peiponen, Kai Erik; Zeitler, J. AxelResolving the rapid water absorption of porous functionalised calcium carbonate powdercompacts by terahertz pulsed imaging

Published in:Chemical Engineering Research and Design

DOI:10.1016/j.cherd.2017.12.048

Published: 01/04/2018

Document VersionPublisher's PDF, also known as Version of record

Published under the following license:CC BY

Please cite the original version:Markl, D., Wang, P., Ridgway, C., Karttunen, A. P., Bawuah, P., Ketolainen, J., Gane, P., Peiponen, K. E., &Zeitler, J. A. (2018). Resolving the rapid water absorption of porous functionalised calcium carbonate powdercompacts by terahertz pulsed imaging. Chemical Engineering Research and Design, 1082-1090.https://doi.org/10.1016/j.cherd.2017.12.048

Resofuncby te

DanielPrinceJ. Axela DepartmCambridgb Omya Inc School od Institutee School o00076 Aa

a r t i

Article his

Received

Received

Novembe

Accepted

Available

Keywords:

Porous m

Pharmace

Functiona

Terahertz

Liquid im

Modelling

∗ CorresE-mai

https://do0263-8762under the

Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 1082–1090

Contents lists available at ScienceDirect

Chemical Engineering Research and Design

journa l h om epage: www.elsev ier .com/ locate /cherd

lving the rapid water absorption of poroustionalised calcium carbonate powder compactsrahertz pulsed imaging

Markla,∗, Parry Wanga, Cathy Ridgwayb, Anssi-Pekka Karttunenc, Bawuahc, Jarkko Ketolainenc, Patrick Ganeb,e, Kai-Erik Peiponend,

Zeitlera

ent of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, CB3 0ASe, UKternational AG, 4665 Oftringen, Switzerland

f Pharmacy, Promis Centre, University of Eastern Finland, P.O. Box 1617, 70211 Kuopio, Finland of Photonics, University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finlandf Chemical Engineering, Department of Bioproducts and Biosystems, Aalto University, P.O. Box 11000,lto, Finland

c l e i n f o

tory:

3 August 2017

in revised form 30

r 2017

28 December 2017

online 5 January 2018

edia

utical tablets

lised calcium carbonate

pulsed imaging

bibition

a b s t r a c t

Cost effectiveness, ease of use and patient compliance make pharmaceutical tablets the

most popular and widespread form to administer a drug to a patient. Tablets typically con-

sist of an active pharmaceutical ingredient and a selection from various excipients. A novel

highly porous excipient, functionalised calcium carbonate (FCC), was designed to facilitate

rapid liquid uptake leading to disintegration times of FCC based tablets in the matter of sec-

onds. Five sets of FCC tablets with a target porosity of 45–65% in 5% steps were prepared and

characterised using terahertz pulsed imaging (TPI). The high acquisition rate (15 Hz) of TPI

enabled the analysis of the rapid liquid imbibition of water into these powder compacts. The

penetration depth determined from the TPI measurements as a function of time was ana-

lysed by the power law and modelled for both the inertial (initial phase) and Lucas-Washburn

(LW, longer time Laplace- Poiseuillian) regimes. The analysis of the hydraulic radius esti-

mated by fitting the liquid imbibition data to the LW equation demonstrates the impact

of the porosity as well as the tortuosity of the pore channels on the liquid uptake perfor-

mance. The tortuosity was related to the porosity by a geometrical model, which shows that

the powder compact is constructed by aggregated particles with low permeability and its

principal axis perpendicular to the compaction direction. The consideration of the tortuos-

ity yielded a very high correlation (R2 = 0.96) between the porosity and the hydraulic pore

radius. The terahertz data also resolved fluctuations (0.9–1.3 Hz) of the liquid movement

which become more pronounced and higher in frequency with increasing porosity, which

is attributed to the constrictivity of pore channels. This study highlights the strong impact

of a tablet’s microstructure on its liquid penetration kinetics and thus on its disintegration

behaviour.

© 2018 The Authors. Published by Elsevier B.V. on behalf of Institution of Chemical

Engineers. This is an open access article under the CC BY license (http://creativecommons.

org/licenses/by/4.0/).

ponding author.l address: dm733@cam.ac.uk (D. Markl).i.org/10.1016/j.cherd.2017.12.048/© 2018 The Authors. Published by Elsevier B.V. on behalf of Institutio

CC BY license (http://creativecommons.org/licenses/by/4.0/).

n of Chemical Engineers. This is an open access article

Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 1082–1090 1083

1. I

Pharmacmost coningredientured viaa selectiopropertieing and dmost castity in a

play a crin respecIncreasindelivery rents, for

access inoral disin

In patablets (Oexcipientare desigseconds,and convfer from

for theseimprovemtrates thshould bmance othe tableticles aninto smacles. Thepartly dupartly duThe convcedures dassess thquantitatdisintegrcontrol th

Liquidhave beeKleinebuSeveral sinto powcamera (2012), graet al., 198Esteban

(Tritt-Goc2014). Anceutical

(Wildensrior compas they arials in athe draw(�1 min)imbibitioseconds.penetratiet al. (20

le 1 – List of the five batches characterised in thisdy. The presented data slightly differ from the data inrkl et al. (2017b) as only a subset of the batch was

ed in this study. Batches B01 and B05 consisting of 5lets, and 6 tablets were measured for the batches

2-B04. The porosities were determined by THz-TDS inbination with the anisotropic Bruggeman model.

ch Diameter (mm) Thickness, L (mm) Mass (mg) Porosity, f (%)

10.04 1.67 216 ± 2 46.2 ± 0.3 10.03 1.64 190 ± 2 51.8 ± 0.5 10.02 1.63 168 ± 2 56.6 ± 0.3 10.03 1.62 146 ± 4 62.0 ± 0.4 10

bitio) ba

hasiormaabletsmisistinz timtive

onst as fo

highd calsity

ly se inteb). Tpactomp

thicturemonfurthts. Tasisertie., 201

M

M

batcrgetts (T

keping tts wsimenon-

the

s the from

gen of mthen

areae fuation of highly-porous particles using a surface modifi-

ntroduction

eutical tablets are well-known as being amongst thevenient ways of delivering active pharmaceuticalt (API) to the patient. Tablets are typically manufac-

powder compaction and consist of API particles andn of various excipients. The physical and chemicals of both API and excipient particles dominate tablet-elivery functionality of the dosage form. However, ines the excipients represent by far the greater quan-tablet and, therefore, it is not surprising that theyucial role in defining the ease of tableting generallyt to material flow, compressibility and compaction.gly, the design of targeted drug release and vectorequires specialist development of functional excipi-

example, to encapsulate an API to provide protectiveto the small and large intestine or to provide rapidtegration.rticular, the performance of orally disintegratingDTs) is strongly impacted by the pore structure of thes and the overall microstructure of the tablet. ODTsned to disintegrate rapidly, usually in the matter of

in the mouth which facilitates easy administrationenience. About 35% of the general population suf-difficulties in swallowing (Sastry et al., 2000), and

patients in particular ODTs provide a significantent in therapy. Once in the mouth, saliva pene-

e dosage form and even a small amount of 1–2 mLe sufficient to achieve disintegration. The perfor-

f an ODT is limited by the rate saliva penetrates intot leading to swelling of the (superdisintegrant) par-d eventually causing the break-up of the compactll agglomerates or the original constituents’ parti-

understanding of this process is severely limited,e to the complex nature of the process itself ande to the lack of suitable measurement techniques.entional disintegration apparatus and testing pro-escribed by the pharmacopoeia are not suitable to

e performance of such rapidly disintegrating tabletsively. Hence, alternative methods to measure rapidation are highly desirable to evaluate ODTs and toe quality of such drug products.

uptake of and penetration into powder compactsn studied by a range of approaches (Quodbach anddde, 2016; Desai et al., 2016; Markl and Zeitler, 2017).tudies were performed to measure the water uptakeder beds and into powder compacts using an opticalHapgood et al., 2002; Nguyen et al., 2009; Desai et al.,vimetric techniques (Nogami et al., 1966; Caramella6; Catellani et al., 1989; Peppas and Colombo, 1989;

et al., 2017) or magnetic resonance imaging (MRI) and Kowalczuk, 2002; Nott, 2010; Quodbach et al.,other technology to resolve the structure of pharma-tablets is X-ray computed microtomography (X�CT)child and Sheppard, 2013). MRI and X�CT are supe-ared to an optical camera or gravimetric techniques

llow to resolve the internal structure of porous mate- non-destructive and contactless manner. However,back of both methods is their long measurement time, which renders them unsuitable to study the liquidn into highly-porous media that fully hydrate within

A very promising tool to analyse such rapid liquidon kinetics is terahertz pulsed imaging (TPI). Yassin

TabstuMaustabB0com

Bat

B01B02B03B04B05

imbi(MCCempperfcal ttranconsherteffecdemwell

Aaliseporocretelarge2017comthe c

Instrusitu

was

tablethe bpropet al

2.

2.1.

Fiveto tamenwerevarytableporoare

afteritatethat

Infaceand

faceto thform

15) coupled a TPI with a flow cell to study liquid cation to

.00 1.61 125 ± 2 67.3 ± 0.4

n and swelling of various microcrystalline cellulosesed immediate-release formulations. These studiessed the impact of the porosity on the disintegrationnce of such tablets. The porosity of pharmaceuti-s can be measured using terahertz technology in asion setting. Bawuah et al. (2016) measured tabletsg of pure MCC and combined with an API by tera-e-domain spectroscopy (THz-TDS) to determine therefractive index and, thereby, the porosity. It was alsorated that this method works for biconvex tablets asr complex formulations (Markl et al., 2017a).ly viable excipient for ODT formulations is function-cium carbonate (FCC), which has a high intra-particle(Stirnimann et al., 2013). FCC based tablets have a dis-parable bimodal pore size distribution, consisting ofr-particle and fine intra-particle pores (Markl et al.,

he inter-particle pores are formed during the powderion and therefore, they can be modified by adjustingaction process.

s study we investigated the interaction of the pore of FCC tablets with liquid during imbibition. The in-itoring approach by means of terahertz technologyer developed to study the rapid imbibition of the FCChe imbibition process was analysed and modelled on

of the TPI data and it was related to the pore structures of the same tablets determined by THz-TDS (Markl7b).

aterials and methods

aterials

hes of pure flat-faced FCC tablets were compacted porosities ranging from 45% to 65% with 5% incre-able 1). The diameter and thickness of the tabletst constant at 10 mm and 1.5 mm, respectively, by

he material weight. The pore structure of these FCCas characterised by Markl et al. (2017b) using mercurytry, X�CT and THz-TDS. Since X�CT and THz-TDS

destructive techniques, the tablets were still intactmeasurement and were used in this study. This facil-

direct correlation of the results from this study with Markl et al. (2017b).eral, FCC is formed in a process whereby the sur-

icrometre sized calcium carbonate particles is etched re-precipitated to create a highly porous, high sur-

material. The naming of the FCC material refersnctionalisation of calcium carbonate as being the

form hydroxyapatite. A typical FCC entering use as

1084 Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 1082–1090

Fig. 1 – Experimental setup of the TPI coupled with a flowcell. (a) Schematic representation of the flow loop. (b) 3Dvisualisation of the terahertz reflection probe and the flowcell. The flow cell has a size of 10 cm × 5 cm × 5 cm. Moredetails about the flow cell are provided by Yassin et al.(2015).

excipienta calciumplate-likenent coninterior o

2.2. T

A commLtd, Camthe hydrhertz meequippedwas set tdelay of 3

The flet al. (20measuretablet siton only oto the liqtrolled bywas sealcomplete

The ean open

with wattank as wwas pum

pump (53equippedLtd, Falmto providations. Tpreventehydrationat outletThe outlrelease thwetting o

The doutlet B

tablet asFig. 2. Threfractivetracking

material)facilitateof waterdetectedPrior to trforms wepeaks ortablet/airterahertzterahertzas well ation measample.

terahertzwaveformkind of in

mmpproied i

1HF

re HFuencectiv

R

L

kineactede thelar btion

primh w

behporeork

n beests

truct dist

(Omyapharm®

, Omya International AG) consists of carbonate/hydroxyapatite structure, in which the

nano-thickness lamellae of the phosphate compo-struct a network of fine pores on the surface andf the FCC particle.

erahertz pulsed imaging

ercial terahertz system (TeraPulse 4000, TeraViewbridge, UK) was coupled with a flow cell to monitoration process of pharmaceutical tablets. The tera-asurements were performed with a reflection probe

with an 18 mm focal length lens. The acquisition rateo 15 Hz and every measurement covered an optical8.8 ps.

ow cell previously developed and utilised by Yassin15) was optimised to enhance the accuracy of thements at the beginning of the hydration process. Thes in a sample holder where it is exposed to the liquidne face (Fig. 1). The surface area of the tablet exposeduid was Awet = 48.4 mm2. The flow in the cell was con-

valves at the inlet and the two outlets. The flow celled with a polyethylene window (PE), which is almostly transparent to terahertz radiation.

xperiment was started with an open inlet valve andvalve at outlet A. The experiments were carried outer at 22.5 ◦C, which was the temperature in the water

is coan aappl

fDG =

whefreqresp

3.

3.1.

The

impSincsimivariaare

whictionthe

netwlatiosuggof ssize

ell as at the outlet valve of the flow cell. The waterped at a flow rate of 13 mL/min using a peristaltic

descriptotinuously

0SN, Watson-Marlow Ltd, Falmouth, UK), which was with a low-pulse pump head (505L, Watson-Marlowouth, UK). This pump head was specifically designede a smooth flow and to minimise pressure fluctu-he presence of an air bubble at the top of the celld water from touching the tablet and therefore, the

process of a tablet was started by opening the valve B and simultaneously closing the valve at outlet A.et B is located at the very top of the cell in order to

e air in the cell completely and to assure continuousf the tablet.ata acquisition was started at the same time whenwas opened. The water then slowly approached the

it can be observed in the terahertz waveforms ine water penetrating the powder compact changes the

index of the wetted material and thus enables theof the penetration front (transient from wetted to dry

by means of terahertz reflection technology. TPI thuss the assessment of the one-dimensional transport

into the tablet. The water front was automatically by a custom-built code using Matlab (MathWorks).acking the liquid front, the measured terahertz wave-re deconvolved to reduce the noise and enhance the

iginating from the interfaces, i.e. air/dry tablet, dry, and dry tablet/wet tablet). In general, the measured

signal is a convolution of the input signal from the emitter and the impulse response of the samples additive noise. The objective of a terahertz reflec-surement is to obtain the impulse response of the

This can be achieved by deconvolving the measured waveform and a reference measurement (a terahertz

of a mirror). However, it is well-known that thisverse filtering amplifies high frequency noise, which

only suppressed by coupling the deconvolution andpriate band-pass filter. A double Gaussian filter wasn this study:

exp

(− t2

HF2

)− 1

LFexp

(− t2

LF2

)(1)

and LF define the pulse width in respect to the highy and low frequency bounds of the band-pass filter,ely.

esults and discussion

iquid imbibition

tics of the liquid imbibition process is strongly by the pore structure in the powder compact (Fig. 3).

intra-particle pore structure of the FCC particles isetween the different batches (Markl et al., 2017b), thes in liquid uptake kinetics of the different batchesarily affected by the inter-particle pore architectureas formed during powder compaction. The absorp-aviour depends on the pore size distribution and

connectivity amongst other factors such as poregeometry and surface energy. The observed corre-tween porosity and liquid imbibition kinetics thus

that each powder compact is an homologous seriesures, in that the features of connectivity and poreribution remain related to porosity, i.e. the basic

rs of the pore structure remain constant or vary con-

in line with the varied tablet compression.

Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 1082–1090 1085

Fig. 2 – Schematic of the setup and deconvolved terahertz waveforms (each waveform is offset by 0.004 a.u.) showing thehydration of a tablet from batch B03.

Fig. 3 – Deconvolved terahertz waveforms of one tablet per batch (each waveform is offset by 0.004 a.u.). (a) B01, (b) B02, (c)B04 and

As taba decreashydratedreflectionindices bamplitud(Verdet c

rdw = nw

nw

where nd

wetted mreflectionmedium

tant for mMarkl et aabsorptioof any feabsence

though th

izuonate po

ll.q. (2)or poes o

terah). Hoact w

(Picke effarklporox of

t. Sinindelitud

(d) B05. B03 is shown in Fig. 2.

let porosity increases from batch B01 to B05, there ise in the total duration for the tablet to become fully. The magnitude of the amplitude of the water front

is governed by the relative difference in refractiveetween the dry and wetted material. The measurede is directly proportional to the reflection coefficientonvention (Holm, 1991)), which is defined as

− nd

+ nd(2)

and nw are the refractive indices of the dry andaterial in the tablet, respectively. In general, the

coefficient and the refractive index of a porousare complex numbers. This is particularly impor-aterials which strongly absorb terahertz radiation.

l. (2017b) presented the effective refractive index andn coefficient at terahertz frequencies. The absenceatures in the absorption coefficient indicated the

tal (Mcarbin thsma

Etive

indicthe

(n = 1cont≈2.4to thin Mlow

indefrontive

amp

of phonon vibrations. They also discussed that evene calcium carbonate is birefringent as a single crys-

from bat(Fig. 3a).

no et al., 2009), the random orientation of the calciume domains in an FCC particle and of the FCC particlewder compact renders birefringence immeasurably

reveals that the reflected pulse can be either nega-sitive depending on the relative change in refractivef the two media. The initial reflection is negative asertz beam traverses from the dry FCC tablet to airwever, the sign changes when the tablet comes inith water. The refractive index of water at 1 THz iswell et al., 2004) and that of the dry material is equal

ective refractive index, neff, of the FCC tablets as given et al. (2017b). neff ranges from 1.61 to 2.19 (high tosity) and therefore it is smaller than the refractivewater causing a positive reflection peak at the waterce the relative difference between neff and the refrac-x of water decreases with decreasing porosity, thee of the reflection peak significantly drops for tabletsch B05 (Fig. 3d) compared to those from batch B01

1086 Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 1082–1090

Fig. 4 – Penetration length (distance travelled by the liquidfront) as a function of time. The average porosity of thetablets from the batches B01-B05 was 46.2%, 51.8%, 56.6%,62.0% and 67.3%, respectively. Only every 10th data point isdisplayed and the shaded area corresponds to the standarddeviation within each batch.

Since

water, pucould alsback facement anand micrThe resupowder wof pharmet al., 202014). Ththe porotion reflewithin ea

FCC inet al., 20builds updisintegrdisintegrtion basewith excvia severswelling

can be reuid uptaktablet. Mgration inand this clations wfacilitateand swelcompone

The raby the LuLaplace athe poresy, as a fuflow as

y(t) =√

Table 2 – Summary of the parameters fitted to thepenetration data. The changeover, yc, is the penetrationlength at which the kinetics change from inertial (y < yc)to Laplace-Poiseuillian (y ≥ yc) flow regimes. This tablelists only the average and standard deviation of thefitting parameters of the power law (y = ktm) and the LWequation (Eq. (3)). The values for each fit are provided inFigs. 6 and 7.

Batch yc (�m) k (mm s−m) m Rh,eq (nm)

B01 109 0.16 ± 0.01 0.51± 0.02 1.16 ± 0.05B02 104 0.20 ± 0.02 0.50± 0.02 1.50 ± 0.11B03 145 0.22 ± 0.01 0.50± 0.02 1.95 ± 0.09B04 163 0.24 ± 0.02 0.52± 0.03 2.61 ± 0.21B05

where �

FCC comthe dynaof water.betweenpropose

s in

tortuaveraengtaulicxpre

= R

s a fny u., 200

co (hen

e),

ium

es of regim

to cliquith ofr t-dge h

theapla

ing ttrat

{a

k

5) coand

h anr pee w

chan larg

regihe peuillian flow regime (Fig. 6). The fitted parameter k

FCC particles are non-swelling and non-dissolving inre FCC powder compacts do not disintegrate. This

o be observed in the terahertz measurements as the of the tablet (Fig. 3) did not move during the experi-

d the powder compacts did not change their shapeostructure after drying the hydrated tablets again.lts clearly demonstrate that the highly porous FCCas specifically designed to enhance the liquid uptake

aceutical tablets (Stirnimann et al., 2013, 2014; Preisig14; Wagner-Hattler et al., 2017; Eberle et al., 2015,e water penetration kinetics are strongly driven by

sity of the tablets (Fig. 4). The small standard devia-cts that the penetration kinetics are highly consistentch batch.

combination with a superdisintegrant (Stirnimann13), which primarily drives the swelling and thus

an internal stress, facilitates the design of a desiredation behaviour as each excipient imparts only oneation mechanism at a time. A design of a formula-d on a mechanistic understanding is more complexipients, such as MCC, impacting on disintegrational mechanisms, which hamper the decoupling of theand the liquid uptake. Mechanistic understandingflected by models which describe swelling and liq-e (Markl et al., 2017c) as well as the break-up of the

odelling the different processes involved in disinte-dependently would simplify the design significantlyould eventually lead to models of commercial formu-hich predict the disintegration behaviour, and this isd by considering the ability to decouple absorptionling by using FCC as the sole absorption-promotingnt.te uptake into porous systems is typically describedcas-Washburn (LW) equation, which combines thend the Hagen-Poiseuille equation and assumes that

are uniform and cylindrical. The penetration length,nction of time t can thus be expressed for a laminar

Rh,eq� cos �t

2�(3)

ablethe

the

cal lhydrbe e

Rh,eq

Rh aKozeet al

Intionregimcalcscalflowtionthe

lenglineachanfromthe Limispene

y(t) =

Eq. (d, k

batclargein linthe

withflow

TPois

correlate

240 0.31 ± 0.03 0.51± 0.01 4.02 ± 0.31

is the contact angle between the water and theponent solid material in the powder compact, � ismic viscosity of water and � is the surface tension

The hydraulic radius, Rh,eq, is defined as the ratio the pore volume to the solid-fluid interfacial area. Weto account for the flow-dependent geometrical vari-the definition of the hydraulic radius by consideringosity, T = Le/L. T is a dimensionless number relatingge length of the fluid path, Le, and the geometri-

h of the sample (tablet thickness), L. The equivalent radius as a function of the tortuosity (Shin, 2017) can

ssed as (see Appendix A for derivation)

hT−1 = af

(1 − f )T−1. (4)

unction of porosity, f, was defined by Carman andnder the consideration of a shape factor, a (Nakayama7).ntrast to y ∝ √

t as described by the LW equa-ceforth referred to as the Laplace-Poiseuillian flow

it is known that the liquid uptake length in compactedcarbonate is directly proportional to t for short time-

the imbibition (henceforth referred to as the inertiale). Schoelkopf et al. (2000) used the Bosanquet equa-

onsider both inertial and viscous forces acting ond. The authors demonstrated that the liquid uptake

compacted calcium carbonate blocks changes from aependence to a

√t-dependence. We also observe this

ere in the measurements of the penetration length TPI data. The changeover, yc, from the inertial toce-Poiseuillian flow regime was determined by min-he root-mean-squared error (RMSE) of the measuredion length against a fitting model expressed as

t + d, if y < yc

tm, otherwise.(5)

nsists of a linear equation and a power law with a,m as fitting parameters. yc was determined for everyd the values in Table 2 reveal that the changeover is atnetration lengths for higher porosity batches. This isith the observations in Schoelkopf et al. (2000), wheregeover was at a larger penetration length for tubeser radii. The initial penetration rate in the inertial

me scales linearly with the porosity (Fig. 5).ower law was fitted to the data from the Laplace-

s linearly with the porosity and the exponent m indi-

Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 1082–1090 1087

Fig. 5 – Initial penetration rate (a in Eq. (5)) as a function ofthe porosity. This parameter was determined from the dataof the inertial flow regime (y < yc).

Fig. 6 – Fitting parameters of the power law (Eq. (5)) as afunction of the porosity using the data from theLaplace-Poiseuillian (y ≥ y ) flow regime.

cates thaThis supequivalenequationflow regim� = 1.002 m46.7◦ (Koias the incite and

the role

structureporous mthe macrrelevant.to high c

Fig. 7 – Correlation of the equivalent hydraulic radius,Rh,h,eq, and the porosity, f. Rh,eq was estimated by fitting theLW equation (Eq. (3)) to the penetration length data fromthe terahertz measurements and it was normalised by theunit area exposed to the water, Awet.

Table 3 – Fitting parameters and correlation performanceof three different porosity-tortuosity models. Moredetails about the models are provided in the respectivereference.

Model a (nm) p R2 RMSE (nm) Ref

Eq. (6a) 3.00 1.19 0.95 0.23 Archie (1942)Eq. (6b) 4.53 3.52 0.96 0.22 Weissberg (1963),

Comiti andRenaud (1989)

Eq. (6c) 10.57 12.33 0.96 0.21 Boudreau and

structureequilibriuThis emprapid abs2006).

The ebatch (seunsurpriThe hydrfine sizeis being

resisted

describedBeside

linked totion of th

therfollowces t

f −p

1 − p

1 + 39

re p

els a 0.96nly

c

t the liquid penetration length is proportional to√

t.ports the use of the LW equation to determine thet hydraulic radius of the powder compacts. The LW

was fitted to the data in the Laplace-Poiseuilliane of every measurement using � = 72.75 N mm−1 andPa s of water and a contact angle of water-FCC of

vula et al., 2011). We used the contact angle of calciteitial advancing and receding contact angles of cal-hydroxyapatite for water are roughly similar. Givenof viscous resistance during absorption in a porous

and the geometrical variability of the surface of aedium (solid and air alternating) we consider that

oscopic contact angle made by a sessile drop is less

by othe

eren

T =

T =

T =

whemod(R2 =the o

The site constraint in an ultra fine capillary leadsapillary forces dragging the liquid through the pore

tortuositdrop to 0

Meysman (2006)

and therefore empirically we suggest the use of them contact angle trending toward the receding value.irical interpretation is supported by the extremelyorption by such fine pore networks (Ridgway et al.,

stimated Rh,eq exhibits high consistency within eache small standard deviation of Rh,eq in Table 2) and,singly, it is strongly correlated to the porosity (Fig. 7).aulic radius ranges from 1.1 nm to 4.3 nm. The very

of the hydraulic radius suggests that the wickingdriven by the finest pores at the wetting front andby the permeability of the sample at long times, as

by Ridgway et al. (2006).s the dependence of Rh,eq on the porosity, it is also

the tortuosity (Eq. (4)). The tortuosity is again a func-e porosity (Fig. 8) and various models were proposed

researchers to describe this relationship. We useding three different porosity-tortuosity models (ref-

o the models are provided in Table 3)

(6a)

ln f (6b)

2p

�(1 − f ) , (6c)

is a fitting parameter. The results for the differentre summarised in Table 3. Interestingly, the best fit) is provided by the model given in Eq. (6c), which isgeometrical model tested. If we neglect the effect of

y (T = 1), the coefficient of determination and RMSE.77 and 0.38 nm, respectively. This clearly demon-

1088 Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 1082–1090

Fig. 8 – Schematic representation of the pore space in thepowder compacts. Highly porous tablets (a) have shorteraverage lengths of the fluid path, Le, than tablets with alower porosity (b). The tortuosity, T, of (a) is thus smallerthan that of (b). (c) is a schematic of the tortuosity-porositymodel as expressed by Eq. (6c). ı is the displacement of thelarge ani

strates tprocess.

Eq. (6(Boudreamuds. Tnonpeneorder to mtablet. It

sarily dirsample. Tto the dition (Fig.actual poprojectinnonintera small gsize of thtortuositand it raare very

tuosity vso-called

The fimated Rh

the radiuindicatesness, whin excelle(2017b), w

Fig. 9 – Analysis of high-frequency fluctuations of theliquid penetration data. (a) Data of one tablet per batch. (b)Batch-averaged penetration depth in frequency-domain.The open

otropiculosit

in thvalu

F

highapid

th depenysedtratied

ce sangeis ti

ions

In p wit

tionassuree pllenteforend oe inlhese

sotropic pore layers.

he effect of the tortuosity on the liquid imbibition

c) was developed by Boudreau and Meysmanu and Meysman, 2006) to predict the tortuosity ofhe model is based on the idea of the assembly oftrating and nonoverlapping blocks (disks, Fig. 8c) in

imic effective aggregated particles that make up theis important to note that these blocks do not neces-ectly represent the individual particles present in thehe disks are aligned on a plane that is perpendicular

rection of compaction. Moreover, the disk distribu- 8c) is obtained by taking a cross section through thewder compact perpendicular to the tablet face andg all the intersected particles onto this plane in asecting fashion. The layers of disks are separated byap of constant width, which is large compared to thee water molecules penetrating into the compact. They decreases monotonically with increasing porositynges from 8.6 (f = 0.46) to 5.5 (f = 0.68). These valueslarge, which is attributed to the fact that these tor-alues account for the “true” tortuosity as well as the

constrictivity of the pores (Boudreau, 1996).tting of Eq. (4) combined with Eq. (6c) to the esti-

,eq yielded a value of p = 12.33, where p is defined ass to thickness ratio of the disks. The high p value

that the disks must be larger in diameter than thick-ich suggests a strongly anisotropic structure. This is

anispendtortuthatone

3.2.

The

of rleng√

t-danalpeneapplreduthe rin thtuat10 ).latedaddito aof thexcetherdepeof th

T

nt agreement with the results reported by Markl et al.hich revealed that the pore space is dominated by

shape of

ing block

circles indicate the maximum for each batch.

ic inter-particle pores with their principal axes per-ar to the tablet faces. We want to emphasise that they in the radial direction is not necessarily the same ase axial direction. Our discussion is restricted to only

e of the tensor-tortuosity.

luctuations of moving liquid front

acquisition rate (15 Hz) facilitates the analysismovements of the water front. The penetration

ata feature fluctuation superimposing the t- anddent behaviour (Fig. 9a). These fluctuations were

on the basis of the frequency-domain data of theion depth. Zero padding and a Hann window wereto increase the number of frequency bins and toide lobes. We analysed only the penetration data in

of 4–12 s as the fluctuations were more pronouncedme span. The frequency and magnitude of the fluc-become larger with increasing porosity (Figs. 9b andarticular the oscillation frequency is strongly corre-h the porosity (R2 = 0.9, Fig. 10a). We performed anl experiment including a flow dampener in order

that the observed fluctuations are not an effecteristaltic pump. The additional measurement is in

agreement with the results reported here and it clearly indicates that the observed oscillationsn the tablet structure rather than on the pulsationet flow.

findings reinforce the need to consider anisotropic

pores and it further reveals that there are larger build-s which have a low permeability. The liquid thus

Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 1082–1090 1089

Fig. 10 – Correlation of the fluctuations with the porosity.(a) Oscillation frequency and (b) amplitude of singlemeasurements as a function of the porosity. Thesefluctuations could not been detected for 3 measurements ofB01 and

by-passea throat

however,erwise ththe interThis surmfine equialong theity factorthe assurates bothchannelsfluid velowhen ine

Furthepore layeity. The

tablets w

4. C

This stuto resolvtablets. Ecritical inlogical fluand at hpharmacnomena

underlyin

Givennot swelcomplex

to perfortechnoloof rapid

ODT.

Acknow

We woulthe FCC

advice. Dneering afunding

lication a(https://d

Appendrelation

The surfafunction

S = 2�R

V = (1 −

with n�R

illaries, tpath, theThe spec

S

V=

he v

2fA

R

g the

h canace a

Sv

2f

f ) Rh

R

re T

ren

ie, G.eterm4–62.ah,

etolaorosigred

05, 12reaunlith139–3

for 2 measurements of B04.

s these blocks of FCC particles and travels throughto the next large pore (see Fig. 8a). This by-passing,

is presumably driven by surface film flow as oth-e inertial retardation of the large volume flow in

agglomerate pore space would slow the imbibition.ise would be consistent with the observably very

valent hydraulic radius. A change in pore diameter streamlines is typically reflected by a constrictiv-

as discussed above. These fluctuations thus supportmption above that the tortuosity in Eq. (4) incorpo-

the “true” tortuosity and the constrictivity. The pore thus constrict and expand leading to variations incity and thus the likelihood of film flow occurringrtial retardation becomes high.rmore, the displacement of the large anisotropic

rs (ı in Fig. 8a and b) increases with increasing poros-fluctuations are less pronounced for low porosityhich is attributed to the lower anisotropy of the pores.

onclusion

dy has successfully demonstrated the use of TPIe the rapid liquid imbibition of highly porous FCCffective disintegration of a pharmaceutical tablet is

ensuring high exposure times of the API to physio-ids, so that the API is absorbed in greater amounts

igher rates, leading to a faster onset of the desiredological effect. By monitoring disintegration phe-

Sv =

T

Seff =

usinR

surf

(1 −

whe

Refe

Archd5

BawuKpin1

Boudu3

on a real-time basis, a deeper understanding of theg mechanisms and factors can be achieved.

Boudreaumuds.

that FCC is practically insoluble in water and doesl, this study provides a useful metric of how morepharmaceutical formulations based on FCC are likelym. The TPI method has proven clear potential to be agy platform for the measurement and quantificationdisintegration processes such as those observed in

ledgements

d like to thank Omya International AG for providingpowder and sharing their valuable experience and.M. and J.A.Z. would like to acknowledge the U.K. Engi-nd Physical Sciences Research Council (EPSRC) for

(EP/L019922/1). Additional data related to this pub-re available at the Cambridge University repositoryoi.org/10.17863/CAM.17255).

ix A. Hydraulic radius–tortuosity

ce area of the pores, S, and the solid volume, V, as aof the hydraulic radius, Rh, can be expressed as

hnLe = 2fAwetLe

Rh

f ) AwetL

2h

≡ fAwet. n, L, Le, f and Awet are the number of cap-he tablet thickness, the average length of the fluid

porosity and the wetted surface area, respectively.ific surface area can then be defined as

2f

(1 − f ) Rh

Le

L.

olume surface area of the pores is modified to

wetL

h,eq

equivalent hydraulic radius, Rh,eq. be related to Rh,eq by considering a constant specificrea:

,eff = Sv

,eq= 2f

(1 − f ) Rh

Le

L

h,eq = RhL

Le= RhT−1,

(A.1)

is the tortuosity.

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