of amorphous lactose is unknown, then the moisture content measurement does not explain how resistant the product is to caking.
3.4 RATES OF MOISTURE SORPTION ON TO LACTOSE :
The rate of sorption of moisture on to both crystalline and partially crystalline lactose is necessary for the mathematical modelling of moisture transport in bulk lactose.
Knowledge of the sorption rates will also improve the understanding of lactose drying, conditioning and caking phenomena. To achieve such an understanding, the rates of moisture sorption onto purely crystalline lactose and spray dried amorphous lactose were determined experimentally.
A Mettler AE200 analytical balance equipped with an RS232 interface connected to a 3 86 IBM compatible computer was used to data-log the change in weight of a lactose sample when applied to a step change in ambient relative humidity. The sample was surrounded by a 1 litre plastic bottle which had the bottom removed. Attached around the base of this surround was 5mm plastic tubing with holes drilled at regular intervals providing a manifold for air distribution around the sample. The top of the surround had a 1 5mm opening to allow air to escape. Air supplied from a Hycal water vapour
generator was introduced into the chamber. Relative humidity and temperature of the air inside the chamber were also recorded using a Grant Squirrel data logger series 1 000. This set up can be seen in Figure 3 . 1 1 .
balance
exhaust surround
..
humidified air 7
Fig u re 3, 1 1 - Sorption rate measurement apparatus
RH/temperature probe
air distribution manifold
The dew point generator was switched on to allow the chamber to reach a steady state condition. The sample was placed into the apparatus in an aluminium moisture dish as a thin layer of up to 3mm deep. In this way a step change was applied to the sample. The balance reading was data-logged along with the chamber relative humidity and temperature.
3.4. 1 SORPTION ON TO a -LACTOSE MONOHYDRATE:
Crystalline 200 mesh lactose, which had been conditioned at high relative humidity to ensure no amorphous lactose was present, was used for the sorption rate experiments. The sample was allowed to reach equilibrium at 20% relative humidity at 30°C as
indicated by constant weight. The water vapour generator was then changed to achieve a 90% relative humidity condition in the sample chamber. Figure 3 . 1 2 shows the change in relative humidity and moisture content of the lactose sample with time.
The variability in the relative humidity evident in Figure 3 . 12 was caused by small variations in the temperature of the controlled temperature room. It is evident in these
results that there is a close coupling between a relative humidity rise and a subsequent
moisture content rise. It should be noted that the relative humidity range investigated is in the exponential portion of the moisture sorption isotherm and therefore it is expected that large moisture content changes occur as a result of small relative humidity changes above 80% RH. 1 00% � 75% :!2 E ::l I Q) 50% .2! !§ Q) c:: 25% 0% o 20 40 60 Time [mins] 80
-Bulk air RH Moisture content
0.1 6% (j) til o 0.12%
�
� 2l C 0.08% 2 c o (.) � ::l 0.04%�
� 0.00% 1 00Figure 3 . 1 2 - Rates of sorption of moisture onto crystalline lactose.
Because the rate of moisture sorption is of the same order of magnitude as the change in relative humidity in the bulk air, it is difficult to see the sorption process alone. To show that the sorption of moisture on to crystalline lactose is fast, the predicted moisture content based on the recorded sample chamber relative humidity was
against the moisture content observed in the experiment. In this way the bulk conditions and the state of the lactose can be compared directly. This is shown as Figure 3 . 1 3 . At the beginning of the trial, there was a slight delay in the response of the lactose weight to that of the air relative humidity. This is due to the time taken for diffusion of water vapour through the lactose bed.
0.25% �.20% � .52l 1: $0.15% c: o (J Q)
,a
0.10% .ra o � 0.05% 0.00% o 10 20 30 40 50 00 70 80 90 100 1 10 120 1 30 1 40 150 Time [mins]- Experimental Predicted using Isotherm
Figure 3.1 3 - Comparison of observed moisture content with that predicted from bulk air relative h�midity.
It is clear from this plot that the rate of sorption of moisture on to crystalline lacto e is fast. This is consistent with what is expected for physical adsorption onto a surface. If a Sherwood number of two is assumed, which corresponds to a stagnant system and hence the slowest system, then it can be predicted that the time constant for this process is of the order of less than a second (see Section 4.2.3 .2). It is evident that it can be assumed that the state of moisture in the voidage of lactose and the solid crystalline lactose phase are in equilibrium as long as thermal equilibrium has been reached. This equilibrium assumption was used in further modelling of moisture transport in crystalline
3.4.2 SORPTION ONTO AMORPHOUS LACTOSE:
Amorphous lactose is much more hygroscopic than crystalline lactose and, as such, has very different moisture sorption behaviour. Amorphous sugars have a large number of internal sites where moisture can be attached. In this way the amount of moisture that can be sorbed in amorphous lactose is much larger than that found on crystalline lactose. It was important to describe the rate of sorption of moisture into an amorphous lactose particle. Knowledge of sorption rates into purely amorphous samples will improve understanding of amorphous lactose crystallisation phenomena and allow the prediction of sorption rates on to partially amorphous lactose particles.
The experimental methodology outlined above for the measurement of sorption rates onto crystalline lactose samples was adopted for the quantification of sorption kinetics of amorphous lactose. A sample of spray-dried amorphous lactose was equilibrated over phosphorous pent oxide for one month to ensure a completely dry sample prior to the
sorption experiments. This sample was then placed in the rate measurement apparatus and the water vapour generator was set to give a chamber relative humidity of 43 . 5%
RH at 30°C. The weight of the sample was then logged and the moisture content change with time was calculated. The change in moisture content of the amorphous sample can be seen in Figure 3 . 14. (j) U) o 0.08
�
0.06 � -0 � C 0.04 Q) - c o o � .3 0.02 U) '0 � o o 5 1 0 Time [hr] 1 5 20Figure 3.1 4 - Rate of moisture sorption onto spray dried amorphous lactose subjected to a step change in relative humidity from a to 43.5% R H .
Because the time for sorption is much greater than that for pure adsorption on to a surface (see Section 3 .4. 1 ) it is clear that this is not the controlling mechanism for the moisture sorption process on to amorphous lactose. Several researchers interpret the high BET monolayer value obtained from amorphous glass isotherms as indicating large internal surface areas, suggesting a highly porous structure (Berlin et at. 1 973, Niediek and Babernics 1 979 and Flink 1 983). In the case of amorphous lactose however, it is clear that diffusion into the surface is the mode of moisture absorption into the particle. Adsorption of moisture is occurs only to the outer surface.
The rate of moisture gain shown in Figure 3 . 14 is the result of two competing rates.
Firstly, diffusion of water vapour must occur from the bulk air into the thin lactose bed. Secondly the water vapour is absorbed into the amorphous lactose particles. In order to estimate the diffusivity of moisture in the amorphous lactose particle it was therefore required to somehow differentiate between these two rate processes.
The rate of sorption into the spherical amorphous lactose particles can be
approximated as a reversible first order approach to an equilibrium moisture content.
d�
=D '(� - �)
=D I(y C
-0dt eq
where
�
is the mass average concentration of absorbed moisture in the amorphous particle,�.q
is the moisture concentration in equilibrium with the air moistureconcentration, C. D I is a constant to do with the rate of diffusion of moisture in the amorphous lactose and
y
is a constant to relate the concentration C to �eq. It can be shown that Y, the fractional unaccomplished change, can be related to the constantD'
and to the Fourier number by the following relationship.y e �D lt
L
6 e -(Tt_miFomel
(TC . m)2
(3. 1 3)If the second and subsequent terms are ignored (true for larger F 0), then it can be shown that D' � TC2DIR2, where D is the diffusivity of moisture in the amorphous matrix and R is the particle radius.
The problem then lies in how to deal with the diffusion through the lactose particle bed. By using Eq (3 . 1 2) to describe the rate of sorption into the amorphous particle, the experiment can be mathematically represented as;