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| Issue 28 |  |
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| Category | Title | Author | ||
| Guest Article | Ultrasonic velocity measurements of the shelf-life of topical formulations | Rolf Daniels |
Ultrasound techniques use the interaction of high-frequency sound waves with matter, in order to generate information about the physico-chemical properties. Such measurements have been established in numerous areas, like medicine, oceanography or material sciences. Therefore it became obvious to use ultrasound measurements to characterize also other systems, e.g. topical formulations. A number of publications could already demonstrate that ultrasound can be successfully used to measure the average particle size, the creaming, the crystallization and the aggregation in dispersed systems.
Basic principles
Ultrasound means acoustic signals in the frequency range from 10 kHz up to approx. 30 MHz. When such a sound wave propagates in a material it forces particles to oscillate. They oscillate around their equilibrium positions with a frequency equal to that of the ultrasonic wave. The movement can be parallel to the direction of propagation, so that the sound wave generates a compressional wave. If the movement is be perpendicular to the direction of propagation, a shear wave is generated (Figure 1).
| Fig. 1: |
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Schematic
representation of the propagation of an ultrasonic wave through
a material. F(t) is a high-frequency, sinusoidal force acting parallel
or perpendicular to the surface of a sample.
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An ultrasonic wave is characterized by its amplitude, frequency, wavelength, and attenuation coefficient. The first two are predetermined by the investigator whereas the latter two depend on the material through which the ultrasonic wave is passing. As the ultrasonic velocity is the product of wavelength and frequency, it is also characteristic of a particular material.
Measurable parameters
Ultrasound measurements make use of three different parameters:
- Ultrasonic velocity
- Attenuation
- Impedance
The velocity of an ultrasonic wave through a material depends on its physical properties. For weakly attenuation materials a simple relationship can be derived:
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where c is the ultrasonic velocity,
is the density and E is the elastic modulus (YOUNG modulus).Hence, the ultrasonic velocity increases with decreasing density and increasing resistance to deformation. Since differences in the elastic moduli of materials are greater than those in density, the ultrasonic velocity is more influenced by the former quantity than by the latter. Moreover, the ultrasonic velocity through a material depends strongly on the temperature. The velocity through water and electrolyte solution increase with increasing temperature whereas that through oil shows a negative temperature coefficient (Figure 2).
| Fig. 2: |
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Ultrasonic
velocity measured in different materials as a function of temperature
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Experimental techniques
Ultrasonic measurements can be performed using either pulsed or continuous wave ultrasound. Most commercial applications use pulse techniques because such instruments are easy to operate, the measurements are non-invasive, rapid, and can readily be automated.
The simplest and most widely used technique to measure ultrasonic velocity is the so-called pulse-echo technique. Figure 3 displays schematically a typical experimental set-up.
| Fig. 3: |
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Typical
experimental set-up for an ultrasonic measurement using the pulse-echo
technique
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A signal pulse propagates through a sample with the path length d and is reflected at the opposite wall of the cell producing an echo. Each echo travels a distance equal to twice the cell length d before it reaches again the transducer (Figure 6). By measuring the time delay between two echoes t the ultrasonic velocity c can be calculated according c = 2d/t.
| Fig. 4: |
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Determination
of the ultrasonic velocity c through a sample using the pulse-echo
technique: c = 2d/t
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Applications
Determination of disperse phase volume fraction
This application makes use of the fact that the ultrasonic properties of an emulsion or suspension vary significantly with varying disperse phase volume fraction. This implies, however, that a significant difference between the ultrasonic velocity of the continuous and the disperse phase exists at a certain measuring temperature (compare Figure 2). Such measurements for the determination of the disperse phase volume fraction can be evaluated using a simple mathematical equation, often referred to as the URICK equation, which relates the ultrasonic velocity c to
the disperse phase volume fraction: |
where
is the density, and 
the adiabatic compressibility. The subscripts 1 and 2 refer to the continuous
and dispersed phases, respectively.The URICK equation, however, neglects scatter of ultrasound which takes place in most real systems. Thus, more precise evaluation needs sophisticated modifications of that simple relationship.
Figure 6 illustrates the ultrasonic velocity through a typical water-in-oil emulsion in dependence from the oil content.
| Fig. 6: |
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Variation
of the ultrasonic velocity with disperse phase volume fraction of
a sunflower oil-in-water emulsion at 20 °C (after [1]).
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Determination of creaming in emulsions
As the continuous and disperse phases have different densities, emulsions show phase separation. In an oil-in-water emulsion the droplets of the usually less dense oil phase move upwards under the influence of gravity and form a cream layer. In contrast, the water droplets in water-in-oil emulsions move downwards due to their higher density compared to the continuous oil phase. They form a sediment. Thus an initially (t = t0) uniformly dispersed emulsion separates with time (t = tx). The disperse phase volume fraction varies as a function of sample height and time. This can be measured easily by ultrasonic measurements when the velocity in a sample cell is determined as a function of height and time (Figure 7).
| Fig. 7: |
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| big version |
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| big version |
| Ultrasonic measurement to characterize the creaming in oil-in-water emulsions. The disperse phase volume fraction as a function of time t and sample height x can be calculated according to the URICK equation. |
For sufficiently precise ultrasonic measurements it is always necessary to carefully control the temperature. In practice, deviations of less than 0.1 °C are intended. Moreover, the sample cells have to be calibrated, i.e. the cell length as a function of height has to be determined. This calibration preferentially uses the double-echo technique with water-filled sample cells. Since the ultrasonic velocity of water is known the cell length can be calculated from the time delay between the first and the second echo (Figure 8). Under such conditions ultrasonic measurements can be performed very precisely, i.e. the ultrasonic velocity (approximately 1500 m/s) can be measured easily with a precision of 1 m/s.
| Fig. 8: |
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Double-echo
technique for cell calibration of the acoustiscan ultrasonic profiler
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For serial investigations the method can be fully automated. The experimental set-up is given schematically in Figure 9. A carousel automatically positions up to 6 sample cells to the site of measurement. There, a transducer pair (transmitter and receiver) is vertically positioned by a stepper motor drive in 1 mm steps. The measurement uses the pulse-echo technique. Data are evaluated automatically with an EXCEL© based computer programme.
| Fig. 9: |
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Schematic
top view of the acoustiscan ultrasonic profiler which allows automatic
determination of the creaming profiles of max. 6 sample cells
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Figure 10 shows some typical results obtained with such an instrument. The samples used are HPMC-stabilized (Hydroxypropylmethylcellulose) hydro-dispersion gels. These systems display different shelf-lives in dependence of the substitution type of HPMC used: Hydro-dispersion gels with HPMC 2906 show no changes in disperse phase distribution within 4 weeks storage in a temperature cycling test (-5/+40 °C). Formulations using HPMC 2208 show first incidence of creaming after one week. This sign of instability becomes more and more obvious during the following weeks. Rapid creaming characterizes systems with HPMC 2910. These hydro-dispersion gels show almost complete phase separation after one week storage.
| Fig. 10: |
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Ultrasonic
profiles of hydrodispersion gels consisting of 20 % neutral oil
(INCI: Caprylic/Capric Triglyceride) and 2.5 % aqueous HPMC solution
(INCI: Hydroxypropyl Methylcellulose) in dependence from the substitution
type.
A: MHPC 2906 B: MHPC 2910 C: MHPC 2208 |
Particle sizing
A further application prospect of ultrasonic measurement is the in situ particle size measurement. This field of application makes use of the fact that at a distinct phase volume fraction the ultrasonic velocity and attenuation varies with particle size and frequency (Figure 11).
| Abb. 11: | |
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(A)
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(B)
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| Velocity (A) and attenuation (B) of ultrasonic waves as a function of particle size, frequency, and disperse phase volume fraction. | |
Particle size distribution can be calculated from the raw data through complex mathematical algorithms when several physical constants of the system are known.
References
- Dickinson E., McClements D.J.: Advances in Food Colloids. London: Blackie Academic & Professional 1995. 178 - 210.
- Froysa K.E.; Nesse O.: Ultrasonic characterization of emulsions. In J. Sjöblom: Emulsions and Emulsion Stability. Marcel Dekker, New York, 1996, 437 - 468.
- Howe A.M., Mackie A.R. und Robins M.M.: Technique to measure emulsion creaming by velocity of ultrasound. J. Dispersion Sci. Technol. 7, 231 - 243 (1986)
- Pinfield V.J., Dickinson E. und Povey M.J.W.: Modeling of concentration
profiles and ultrasound velocity profiles in a creaming emulsion: Importance
and scattering effects.
J. Colloid Interf. Sci. 166, 363 - 374 (1994)
- Povey M.J.W.: Ultrasound studies of shelf-life and crystallization.
In: New physico-chemical techniques for the charaterization of complex
food systems (Ed.: E. Dickinson). London: Blackie Academic & Professional
1995, 196 - 213.