We have studied the imbibition and dissolution of a porous material in two separate scenarios: (1) whenthe porous material contains a surfactant powder and (2) when the porous material is dissolved ina surfactant solution. We show that the dissolution kinetics in both scenarios is significantly affectedby the presence of the surfactant and results in an increase in the characteristic imbibition time ofthe porous material, which can be well understood in the framework of the classical law of capillarity.Slowing of the imbibition kinetics was found to be affected by a modification of the liquid wettingproperties, but is also affected by a variation in the solubility of the porous material in the presenceof the surfactant. Furthermore, there is a depletion effect of the surfactant inside the rising liquid, whichis in good agreement with previous work and theoretical predictions.
Porous materials are encountered in a wide variety of applica-tions in which they are either plunged into or invaded by a liquidphase, such as during oil extraction [1], imbibition of water ingranular materials like sand [2,3] or concrete [4,5], wetting of fab-rics [6], and filtration processes [7]. The invasion of the material bythe liquid is a capillary problem that can be complicated when themedium simultaneously dissolves into the liquid phase [8]. Thisis typically the case in applications where the porous material isa tablet formed by a compacted powder, such as in pharmaceu-ticals, detergents, and food formulation additives. In this context,we can call a porous material an active medium that is simulta-neously invaded and dissolved by the surrounding liquid phase. Itsactivity may be of various types, but mainly arises from its compo-sition. Some common active materials are pharmaceutical tabletsthat slowly dissolve into a liquid phase that may be water or a bi-ological medium, such as saliva or gastric fluid. In such instances,the porous matrix tablet is immersed in the liquid and any activechemical substances within the pharmaceutical tablet slowly dif-fuse from the interior to the surrounding medium. In the case ofan insoluble matrix, the kinetics of delivery is mainly driven by thediffusion of the molecules through the immersed matrix.
In other applications, such as with detergent or cleaning prod-uct tablets, the active material is the main constituent of theporous medium. In such instances, the activity of the material ortablet is driven by dissolution of the porous material, which inturn results from the combined effects of imbibition by the porousmedium and simultaneous dissolution of the porous material. Nor-mally, a surfactant is present with the tablet in order to providea cleaning function to the formulation. However, the surfactantcan impede efficient tuning of both the mechanical and dissolu-tion properties of the tablet. First, the general mechanical behaviorof surfactant-containing tablets is usually worse than the equiva-lent non-surfactant-containing formulation. Second, dissolution ofsurfactant crystals in water may occur through transient formationof lyotropic liquid crystalline phases with high viscosity, which re-sults in a decrease in their dissolution rate [9]. Third, the presenceof surfactants in solutions leads to a change in the wetting prop-erties of the dissolving liquid and consequently in the imbibitionkinetics in a porous system. This case has been the subject of nu-merous experimental and theoretical studies [10–14].
In this context, industrial research has shown a decrease inhardness of bleach tablets when 2%, w/w, of an anionic surfac-tant is added to the initial powder blend. At the same time, it wasalso observed that the tablet dissolution time was twice as largewhen at constant porosity. Similar observations have been reportedwhere the effects of surfactants on tablet dissolution times are de-scribed [15]. In fact, a surfactant can improve the dissolution ofhydrophobic compounds [16], but may also prevent disintegrationagents from swelling [17].
Recently we studied the dissolution of porous tablets formu-lated without any surfactant [8]. In this present study, we havefocused on the influence of a small amount of surfactant eitherintroduced by initial integration into the tablets as a powder ordissolved in the invading solution. We study the impact of the sur-factant on the dissolution kinetics and mechanical properties ofthe tablets. The presentation of our results is organized into threesections described as follows.
In Section 2, we present the materials and the experimentalcharacterization techniques. In Section 3, we show the results ob-tained when the surfactant is present in the initial powder blendbefore the tableting process. By varying the nature of the fluidused to immerse the tablet, we can decouple the two processesinvolved in the whole dissolution process, i.e., the imbibition andthe powder dissolution kinetics. In Section 4, we investigate theeffect of the surfactant when it is introduced into the aqueoussolution used to dissolve a tablet containing no surfactant in theinitial powder blend. We show that the influence of the dissolvedsurfactant depends on the porosity, which is due to its adsorptiononto the wall of the porous medium. Finally, we conclude on thedifferent possible explanations of the dissolution-delaying effect ofthe surfactant.
2. Experimental system and characterization techniques
2.1. Tablet composition and characteristics
The porous matrix studied contains at most two components:(1) a chlorine provider (sodium dichloroisocyanurate or DCCNa,C3N3O3Cl2Na), which is used as a disinfectant in industrial anddomestic applications and constitutes between 98 and 100% of thetablet; and (2) an anionic surfactant (sodium dodecyl sulfate orSDS), which does not exceed 2% of the tablet composition. Theporous matrix was realized by compressing the powders (previ-ously mixed in the case of the 2%-surfactant-containing tablets)using a lab-scale alternative tableting machine (Korsch, Type EK0,Korsch Maschinenfabrik, Germany) with 1 cm2 flat punches anda die volume of 1 cm3. The pressure was adjusted from 30 to300 MPa to produce tablets with controlled porosity.
We have systematically compared the properties of these twosystems (with and without surfactant) in terms of mechanicalproperties, porosity structure, and dissolution behavior. Through-out our discussion, the one-component system will be referredto as the “pure system” and the two-component system as the“mixed system.”
The DCCNa and SDS powders were characterized prior to theircompression. The particle-size distributions were determined us-ing a laser diffraction analyzer (Mastersizer 2000, Malvern Instru-ments). The volume equivalent median diameter (D0.5) was calcu-lated from three measurements. The powder specific surface areas(the areas of powder/gas interface) were determined by nitrogenadsorption (Gemini 2360 analyzer, Micromeritics Instruments). Fi-nally, the pycnometric density of the powder, dpycno, was deter-mined using a helium pycnometer (Accupyc 1330, MicromeriticsInstrument). These physical characteristics are summarized in Ta-ble 1. For a detailed discussion of the characteristics of the pa-rameters listed in Table 1, the authors recommend Refs. [18,19] forfurther reading.
The system porosity can be deduced from the pycnometric den-sity of the powder and the apparent density of the tablets (dtablet),which is in turn determined simply by a measurement (24 h af-ter manufacture) of the tablet weights (with a precision of 0.1 mg,AE 160, Mettler) and dimensions (with a Linear Tools digital caliperwith a precision of 0.01 mm). The porosity (φ, %) is determined bythe expression
φ = 100
(1 − dtablet
dpycno
). (1)
The tablet pore size distributions are measured using a mercuryintrusion porosimeter (AutoPore IV Micromeritics Instruments).The matrices are immersed in liquid mercury and the volumes ofliquid intruded into the pores of the tablets are measured as afunction of the applied pressure. From the total intruded mercuryvolume (V Hg) and the apparent volume of the tablet (V tablet), wehave access to another evaluation of the tablet porosity (φHg, %), asgiven by
φHg = 100V Hg
V tablet. (2)
Each intruded volume corresponds to an applied pressure �P .Knowing the mercury surface tension (γHg = 485 mN/m) and con-tact angle θ at the solid surface (θ ∼ 140◦), one may deduce thecharacteristic pore radius, RHg, corresponding to each applied pres-sure �P from the Laplace equation
RHg = 2γHg cos θ/�P . (3)
The pore size diameters are calculated and the evolution of thedifferential volume of intrusion is plotted as a function of the poresizes. A mean pore diameter (volume) is calculated for each poros-ity distribution. The “median diameter” on the volume basis isdefined as the diameter of the 50% point on the volumetric cu-mulative distribution.
The tensile strength of the tablets, Rd (MPa), is deduced fromthe value of the maximal diametral breaking force, determined bya diametral compression test (Schleuniger-2E, Switzerland) [20],according to the equation
Rd = (2F )/(π Dh), (4)
where h and D are respectively the tablet height and diameter.
2.2. Measurements of the dissolution properties
The SDS and DCCNa dissolutions were first followed using sur-face tension measurements and then second, using chloride selec-tive electrode potentiometry measurements (Electrode RadiometerAnalytica, ISE 25Cl). In the mixed system, we thus confirmed thatthe two species dissolve simultaneously, and subsequently, theglobal dissolution kinetics was followed using conductimetry. In-deed, the DCCNa and SDS molecules dissociate into charged ionswhen dissolved in water and consequently, the solution conduc-tivity is proportional to the global concentration. The tablets wereimmersed in 300 ml of distilled water, with vigorous stirring inorder to ensure good homogeneity of the solution. The solutionconductivity was measured using a conductivity meter (CDM210,Radiometer Analytica, France) with a two-pole conductivity cell(CDC641T, Radiometer Analytica, France). The cell design permitscontinuous measurements due to free flow of a solution throughthe two platinum plates. The final dissolution time was measuredwhen the conductivity was stabilized, i.e., when all the compo-nents were dissolved.
346 N. Brielles et al. / Journal of Colloid and Interface Science 328 (2008) 344–352
Fig. 1. (a) Scheme of the set-up used to measure the imbibition of a tablet from thebottom. (b) Enlighted illuminated tablet: the wetted part looks whiter.
2.3. Measurements of the imbibition properties
In earlier studies, two experimental methods have been em-ployed for measuring the imbibition kinetics of a nondissolvingfluid into porous materials. The first one consists of direct mea-surement of the liquid penetration length inside the sample as afunction of time [2,8,21–27]. The second consists of weighing theamount of liquid invading the medium as a function of time [3,6,7,28–32]. As previously discussed, both experiments were shownto lead to similar results [33,34]. In this paper, we used a methodbelonging to the first type of approach:
(i) Each tablet was dipped into a low-viscosity silicone oil (Flukasilicone oil DC 200, of viscosity 10 mPa s) that wets the ma-trix but does not swell or dissolve the components (Fig. 1a).The progression of the silicone front is then followed by back-lighting the tablet. The portion that is wetted by the siliconeoil indeed looks different from the dry part (Fig. 1b). The im-bibition length h was measured as a function of time.
(ii) To study the coupling between the processes of imbibition anddissolution, we also measured the time evolution of the imbi-bition length of the tablets when immersed in water. This wasachieved by immersing each tablet in an aqueous potassiumpermanganate solution ([KMnO4] = 4 g/L) in order to color thesolution. The tablets were then removed from the KMnO4 so-lution at various times t and cut into two pieces to measurethe wetted thickness h (Fig. 2). By repeating this operationseveral times with many different tablets, the h = f (t) kineticcurves can be plotted for tablets with various porosities. Theimbibition length was measured from images captured for thepartially invaded tablets using a ruler (Fig. 2b). From each pic-ture we deduce an average wetted length (see the schemein Fig. 2a at time t = 3 min). Since the imbibition front canbe quite irregular, we repeated the experiments using severaltablets. The dispersion of the results obtained is reflected bythe error bars plotted in Fig. 10.
3. Results and discussion
3.1. Compared porosities
The porosity distribution measured using Hg penetrometrywithin the two systems is presented in Fig. 3.
The porosity distributions were found to be similar regardlessof the total tablet porosities. Moreover, the median diameter calcu-lated from porosity distribution does not significantly change fromone system to the other (Fig. 4).
Consequently, a difference in porosity structure between thetwo systems, in their dry state, cannot explain the decreasing dis-solution kinetics. In the next section, we will more precisely study
Fig. 2. Scheme of the set-up used to measure the imbibition length in the case of atotal immersion in water.
Fig. 3. Porograms of the pure and the mixed systems at various porosities.
the imbibition kinetics in order to understand the surfactant rolein the disintegration process.
3.2. Compared mechanical properties and dissolution kinetics
Earlier measurements [18] of the tensile strength, Rd , as a func-tion of porosity for the pure and the mixed systems showed that
N. Brielles et al. / Journal of Colloid and Interface Science 328 (2008) 344–352 347
Fig. 4. Evolution of the median pore radius measured by mercury porosimetry asa function of tablet porosities for the pure and the mixed systems.
Fig. 5. Compared evolution of tablet dissolution times as a function of porosity forthe pure and the mixed systems. As soon as the tablet porosity is lower than 25%,we observe that the presence of surfactant significantly increases the dissolutiontime. This delay may be explained.
Table 2Characteristics of the surfactants used.
GEROPON® T36 Sodium polycarboxylate(copolymer of maleic anhydrideand diisobutylene)
the interparticulate bonding is weaker in the presence of SDS. Thisloss of hardness usually entails a decrease of dissolution time.
To illustrate the delaying effect induced by the surfactant, wehave plotted in Fig. 5 the evolution of the final dissolution time, t f ,as a function of porosity for both systems, which can be deducedfrom conductivity measurements.
As soon as the tablet porosity is lower than 25%, we observethat the presence of surfactant significantly increases the dissolu-tion time. This delaying effect is very general and we observe itfor a variety of different molecules (various HLB, types of polarheads, counterions, etc.), such as the ones mentioned in Table 2.The observed delaying effect is always qualitatively the same, asillustrated in Fig. 6. In the remaining discussion we will only treatthe case of SDS, which was the primary surfactant used in ourstudy.
The tablet dissolution delay effect caused by the surfactantcan be explained by differences in the tablet dissolution kinet-ics. In fact, previous work performed on the pure system [8] hasshown that dissolution kinetics change according to tablet porosity(Fig. 7), and three specific regimes were identified:
Fig. 6. Compared evolutions of tablets dissolution times as a function of porosity forthe pure system and systems containing various surfactants.
1. High porosity: Imbibition is much faster than dissolution.The tablet disintegrates in a few seconds (fast disintegrationregime).
2. Low porosity: The average pore size is small and imbibition ismuch slower than dissolution. In this case, the water does notsignificantly penetrate the system and the dissolution speed isproportional to the outer surface of the tablet (erosion regime).
3. Intermediate porosity: Between these two limits, the tabletfirst dissolves according to an erosion process and then quicklydisintegrates when the whole tablet is wetted by water (inter-mediate regime).
These three different kinetic regimes are also observed in themixed system. However, the porosities limiting the three regimeshave shifted toward higher values in the presence of SDS, as shownin Table 3.
The fact that the tablets dissolve according to an erosion pro-cess when their porosity is below 15% probably reveals a slowerimbibition for tablets with surfactant. This difference in imbibitionkinetics cannot be explained by the presence of smaller pores inthe mixed system, as no significant differences were observed onthe porograms in Fig. 3.
3.3. Imbibition kinetics
3.3.1. Imbibition by a nondissolving liquidMany studies have been completed dealing with the imbibition
of porous materials by a wetting liquid. Materials as various assand [2,3], rocks [1], fabrics [6], papers [2,3,32], silica or CaCO3grains [23,25], and porous membranes [7] have been the subjectsof several such experimental investigations. A general feature of allexperiments performed is that, at least in the short-time regime,the square of the measured (or deduced) wetted length h roughlyvaries linearly with time t . This behavior is in good agreementwith the prediction of a now classical law on capillarity, whichis alternatively referred to as the Lucas–Washburn law [35,36]. Toobtain this law, one considers a fluid traveling through a capillaryand in a laminar flow. The loss of pressure �P due to the viscousenergy loss is described by the Poiseuille law,
�P = 8ηh
R V
dh
dt, (5)
where �P is the pressure drop inside the capillary, η the fluiddynamic viscosity, h the length filled by the fluid, t the time, andR V the hydraulic radius.
The Laplace law provides another expression for this pressuredrop that is due to the curvature of the meniscus formed insidethe capillary tube,
348 N. Brielles et al. / Journal of Colloid and Interface Science 328 (2008) 344–352
Fig. 7. Dissolution kinetics of the pure (a) and the mixed SDS–DCCNa (b) systems at different porosities.
Table 3Comparison of the different porosities φ limiting the different dissolution regimes.
Tablet Kinetics
Erosion Intermediary Disintegration
Pure system φ < 10% 10 < φ < 20% φ > 20%Mixed system φ < 15% 15 < φ < 25% φ > 25%
�P = 2γ cos θ
RL, (6)
where �P is the pressure drop, γ the surface tension, θ the con-tact angle, and RL the capillary radius.
From Eqs. (5) and (6), and neglecting the contribution of grav-ity, one can deduce what is referred to as the Washburn law(through time integration between 0 and t) [35,36],
h = RW γ cos θ
2ηt = DW t, (7)
where
RW = R2v
RL. (8)
RW is called the Washburn radius and DW has the dimensions ofa diffusion coefficient.
In the case of a network of identical cylindrical capillaries, thislength is equal to the capillary radius r. This equation is obtained
when the imbibition length is much smaller than the equilibriumimbibition length, the so-called Jurin height,
h J = 2γ cos θ
rgρ, (9)
where ρ is the liquid density. To establish this law, the porous ma-terial is considered as composed of parallel capillaries of averageradius RW , which stands to reason as a very crude approxima-tion. Remarkably, however, earlier studies [1,4,5,7,8] showed thatthis simple equation can provide a sufficient description for theimbibition of a wide variety of materials. However, it comes as nosurprise that in certain situations, e.g., when the size distributionof pores is bimodal [6] or the contact angles show some dynamicvariations during the imbibition process [26], deviations from thissimple law are observed. Despite the limitations, kinetic behaviorconsistent with Eq. (7) is most of the time observed.
In the case of the two systems studied in this paper, the im-bibition kinetics, measured with a low-viscosity silicone oil, areplotted in Fig. 8. The imbibition occurs by the bottom of the tabletas described in Fig. 1. It is possible to fit the data with the Lucas–Washburn equation, as good linearity is obtained between timeand the square of the wetted length. A Washburn radius can thenbe deduced from the slope of the straight lines (γ = 20 mN/m,cos θ ∼ 1, and η = 10 mPa s).
The RW radii deduced from the h2 = f (t) curves are hard tocompare with the physical length scales that are present in the
N. Brielles et al. / Journal of Colloid and Interface Science 328 (2008) 344–352 349
Fig. 8. Imbibition kinetics of silicone oil in tablets of various porosities.
Fig. 9. Evolution of RW as a function of porosity for the two systems. The solid lineis only a guide for the eyes.
material [37]. Also, the values that we deduced here are obtainedby considering a zero contact angle between the liquid and thesolid, an approach that is difficult to verify in our case. Therefore,we will refrain from using the absolute values of RW and will in-stead only consider the evolution of RW from one sample to theother.
In Fig. 9, the Washburn radii are plotted as a function of porosi-ties for the two systems. No difference is visible between the twogroups of tablets, indicating that the surfactant present does notmodify the imbibition so long as dissolution is not coupled to im-bibition.
3.3.2. Imbibition by waterIn this section, we investigated the case where water is used as
the wetting liquid, i.e., when dissolution is coupled with imbibi-tion. To be as close as possible to real dissolution conditions, wechose to report the imbibition kinetics observed when the tabletsare totally immersed in water (Fig. 2). Once again, the square ofthe wetted length is plotted versus time according to the tablets’porosities (Fig. 10).
Even if some deviations from the Washburn law can be ob-served for slowly dissolving tablets [38], it is still possible to de-duce a Washburn radius from the experimental data. A comparisonbetween the Washburn diffusion coefficients DW obtained withthe two systems confirms that the surfactant addition decreasesthe imbibition kinetics over the whole range of porosity values(Fig. 11).
This result shows that the surfactant is responsible for a delayin the water imbibition process, i.e., only when it is dissolved inwater.
Fig. 10. Evolution of the square of wetted length as a function of porosities for thepure (filled symbols and solid lines) and the mixed systems (empty symbols anddashed lines).
Fig. 11. Evolution of the Washburn diffusion coefficient DW as a function of tabletporosities for pure (empty symbols) and mixed (filled symbols) systems.
A first possibility of explaining this effect would be that the de-lay comes from transient and local appearances of lyotropic liquidcrystal SDS/water phases during the SDS grain dissolution process.Earlier work [9] has indeed shown that such transient states resultin an increase in the global kinetics of surfactant dissolution. How-ever, our attempts (using X-ray and freeze fracture transmissionelectron microscopy) to observe the presence of such lyotropic liq-uid crystal phases inside the pores of the previously wetted mixedsystem tablets were unsuccessful.
A second, and very likely, possibility would be that, when dis-solved in water, the surfactant changes the liquid wetting proper-ties γ cos θ , thus resulting in a decrease in DW . We investigate thispossibility in the next section.
4. Kinetics of dissolution in surfactant solutions
To quantify the impact of surfactant on the imbibition prop-erties, we studied the two systems when immersed (using theexperimental method described in Fig. 2) in aqueous SDS solutions(from 0 to 10 g/L). From the obtained imbibition kinetics, we de-duced the associated Washburn diffusion coefficients for differenttablet porosities and SDS solutions concentrations. In Fig. 12, weplotted the compared values of the DW of the mixed SDS/DCCNatablets (of three different porosities) when immersed in pure wa-ter and SDS solutions. No significant differences are observed inthis case, whatever the SDS concentration.
In contrast, the results obtained with the pure system are dif-ferent and depend on the tablet porosities (Fig. 13). For the tabletsof highest porosity, we observe a significant decrease in the imbi-
350 N. Brielles et al. / Journal of Colloid and Interface Science 328 (2008) 344–352
Fig. 12. Mixed SDS/DCCNa tablets: compared evolution of the Washburn diffusioncoefficients as a function of porosities when immersed in pure water or SDS solu-tion (10 g/L).
Fig. 13. Evolution of Washburn diffusion coefficient as a function of DCCNa tabletporosities and SDS solution concentration (0 to 10 g/L).
bition kinetics as SDS was introduced into the invading liquid. Thisis consistent with previous experiments and can be partially ex-plained by the decrease in surface tension when SDS is introducedinto water. Indeed, the Washburn diffusion coefficient DW is di-rectly proportional to the surface tension (Eq. (7)). However, thecoefficient is reduced by a factor of 10 while we experimentallymeasured a factor of at most 2.5 for the ratio of the surface tensionin the two systems (DCCNA/water and DCCNa/[SDS] = 10 g/L watersolutions). Equation (7) also involves other parameters includingthe contact angle and the solution viscosity; however, these pa-rameters are the subject of later discussion.
The results obtained for more compacted tablets are surpris-ingly quite different. As porosity is reduced, the delaying effect in-duced by the surfactant becomes less pronounced and is no longersignificant at φ = 9%. In this latter case, the addition of surfactantis no longer altering the imbibition kinetics. This effect may be dueto the adsorption of dissolved SDS molecules at the solid/liquid in-terface between water and the tablet solid surface.
When surfactant molecules are present in capillaries, equilib-rium takes place between the free molecules and the ones ad-sorbed onto the capillary walls. This equilibrium can couple withthe dynamic process of imbibition of the surfactant solution inthe capillary tube [12–14,39,40]. In such a situation, it has beenargued [10,11,14] that the surfactant concentration along the cap-illary can decrease as a consequence of surfactant adsorption ontothe capillary walls (Fig. 14). This concentration can even tend to-ward zero if all the surfactant molecules can adsorb at the surfaceof the capillary tube while the diffusion of the molecules from theouter solution is slower compared to the imbibition speed.
Fig. 14. Surfactant concentration profiles during the imbibition of a capillary tubeby a surfactant solution. C0 is the surfactant concentration at the bottom of thecapillary and Cm is the surfactant concentration in the meniscus [10,11].
Estimation of the surfactant molecule diffusion coefficient Dcan be performed using the Stokes–Einstein relation,
D = kT
6πηR, (10)
where kT = 4.14 × 10−21 J is the thermal energy at 300 K, η theliquid viscosity, and R the molecule’s characteristic size (typicallyR ∼ 1 nm for SDS). We find here that D ∼ 2 × 10−10 m2/s, whichis small compared to the previously measured imbibition diffusioncoefficient (4 × 10−9 < DW < 8 × 10−7 m2/s). If the characteristictime of surfactant adsorption is short compared to the two otherprocesses (which is the case in such confined geometries), the dif-fusion of surfactant molecules from the outside of the tablet to theinside of the capillaries cannot compensate for the loss of surfac-tant due to its adsorption onto the capillary walls.
In the course of our study, we also evaluated the quantityof surfactant molecules that can theoretically adsorb onto thecapillary walls. Though it is difficult to foresee how surfactantmolecules may adsorb on interfaces that simultaneously dissolve,we made the hypothesis that surfactants form bilayers at the DC-CNa surface. In this configuration, the SDS polar heads are in con-tact with the hydrophilic DCCNa at one end and with water at theother end.
We also considered that the tablet porous structure can be de-scribed as a group of parallel capillaries with an average diameterR equal to the median diameter obtained from mercury porosime-try. The amount of SDS molecules Nads that can adsorb onto thesurface is
Nads = 4π RlcANa
, (11)
where A is the area per adsorbed SDS molecule (typical values ofA ∼ 0.5 nm2 are reported [41,42]), Na the Avogadro number, andlc the total capillary length.
The number of SDS molecules N0 that are present in the solu-tion inside the capillaries of total length lc is
N0 = C0π R2lc, (12)
where C0 is the bulk surfactant concentration (10 g/L in our case).From this, one can deduce the ratio
N0
Nads= C0 R ANa
4. (13)
The value of this ratio depends on the capillary radius and conse-quently, on the tablet porosity (Fig. 12). Therefore, one can define
N. Brielles et al. / Journal of Colloid and Interface Science 328 (2008) 344–352 351
Fig. 15. Compared evolution of the Washburn diffusion coefficients as a functionof tablet porosities and for three cases: ( ) pure DCCNa tablets immersed in purewater; ( ) pure DCCNa tablets immersed in SDS solution (10 g/L); ( ) mixed DC-CNa/SDS tablets immersed in pure water.
a critical porosity below which the specific surface of the tabletsallows for adsorption of all the available molecules (i.e., whenN0/Nads ∼ 1). We found a critical porosity φc ∼ 14%, correspond-ing to a critical median radius Rc = 380 nm. This value is in goodagreement with our experimental data.
This simple argument can explain the different behaviors ob-served previously for tablets with low or high porosity. Indeed,when tablets with porosity below 14% are wetted by an SDS so-lution, all the surfactant molecules adsorb at the DCCNa surfaceas the solution passes along the capillary. As a consequence, nosurfactant molecules remain present in the liquid front and theimbibition process is not altered as compared to the case of purewater. By contrast, as observed in Fig. 15, for tablets with highporosity, some SDS molecules are still present in the solution andthe imbibition is slowed. For tablets that contain SDS grains insolid form, the grains constitute some reservoirs of molecules thatremain available in the liquid front. In such case, whatever theporosity of the tablet, the imbibition process is always delayed.
As previously discussed, the decreased imbibition kinetics canonly be partially explained by the decrease in surface tension γ .We now discuss the possibilities for the changes of the other in-volved parameters that are present in Eq. (7), i.e., the viscosity ηand the contact angle θ .
1. Viscosity effects: The viscosity of SDS aqueous solution varieswith SDS concentration. When the SDS concentration is be-low the critical micelle concentration, the viscosity is close tothat of water. Thus, it is increasing with the micelle concen-tration. For instance, we measured that a solution at 20%, w/w,of SDS is five times more viscous than water. Such an increasewould explain the decrease of the imbibition coefficient, butonly in the case where the SDS is integrated as solid grainsinside the tablet and not when it is previously solubilized inthe solution. Similarly, we noticed that the dissolution of SDSgrains is strongly decreased in a saturated DCCNa water so-lution. In this case, we observed the formation of a gel-likesuspension of SDS crystallites in the solution. Here also theformation of such a gel phase cannot explain the delay that isobserved when SDS is previously solubilized inside the water.However, it might contribute to the decrease of the dissolu-tion rate in the case when SDS grains are incorporated in theinitial matrix.
2. Contact angle effects: In the past 10 yr, several studies haveevaluated the possibility of autophobic effects when surfac-tant solutions spread onto a hydrophobic surface [39]. Indeed,surfactant molecules may adsorb above the contact line be-tween the three involved phases during a wetting event. As a
consequence, the surface gets covered by a monolayer of ad-sorbed surfactants that lay their hydrophobic parts in the gasphase, thus turning the initially hydrophilic surface into a hy-drophobic one. In such cases, the contact angle increases andcan even lead to a dewetting phenomenon. However, we haveno experimental proof for such behavior in our system.
5. Conclusions
Our results show that the characteristic time for the dissolutionof a porous tablet is greatly increased when surfactants are presentinside the tablet, even in very low relative proportions. This ob-servation cannot be explained by mechanical or structural effects,since our study shows that the mechanical strength is decreased,while the porosity characteristics of the system do not change assurfactants are introduced in the formulation. We demonstrate thatthe observed time decrease is rather due to a reduction of theimbibition process when the invading liquid is a solvent of thesurfactant. Using a classical description of the process in terms ofcapillarity, we measure the variation of the imbibition coefficientswhen some surfactants are present in the system, either as crys-talline grains previously mixed in the initial powder blend (case 1)or when dissolved in the invading water solution (case 2). Themeasured coefficient depends on the wetting and viscous prop-erties of the solvent with respect to the solid porous matrix. Thesurfactant-induced delaying effect can be only partially explainedby a decrease in surface tension. In case 1, we show that the de-laying effect might also be due to the partial insolubility of thesurfactant in the water saturated by the matrix component. Indeed,we observed the formation of a gel-like phase associated withthe formation of a network of undissolved surfactant crystallites.This gel results in an increase of the solution viscosity that mayexplain the consequent decrease of the measured diffusion coeffi-cient. Such an argument is invalid for case 2, where the surfactantconcentrations are locally too low to generate the gel phase. Incase 2 we suggest that the observed delay might be explained bya changing of the wetting contact angle due to some kind of au-tophobic effect. However, no experimental proof can be providedto assess our hypothesis. Also, still in case 2, we have shown thatwhen a surfactant solution invades a porous medium, there is astrong adsorption of the surfactant onto the porous matrix, whichfor materials with high specific area can lead to a depletion of sur-factant molecules in the meniscus of the invading liquid, in goodagreement with earlier works [10,11,14].
Acknowledgments
This work was partly funded by Eurotab Company. A financialcontribution from the Conseil Régional d’Aquitaine is also grate-fully acknowledged. The authors thank M. Linossier and O. andP. Desmarescaux for their interest in this work. D. Roux is grate-fully acknowledged for being at the origin of this collaborationbetween CNRS and EUROTAB Company. The authors thank Y. An-guy and J. Lux for fruitful conversations and N. Hearns for carefulreading of the manuscript. We also thank H. Deleuze and M. Birotfor their help during the mercury porosimetry measurements.
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