In order to access the physics of the sensor concept and check the transferability of the simulation approach, an analysis of the simulation’s input parameter is performed regarding their sensitivity towards the transmission and the signal features.
As initial settings, the reference geometry is chosen to match the experimental conditions, and the channel aspect ratio is set to be unity to avoid major discrepancies concerning the simplified disperse phase shape. The actual physical channel dimensions are considered not to be of importance due to the geometrical scalability of the entire constellation. By definition, the received position dependent signals are normalized to the disperse phase (high level - 1) and the continuous phase (low level - 0) to establish a good comparability with the experiment. This convention is used for all further parameter studies.
Fig. 3.9.: a) Relative numerical error ϵrel
ud of the slope derivation algorithm for various initial scal- ing velocities uinit
d b) Plausibility proof of simulation algorithm. Comparison between system water/n-dodecane ( ) and disabled absorption and refraction ( ). Minor deviations from the expected straight dashed line are observable. The deviation occurs due to trigonometrical roundup error at flat angle of incident for light rays hitting the droplet
Since flow conditions affect the disperse phase cap geometry, the front end of the droplet stretches while the rear compresses (Taha and Cui, 2006) due to inertial effects. The parameter is varied for Cad-numbers up to 0.5 according to the proposed correlation
(acap,b“ r0.4..1.0s). Values acap,bą 1 are just mentioned to identify the optical coherences.
In real flows the only appear at the front cap.
The on- and offset of the signal appears to be independent of the cap curvature while the signal peaks change significantly. While sharper caps (aspect ratio acapě 1) form the largest
focus points and therefore the highest signal peaks, all other geometries distribute the light over a larger area (Fig. 3.10 a) ). At half level 0.5 between high and low level, the signal slope decreases with reduced aspect ratio. This appears to be counterintuitive since one would expect that a shorter the cap results in a steeper signal slope.
The aperture diameter within the sensor’s light path affects the detectable amount of light. The minimum diameter of dap= 0.55 wChannelensures a reasonable amount of transmitted
energy. The maximum diameter is considered to be dap = 0.85 wChannel since intensity
Fig. 3.10.: Normalized transmission for different droplet configuration in the sensitivity analysis.a) Influence of the disperse phase cap geometry acap,bon the resulting NIR transmission signal. Despite the smaller dimension of the compressed disperse phase back, the slope decreases due to the interplay of shape a focal effect. Elongated high aspect ratio caps generate sharper focus points and result in a steeper signal. acap,b“ 1.2 ( ) acap,b“ 1.0 ( ) acap,b“ 0.8 ( ) acap,b“ 0.6 ( ) acap,b“ 0.4 ( )b) Influence of the aper- ture diameter on the resulting NIR transmission signal. The aperture restricts the amount of stray light, thus enhances the signal to noise ratio. Smaller apertures produce higher relative peak values due to the chosen signal normalization convention. dap“ 0.85wch ( ) dap “ 0.75wch( ) dap “ 0.76wch( ) dap “ 0.55wch ( )c) Influence of the refractive index difference ΔRI* = (RI
c-RId) on the resulting NIR transmission
signal. system water/n-dodecane ΔRI*=-0.08 ( ) ΔRI*=-0.053 ( ) ΔRI*=-0.027 ( ) ΔRI*=0 due to a matched refractive index no peaks appear ( ). The signal
peaks seem to increase with a RI*, but this is based on the signal normalization. Higher RI* lead to large peaks in the not normalized signal, but are also increasing the disperse phase transmission plateau because of light focusation crosswise the channeld) Influence of the absorption difference Δk*= (k
c-kd)/kcon the resulting NIR transmission signal. Δk*=1
( ) Δk*=0.66 ( ) Δk*=0.33 ( ) Δk*=0 ( ). Variations in the absorption
difference of both phases lead to changes in the slope and signal peak in the normalized signal. The peak level in the original signal remains constant because it only depends on the refractive index difference
The size of the aperture strongly influences the normalized signal (Fig. 3.10 b) ). The smaller the aperture, the more pronounced is the influence of the focus points. The absolute light level decreases with reduced diameter, while the focus points cause a relative exaggeration
of the peak intensity. The signal minima decrement significantly, due to refraction at the disperse phase interface.
Regarding accuracy, a moderate slope is preferable. However, a wider section of the microchannel resulting in less slope change is not preferable, since the large aperture leads to a low signal to noise ratio: Transmitted light from both the interfacial droplet cap area and the cylindrical part enters the detector as well as additional stray light. Contrarily, a smaller aperture shows significant slope differences at the droplet caps due to the large refraction influence.
The clear signal sensitivity to the aperture diameter implies the importance of uniform size throughout the measurement. An aperture diameter of 0.65 wChannelfor both simulation
and experiment has been chosen to implement a good trade-off between the signal slope steadiness and an overall low signal to noise ratio.
Analog to the variation of aperture diameter the refractive index of the disperse phase is changed from the experimental difference applied (n-dodecane/water) towards a refractive index match. The transmission signal shows significant changes in the signal’s high and low peaks and a strong influence of the refractive index can be observed (Fig. 3.10 c) ). In the case of matched refractive indices, a light transmission difference between both phases is visible due to the absorption properties of the liquids. This showcases the capability of the NIR-sensor to even work under difficult optical conditions (RI-matching). Under those circumstances, the characteristic signal peaks vanish and the signal transition between the two levels appears to be steady and almost symmetric.
The absorption difference between both phases has a defined influence on the absolute transmission signal strength, which results especially in a higher signal strength for the disperse phase in case of lower absorption. In the normalized signal, this behavior shows as lower signal peaks and a flattened slope, although the refractive index itself influences the heights of the peaks (Fig. 3.10 d) ). Thus a larger difference in the absorption of both phases improves the slope characteristics.
The sensitivity analysis clarifies, that the influences on the transmission signal are mainly related to flow invariant properties such as experimental design and material properties. The only velocity dependent parameter is identified to be the droplet shape and therefore the cap aspect ratio (Fig. 3.10 a) ). The front shape is more sensitive to the flow conditions than the disperse phase rear. Thus, to determine a suitable signal section, it is more accurate to consider the rear cap for the slope derivation. The remaining error due to changes in the assumed droplet shape is discussed in the next chapter.