Biomedical Engineering Reference
In-Depth Information
Extracted viscosities from impedance measurements along reported values of the liquid
viscosities are illustrated in Figure 3.
Liquid viscosities were estimated from Equations 7 and 8 but better accuracy was obtained
with Equation 7 that was derived for waveguides containing liquids (Mert et al., 2004).
Results of the calculated viscosities are illustrated in Figure 3.
2.1.2 Flexible wall containers
When the walls of the waveguides are not rigid, during propagation of the waves the walls
of the container expand and the overall liquid bulk modulus decreases leading to reduced
sound velocity in the liquids. In addition, the fluid velocity cannot be assumed to be 0 at the
can wall due to the expansion of the wall. These conditions make the governing equations
used to estimate the wave attenuation and other relevant acoustic parameters very elusive,
thus it is not possible estimate the liquid viscosity directly. One can overcome this problem
by an empirical approach, which is by defining the quality factor
Q
, which is determined
from the following equation:
o
Q
(9)
2
1
and are the frequencies at which the amplitude of mechanical impedance response is
equal to half the actual value at resonance and is the resonance frequency (Kinsler et al.,
2000). If the quality
Q
is known in a given container-liquid system it would be possible to
have an estimation of the viscosity of the liquids contained in the container, which would
serve for quality control purposes. To prove that concept Mert and Campanella (2007)
performed a study where a shaker applied vibrations to a cylindrical can containing a liquid
using a system, schematically shown in Figure 1. The vibration was able to move the can
containing the liquid, and a wave was generated through the liquid, which reflected back in
the interface between the liquid and the headspace to form standing waves resulting from
composition of the forward and reflected wave. Properties of the standing waves were
measured in the frequency domain, and in particular the resonance frequency and the
amplitude of the wave at that resonant frequency were obtained and using a calibration
curve approach related empirically to the rheological properties of the liquid. It is important
to note that these measurements do not provide the true viscosity of the testing liquid
because the walls of the can are not rigid and deform significantly due to the vibration.
Despite of that the properties of the standing waves, measured by the quality
Q
, were highly
correlated with the rheology of the liquid, which was tested offline in a rheometer (Mert and
Campanella, 2007). Results shown in Figure 4 are a frequency spectra for the liquids
reported in Table 1.
Quality factors
Q
for the testing liquids can be estimated from the two peaks observed in
Figure 4 and potted as a function of the liquid viscosity as illustrated in Figure 5. However,
as shown in Figure 4, the first resonances peaks do not seem to provide sufficient resolution
and the second resonance peaks, at higher frequency, are used to find a relationship with
the liquid viscosity.
Although interesting from an academic standpoint correlations like the one shown in the
Figure 5 are not of practical applicability. However, if the can/cylinder contains a product
