Mohamed A Ali1, Hary L Razafindralambo2, Giuseppina Conti1, Joël De Coninck1. 1. Physics of Surfaces and Interfaces Laboratory, University of Mons, 19, Avenue Maistriau, B-7000 Mons, Belgium. 2. Gembloux Agro-Bio Tech, TERRA Teaching and Research Centre, University of Liege, Avenue de la Faculté 2B, B140, B-5030 Gembloux, Belgium.
Abstract
Most probiotic-based products are available in powder particles under different solid-state forms. Such diversity can affect the probiotic stability, viability, and performance at different stages of processing, storage, and use. Here, we apply complementary physical chemistry techniques to characterize the bulk and surface properties of probiotic powder particles under different forms and report quantitative results of a highly concentrated multistrain reference product. The solid particle morphology, size/shape distribution, and the powder surface wettability in the compressed disc and porous packed bed forms are successively measured by sessile drop and capillary rise techniques. A complete wettability of the disc surface is observed through equilibrium contact angle measurements for various solvents, whereas the associated capillary rise data exhibit two regimes: a power law regime for the first few moments followed by a second regime, which can be described using Darcy's law. The use of this modeling approach shows the possibility of assessing the particle-packed bed permeability and porosity. These results open a new route of the structure-activity relationship study on the impact of probiotic solid particles on their functionalities and performance in promoting health benefits, related particularly to the human and animal gut permeability. This statement also strengthens the idea of using the compressed disc technique for easily performing probiotic wettability measurements.
Most probiotic-based products are available in powder particles under different solid-state forms. Such diversity can affect the probiotic stability, viability, and performance at different stages of processing, storage, and use. Here, we apply complementary physical chemistry techniques to characterize the bulk and surface properties of probiotic powder particles under different forms and report quantitative results of a highly concentrated multistrain reference product. The solid particle morphology, size/shape distribution, and the powder surface wettability in the compressed disc and porous packed bed forms are successively measured by sessile drop and capillary rise techniques. A complete wettability of the disc surface is observed through equilibrium contact angle measurements for various solvents, whereas the associated capillary rise data exhibit two regimes: a power law regime for the first few moments followed by a second regime, which can be described using Darcy's law. The use of this modeling approach shows the possibility of assessing the particle-packed bed permeability and porosity. These results open a new route of the structure-activity relationship study on the impact of probiotic solid particles on their functionalities and performance in promoting health benefits, related particularly to the human and animal gut permeability. This statement also strengthens the idea of using the compressed disc technique for easily performing probiotic wettability measurements.
Nowadays, probiotics
are among the most investigated research topics,[1] owing to their beneficial effects on human,[2] animal,[3] and plant[4] species. These living microorganisms are able
to promote the host health by playing both preventive and therapeutic
roles against numerous diseases, when they are used in adequate amounts.[5] Among the most important probiotic action mechanisms
include the competition for nutrients and adhesion sites with intestinal
or plant pathogens, the production of metabolites (bacteriocins, organic
acids, antioxidants, enzymes, and biosurfactants), and the immune
system modulation.[6] Moreover, probiotics
may be considered as functional biocolloids, ranging from 1 μm
(lactic acid bacteria) to 10 μm (yeasts) average particle sizes,
commonly used as bioactive ingredients for food, dietary supplements,
and pharmaceutical and cosmetic products under well-defined regulations.[7] Most of them are available in powder particles
at the solid-state or in liquid dispersed system forms.[8] Consequently, they possess like any colloidal
particles a couple of nano- and microscopic properties able to control
their main activities and techno-functionalities. Even though much
information is now available on probiotic properties (mechanisms,
quality, safety, and clinical performance), a lot is still ignored,
particularly those of their surface and colloidal physical chemical
properties.[9] However, each probiotic strain
has its specific properties that govern its activities and performances
in single and in mixed systems with other strains and functional components
such as bulk agents, protectants, prebiotics, and so on.[10]The degree of probiotic-containing products
to promote health benefits
depends on the capacity of the material to deliver viable functional
bacteria in the adequate dose.[11] Most are
stored and delivered under powder particles, mainly obtained from
a freeze-dried or spray-dried liquid dispersion.[12] Their quality, safety, and performance depend on strains,
doses, excipients, and adjuvants, which constitute the powder formulation.[13] Moreover, powder properties impact the functionality
of the product, which is also dependent on the manufacturing processes,
either directly through the changes in physical and chemical properties
or indirectly by affecting the product stability and bacterial viability
during storage.[10] On one hand, the powder
stability under varying temperatures and moisture content during storage
is crucial.[14] On the other hand, the adhesion
and colonization of probiotics at the solid-in-fluid phase to binding
sites in the gut is the key to success of their high performance and
efficiency for human or animal health.[6]In general, physical and chemical properties of powder particles,
including surface and bulk properties (nano- and microscopic properties)
impact various functionalities (macroscopic consequences) such as
wettability, flowability, dispersibility, and stability, which involve
gravity, friction, cohesion, and adhesion forces.[15] Consequently, the characterization of probiotic-based product
solid particles or under powder form is of great interest while being
less investigated until now. Physical and chemical properties of probiotic
particles in the powder state are relevant in probiotic viability
and performance by controlling physicochemical (e.g., oxygen permeability
and water activity), biological (e.g., surface membrane adhesion and
aggregation), and/or physical (e.g., crystal formation and size, storage
temperature, etc.) factors during probiotic processing, storage, and
activities in the host.[16] In fact, the
drying techniques and delivery forms (powder beads, tablets, capsules,
liquids, etc.), which depend on the physical and chemical properties
of the matrix source (e.g., powder particles and dispersion) and the
target (e.g., human gut), influence the probiotic performance/efficiency.[17] Thus, significant changes in these fundamental
parameters may considerably affect the cell viability, adhesion capacity,
and growth/colonization, which could play an important role in the
probiotic mechanism related to the intestinal barrier function.[18] Recently, the physical and chemical characterization
of mono- and multistrain probiotics at the liquid- and solid-states
has been initiated.[8] In such studies, powder
samples have been characterized in terms of size distribution and
surface properties that were assessed by probiotic lawn preparation
on porous solid substrates. Besides, a coupling calorimetric technique
(thermogravimetric analysis–differential scanning calorimetry
(TGA–DSC)) has been successfully used for thermal profiling
of powders, providing fingerprints, and predicting fundamental data
for each sample.[19] However, other key parameters
such as the particle specific surface area or wettability also have
their importance in the characterization of probiotic powder samples
since this information is related to the developed surface to react
with some liquid, that is, dispersing media and body fluids. Indeed,
a very large surface area to volume ratio of solid particles of small
size increases the possibility of accelerating the product oxidation
by a large interstitial volume and an increase of the powder permeability
toward water and oxygen will affect the powder stability during its
storage. This parameter is sensitive to the particle size and shape,
and obviously to the powder wettability. On one hand, a lower porosity
or permeability reduces the moisture absorption or oxygen transfer
from the ambient air inside powder particles, and on the other hand,
a higher surface hydrophobicity or lower wettability limits the water
absorption initially induced to powder surfaces.This article
reports on the methodology and results of an investigation
performed on probiotic powder particles by using complementary techniques
and approaches belonging to a series of physical chemistry tools recently
reviewed.[9] For this purpose, probiotic
powder samples of the reference have been prepared under different
solid-state forms (bulk, compressed disc, and packed-bed column) and
have been characterized in terms of particle size/shape distribution
and surface wettability measured by the well-known sessile drop and
capillary rise techniques.[20] Present results
show, for the first time, the successful use of Darcy’s law
to quantify capillary rise experimental data and provide subsequently
the powder particle bed permeability and porosity, rarely measured
for probiotic quality and performance controls. A multistrain and
highly concentrated probiotic powder has been chosen as the reference
because it is currently used for the determination of the quality
and genuineness of tests proposed for certifying probiotic consistency
and quality.[18] Our approach also opens
a new potential way to structure–function relationship studies.
We believe these probiotic powder particle properties are related
to their biological activities involving cell adhesion and colonization
mechanisms in model and real systems. Another interest in knowing
the powder permeability or porosity to fluids is the possible correlation
between the cell viability and the presence of air (oxygen) and/or
moisture in inter- and intra-particle pores.
Results and Discussion
The particle size and shape distribution, surface wettability,
and the liquid permeability as well as the porosity of probiotic particles
have been successively measured in this article on fine and bulk particles
under two forms, either in a highly compressed disc or in compact
porous bed, by using a standard multistrain and highly concentrated
probiotic powder previously fingerprinted.[19] Our goal is to pursue the physical chemistry assessment of probiotic
powders under different states and with different tools,[9] to identify at the microscopic scale some relevant
key parameters and basic properties of solid particles that could
control their macroscopic functionalities.
Powder Particle Properties
Figure illustrates
a typical scanning electron
microscopy (SEM) image of the probiotic powder sample, showing a diameter
ranging from a few to 200 μm. Powder particles appear in majority
quite spherical in shape according to the images taken under well-defined
conditions of experimental preparation and observation.
Figure 1
Scanning electron
microscopy images of the probiotic powder.
Scanning electron
microscopy images of the probiotic powder.Figure illustrates
the results of the granulometry analysis. It shows the cumulative
probability distributions in the size and shape of three independent
probiotic particle samples. There are numerous parameters to characterize
the shape of particles. We have chosen to present the convexity measurement
defined as the ratio between the particle area and the convex shell
estimated from a rubber band fitted on each particle. Most of the
particles form convex objects and the roundness factor is around 71–72%,
supporting the SEM observations. The particles appear heterogeneous
and contain at least two population groups around 0.3 μm (∼20%
in number) and 3.0 μm (∼80% in number) mean diameters.
Figure 2
Probiotic
particle (A) cumulative size distribution and (B) cumulative
shape distribution.
Probiotic
particle (A) cumulative size distribution and (B) cumulative
shape distribution.Table lists some
particle diameter percentiles from different packages. Results show
quite reproducible data characterized by a half population diameter
percentile (P50) mean value of 1.830 ± 0.017 μm for the
three independent packaged samples. Such statistical data represent
the average of more than 100 particles in single, aggregates, and/or
agglomerate forms containing various ingredients. These are typically
constituted in majority by probiotic strains, mainly in cocci and
rod shapes, and in minority by maltose and SiO2. These
data essentially indicate that most particles have their percentile
size around 1–3 μm. The main average particle sizes of
probiotics around 1–3 μm as observed through our image
analysis have the same order of magnitude than the hydrodynamic diameter
values (∼2 μm) measured by dynamic light scattering (DLS)
using a cumulant algorithm.[8] When determined
in particle-in-gas sizing mode by laser diffraction and expressed
in number distribution, the same data provided a diameter d around 3–4 μm (Figure S3). That means that the probiotic powder mainly contains fine
or isolated cell particles and minor aggregate/agglomerate ones, as
shown in the representative SEM image. The smallest particle population
appearing in the cumulative distribution size (∼0.3 μm)
possibly corresponds to other minor ingredients, i.e., silicon oxide
and maltose particle aggregates, commonly used in probiotic products.[12] Thus, the image analyzer appears more appropriate,
sensitive, and only requires the smallest amount of the sample compared
to the diffraction technique for sizing probiotic powders at the solid
state.
Table 1
Particle Diameter Percentiles of Three
Samples from Different Packagesa
in microns
P10
P25
P50
P75
P90
sample 4
0.325
0.976
1.840
2.820
4.110
sample 5
0.325
0.459
1.810
3.790
6.320
sample 6
0.325
0.859
1.840
2.980
4.770
mean ± SD
0.325 ± 0.000
0.765 ± 0.271
1.830 ± 0.017
3.197 ± 0.520
5.067 ± 1.134
P means the particle diameter percentile
for 10, 25, 50, 75, and 90% of the population.
P means the particle diameter percentile
for 10, 25, 50, 75, and 90% of the population.
Powder Compressed Disc Properties
Equilibrium contact
angles measured with all tested solvents of various physicochemical
properties reach zero very quickly (after 500 ms), indicating the
total wettability of the compressed powder surface of the probiotic
sample. Figure illustrates
the spreading of the solvent or Milli-Q water drops (5 μL) deposited
on the probiotic disc surface.
Figure 3
Spreading of different liquid drops (respectively,
heptane, ethanol,
methyl ethyl ketone (MEK), and water) on a compressed probiotic disc
versus time (in seconds).
Spreading of different liquid drops (respectively,
heptane, ethanol,
methyl ethyl ketone (MEK), and water) on a compressed probiotic disc
versus time (in seconds).All the measured contact angles are very small, compatible with
zero, which means that Zisman’s critical surface tension of
these probiotics is very large.[21] The corresponding
surfaces are therefore highly wettable. This property is, of course,
very important to characterize how these probiotics interact with
body fluids. Such properties are in agreement with previous results
of our experiment using another preparation mode of the probiotic
solid surface measured by a static advancing water contact angle method.[8] There, the contact angle was immediately determined
after drop deposition and a probiotic lawn was prepared on a porous
filter support from a known amount of particle dispersion preparation.[22] As the majority of strains of such a multistrain
probiotic powder are constituted by Streptococcus thermophilus (>60% of total strains),[23] such a
result
would be expected owing to the high surface affinity for water of
this bacterial species, besides the presence of a hydrophilic anticake
agent SiO2 in the powder. The sessile drop method combined
with the compressed disc preparation under the same defined pressure
(3850 bar) provides reproducible data and appears as a very practical
tool for probiotic characterizations.
Powder-Packed-Bed Properties
Figure illustrates
the increase of the liquid mass
squared into the powder column over time. Reproducible results for
each liquid are obtained with a compaction time larger than 20 min.
Clearly two regimes can be observed in the capillary rise for each
liquid: a power law behavior during the first few seconds (2–3
s) and then a diffusive regime for all the considered liquids. We
attribute the first regime to the liquid penetration across the initial
layers, which are first constituted by the filter paper followed by
a small particle layer of probiotic samples. This second thin layer
above the filter paper may result from the powder sample segregation
due to the tapping procedure. We have thus used the function b·tα + c to describe the first regime and p·t + q to describe the second one. Table provides the power
index α and the slope for each solvent.
Figure 4
Increase of mass m2 (g2)
during the capillary imbibition as a function of time (s) for the
first 10 seconds. The error bars correspond to the statistical errors
associated with four different experiments and are represented by
fill areas. The three considered solvents are, respectively, ethanol
(circle), heptane (square), and MEK (triangle).
Table 2
Fitted Parameters (Power Index and
Slope) Describing the Capillary Rise in Probiotics for Ethanol, Heptane,
and MEK
liquid
range (s)
power index
α (m2 ∼ tα)
range (s)
slope p (g2/s) (m2 ∼ p·t)
heptane
0–3
0.165 ± 0.019
4–10
0.00142 ± 8 × 10–5
ethanol
0–3
0.370 ± 0.008
4–10
0.00231 ± 9 × 10–5
MEK
0–3
0.114 ± 0.032
4–10
0.00091 ± 3 × 10–5
Increase of mass m2 (g2)
during the capillary imbibition as a function of time (s) for the
first 10 seconds. The error bars correspond to the statistical errors
associated with four different experiments and are represented by
fill areas. The three considered solvents are, respectively, ethanol
(circle), heptane (square), and MEK (triangle).Clearly, in the second
regime, all the considered liquids imbibe
the probiotic powder with one characteristic slope. The slope of the
linear fits over time periods above 3–4 s until 10 s to minimize
evaporation effects can be easily measured. From these slopes, it
is easy to get the effective radii Reff computed using Darcy’s formula (eq ), as well as the permeability K determined from the slopes of different solvents using eq .Since the particle size
distribution is mostly concentrated with
a mean diameter around d ∼ 3 μm, we
can use the semiempirical Kozeny–Carman from eq to relate macroscopic parameters
such as permeability to microscopic ones, like particle arrangement.From our data, we get an estimate of Reff of the order of 350–500 μm, which makes sense within
a probiotic tube of radius 5 mm. Figure shows the graphical presentations of the
relationship between the permeability K with d = 3 μm (the mean diameter of the particles) and
the porosity, providing porosity values between 80 and 90% for ethanol,
heptane, and MEK.
Figure 5
Permeability versus porosity determining probiotic porosity
values
for different solvents, from top to bottom ethanol, heptane, and MEK.
Permeability versus porosity determining probiotic porosity
values
for different solvents, from top to bottom ethanol, heptane, and MEK.The porosity is thus rather similar for all the
considered liquids,
turning around an average value of 85% for the porous compacted probiotic
sample loaded in the glass tube. When the wettability is measured
with a more porous material or powder-packed bed by using the capillary
rise method, the recorded data fit well to Darcy’s law that
correlates permeability to the liquid flow rate,[24] and not at all to Washburn’s equation (Figure S3). Another advantage of Darcy’s
law is to provide the liquid permeability of the powder bed, or its
equivalent porosity, via the Kozeny–Carman model. Considering
the particle mean diameter d = 3 μm, this approach
provides an average of powder porosity (∼85%) that corresponds
to the bulk porosity values (50–80%) reported for Lactobacillus paracasei probiotic powders prepared
by different drying techniques.[25] These
values represent the sum of the connected porosities or interparticle
pores (30–70%) and the isolated porosities or intraparticle
pores (∼10%) of L. paracasei samples.Globally, this work reveals that the compressed disc
technique
for wettability measurement and the capillary rise experiments allow
surface properties of probiotic powders to be characterized.To be complete, we have also studied the capillary rise experiment
using a more viscous liquid, benzyl alcohol, for which the liquid
is expected to penetrate into the powder with a smaller speed. Figure shows the capillary
rise in the probiotic powder sample using this liquid. There are again
clearly two different regimes: a power law and a linear regime. The
fitted parameters are given in Table .
Figure 6
Capillary rise in the probiotic for benzyl alcohol: m2 (g2) versus t (s).
The error
bars correspond to the statistical errors associated with four different
experiments and are represented by fill areas. The two fitting curves
are a power law for the first moments and a straight line for longer
times. The fitted parameters are given in Table .
Table 3
Fitting Parameters (Power Index and
Slope) for the Benzyl Alcohol Capillary Rise
liquid
range (s)
power index
α (m2 ∼ tα)
range (s)
slope p (g2/s) (m2 ∼ p·t)
benzyl alcohol
0–30
0.366 ± 0.005
40–100
0.00036 ± 2 × 10–5
Capillary rise in the probiotic for benzyl alcohol: m2 (g2) versus t (s).
The error
bars correspond to the statistical errors associated with four different
experiments and are represented by fill areas. The two fitting curves
are a power law for the first moments and a straight line for longer
times. The fitted parameters are given in Table .From this
slope, we can estimate the effective radius Reff, which is of the order of 400 μm leading again
to a porosity of 90%. The fact that here we have to consider a first
regime of 30 s is due to the viscosity of benzyl alcohol. The time
required to cross the first layers of the sample has to be larger
in the latter cases. Last but not the least, we have also measured
the capillary rise of Milli-Q water in the probiotic column. The results
are presented in Figure and complement our wettability measurements as described above.
The associated slope for Darcy’s regime is 2.95 × 10–4 ± 1.2 × 10–5 (g2/s) leading to an estimate for the effective radius Reff of 250 μm and a porosity of 85%.
Figure 7
Capillary rise in the
probiotic for water: m2 (g2) versus t (ms). The error
bars correspond to the statistical errors associated with four different
experiments and are represented by fill areas. The two fitting curves
are a power law for the first moments and a straight line for longer
times.
Capillary rise in the
probiotic for water: m2 (g2) versus t (ms). The error
bars correspond to the statistical errors associated with four different
experiments and are represented by fill areas. The two fitting curves
are a power law for the first moments and a straight line for longer
times.
Conclusions
In
conclusion, the use of various physical chemistry techniques
to characterize colloidal and surface properties of a reference probiotic
powder under various solid particle forms provides coherent and reproducible
results. The powder material is mainly constituted of fine and isolated
particles, as well as aggregates or/and agglomerates up to 200 μm
rather spherical in shape, and having a typical mean diameter about
3 μm. Its surface wettability measured for different solvents,
either in a highly pressed disc by sessile drop or in a porous compacted
solid by capillary rise shows the same trend characteristic of high
critical surface tension. The powder is highly wettable. On one hand,
the equilibrium contact angle measurements show complete wettability,
independent of the physical and chemical characteristics of the solvents.
On the other hand, the capillary rise data by far fit better to Darcy’s
law instead of the commonly used Washburn equation and is fully compatible
with complete wettability. The use of this modeling approach leads
to the possibility of assessing probiotic powder permeability and
porosity. These physical properties are interesting for evaluating
some performance indicators of strain stability and viability during
the powder storage, as well as their adhesion capacity to the binding
sites and colonization into the gut under various forms at the solid-in-fluid
state. This research will open a new route to investigate the relationship
between physical probiotic powder properties, functionalities, and
performances for promoting health benefits of living species, such
as the impact on the gut permeability modulation, and the cell viability
due to the presence of air (oxygen) and/or moisture in inter- and
intraparticle pores.
Materials and Methods
Probiotic Samples
Probiotic samples used in this investigation
are a multistrain-based food supplement (vivomixx, reference number
VSM003NM), kindly provided by Professor Claudio de Simone, as previously
described and fingerprinted.[19] All samples
are used as received in the dry powder state, hermetically sealed
in bundles containing 4.4 g of the material. Vivomixx is a mixture
of highly concentrated (450 × 109 CFU) eight bacterium
strains, including S. thermophilus, Bifidobacterium breve, Bifidobacterium
longum, Bifidobacterium infantis, Lactobacillus acidophilus, Lactobacillus plantarum, L. paracasei, and Lactobacillus delbrueckii subsp. bulgaricus. Maltose and silica dioxide (<5% in weight) are the other minor
ingredients of this probiotic formulation. Sample fingerprints have
been attested not only by the decomposition and transition thermal
profiles (Figure S1) but also the black
carbon and residual inorganic material content at 600 °C (∼30%
in weight).
Scanning Electron Microscopy (SEM)
The probiotic powder
is used as provided, and its surface morphology has been observed
in a Hirox SH-3000 scanning electron microscope (Hirox Company, Japan)
with a voltage of 15 kV. Prior to SEM observation, the surfaces were
sputtered with gold in a Denton Desk V Sample Preparation system (Denton
Vacuum L.L.C.).
Size and Shape Distribution
A granulometer
500 Nano
(OCCHIO, Angleur, BE) has been used to characterize the size and shape
distributions of the probiotic particles. Briefly, the powder is deposited
in a plastic bag under the dispersion bell, the vacuum is launched
and the plastic is then pierced, thus allowing the dispersion and
the deposition of the latter on a glass slide located under the bell.
Then, the bell is removed and the glass slide passes into the measuring
cell, where the powder is scanned and counted (sizes and shapes) by
means of optical techniques. Then, a careful image analysis is developed
using algorithms according to Hart et al.[26] The Occhio 500 Nano used in this study is equipped with a high resolution
6.6 mega pixel progressive scan camera and a telecentric superzoom
lens to image particles with a standard resolution down to 400 nm.
This resolution is achieved by using a violet LED backlighting instead
of conventional white light.
Sample Preparation
Compressed Disks
Probiotic sample disks are prepared
by compressing powders into pellets with a pressure around 3835 bar
corresponding to 5 tons in weight by using a manual hydraulic press
(Specac). The corresponding surface is then compacted with no visible
cracks and is used for the measurement of the static contact angle
without chemical alteration.
Packed-Bed Columns
A probiotic powder sample (0.5 g)
is weighed and loaded in the glass tube (radius = 0.5 cm) closed by
a filter paper at the bottom. The powder is then packed by applying
5000 taps done with a jolting volumeter model Stav II (J. Engelsmann
AG, Germany) for getting reproducible measurements. This apparatus
helps to compact the powder by moving up and down (tapping) under
a camshaft rotation at 250 rpm. An optimum number of 5000 taps is
applied for 20 min.
Wetting Solvents
Four representative
liquids with a
wide range of physicochemical properties and applications have been
selected (ethanol, heptane, MEK, and benzyl alcohol) for specific
reasons: ethanol as the reference solvent, heptane as the low surface
tension solvent, and benzyl alcohol and methyl ethyl ketone as solvents
commonly used in industries. Ethanol and methyl ethyl ketone (MEK)
were from Chemlab (Zedelgem, Belgium) and heptane and benzyl alcohol
were provided by Sigma-Aldrich (St. Louis, MO). Table lists all solvent characteristics.
Table 4
Physical Properties of Different Solvents
for Wettability Measurements at 25 °C
solvent
viscosity (mPa·s)
density (g/cm3)
surface
tension (mN/m)
ethanol
1.368
0.789
21.80
heptane
0.580
0.684
19.66
MEK
0.400
0.800
23.97
benzyl alcohol
5.474
1.044
36.80
Sessile
Drop Method
The static contact angles were
measured with a drop shape analyzer DSA 100 from Krüss (Hamburg,
Germany) by depositing a 5 μL drop of the liquid on the probiotic
disc using the sessile drop method.
Capillary Rise Method
The capillary rise of various
solvents (Table )
into the packed-bed column with probiotic powder was monitored with
a MK100 tensiometer from Krüss (Hamburg, Germany) by continuously
measuring the change in the mass of the liquid penetrating the sample
over time, the liquid mass (m) being connected to
its height (h) bywhere ρ represents the liquid density
and Reff the effective radius characterizing
the column imbibition.Two mathematical models are commonly
used for studying the dynamic capillary rise phenomenon monitored
by the height penetration h of the liquid wetting
the tube or the effective tube as a function of time t.[27−34] The theoretical aspect is detailed in the available Supporting Material. Briefly, the two models
are based on (1) Lucas–Washburn equationwhere γ denotes the surface tension, cos θ
the
contact angle, R the tube radius, and η the
viscosity. In this case, the porous medium is considered as a model
tube of radius R.[35−37]Let us point out
here that the short time behavior of the capillary
rise can be affected by the friction between the movement of the air–liquid
interface and the solid surface when the liquid penetrates into the
tube, as illustrated by Martic et al.[31] A nonuniform pore size distribution in porous media can also lead
to the erroneous application of this model.[35] Short time behaviors are thus always difficult to analyze in detail.
(2) Darcy’s lawwhere K is the so-called
permeability and Reff the effective radius.
This second model based on Darcy’s law relates the average
velocity of a liquid to the pressure gradient for the case of powders
or porous media.[36]By substituting R with Reff in eq , and
combining it with eq , one can deduce the following relation between K and ReffIn terms of mass, we thus getAccording to Darcy, fitting the data m2 versus t using a linear function p·t + q for different liquids, we
will have access to the slopes p (one per liquid),
which are characteristics of the porous structure. The ordinate q is here to take into account the origin of time for the
capillary rise.From the kinematics of imbibition in a porous
media, we can thus
extract the effective radius characterizing its permeability or equivalently
its porosity (Φ) through the semiempirical Kozeny–Carman
approach,[37,38] as follows where d represents the particle
mean diameter.
Authors: Mershen Govender; Yahya E Choonara; Pradeep Kumar; Lisa C du Toit; Sandy van Vuuren; Viness Pillay Journal: AAPS PharmSciTech Date: 2013-09-25 Impact factor: 3.246