Bubble plot

We thank Lori Giver, Seran Kim, and Phil Patten for critical input and Mark Welch for the bubble plot of subtilisins. 

An illustrative way to visualize the flow/toughness/heat balance is to view the key resin properties in a bubble plot as shown in Figure 15.9. It can easily be... 

Figure 15.9 Bubble plot of melt flow rate (bubble) versus Vicat heat distortion and notched Charpy...

Figure 47.5 is a two-dimensional (2D) bubble plot that illustrates another perspective of examining the relationship between the predictor variables and biomarker response. In essence, the hgure is a 2D representation of three-dimensional data. The baseline biomarker values are on the y-axis, C ax is on the x-axis, and... 

FIGURE 47.5 A two-dimensional (2D) bubble plot used to examine the relationship between the exposure metric (Cmax) and safety biomarker response. Active treatment subjects from studies 1 and 2 are denoted by Is and 2s, respectively, and p s are placebo subjects from both studies. The bubbles (open circles) indicate the safety biomarker responses and the severity of the response is depicted by the size of the circles. 

Figure 13 LCxGC-FID bubble plot relative to an experiment carried out on edible oil TAGS. The x-axis defines the LC fraction number, while the y-axis defines the TAG carbon number. The reconstructed LC chromatogram shows the saturated, mono-, di-, tri-, and higher-than-tri-unsaturated TAGs [48].

In the following we display several representations that depict aspects of the design meeting. Figure 4 is a bubble plot that illustrates the relative amounts of time that each of the group members spent on Broad, Close, and Group issues. 

To better understand individual contributions, the bubble plot shown in Figure 4 was created to illustrate the relative emphasis that each team member spent talking about Broad, Close, and Group issues. In the plot, each circle s area is proportional to the amount of time spent by each individual on those topics. A quick inspection... 

The bubble plot in Figure 4 showed that Sandra considered more Broad contextual issues than Close issues. The specific ratio of Broad to Close segments for Sandra was 2 1. The next closest team member s ratio was Rodney s which was 1 1. Obviously, the density of the segments marked on Sandra s timelines pale in comparison to those on Tommy s timelines (Fig. 7) or even to Patrick s in the next section. However, her importance to the team was not only the technical competence she possessed, but appears to have a lot to do with her ability to broaden the focus of the team s conversation and to represent important stakeholders in the design process. 

Fig. 4. Some of the post-processing plots available in Kimeme (a) 3D bubble plot (b) generation plot (c) matrix plot (d) box plot (e) parallel plot (f) PCA plot (g) 2D scatter plot (h) 2D scatter plot with probability density function (i) 3D scatter plot-...

A plot of (dP/dL)p/(dP/dL)sL versus (1-Rc) results in three distinct lines shown in Figure 27, where the values of the constants a and b are indicated. The three ranges correspond to approximately the bubble-slug, stratified, and annular flow regimes. Formulas to calculate for substitution into the above equation are ... 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

The maximum particle size obtained in an experimental study using a stirred tank (Figure 8.15) and bubble column (Figure 8.11c) respectively is plotted against the estimated average shear rate in Figure 8.17. 

This is close enough to 1,533 mm actual temperature might be 265°F, although plotted data are probably not that accurate. Because the feed enters at 158°F and its bubble point is 266°F, the feed is considered sub-cooled. 

Although each plot must be for a specific system of conditions, Figures 8-102 and 8-103 are extremely valuable in analyzing the action of a bubble tray. 

B. A second and also successful method accounts to a certain extent for the aeration effect, based on test data from many references. This method is not quite as conservative when estimating total tower pressure. This follows the effective head concept of Hughmark et al. [31]. Effective head, hg, is the sum of the hydrostatic head plus the head to form the bubbles and to force them through the aerated mixture. Figure 8-130 is the correlation for hg plotted against submergence, hji [31]. See Dynamic Liquid Seal. ... 

Figure 2.42 shows boiling curves obtained in an annular channel with length 24 mm and different gap size (Bond numbers). The heat flux q is plotted versus the wall excess temperature AT = 7w — 7s (the natural convection data are not shown). The horizontal arrows indicate the critical heat flux. In these experiments we did not observe any signs of hysteresis. The wall excess temperature was reduced as the Bond number (gap size) decreased. One can see that the bubbles grew in the narrow channel, and the liquid layer between the wall and the base of the bubble was enlarged. It facilitates evaporation and increases latent heat transfer. 

If a gas bubble adheres to an electrode surface being in contact with an electrolyte solution, the contact angle can be measured as an indicator of the interfacial tension and its change. The respective relationship is cos 6= (y ni - y,m)/ g,s with g, s, m referring to the gas, solution and metal phase respectively. It was initially observed by Mdller, that 6 changes with E [08M61]. Assuming that s and do not depend on the electrode potential a plot of relationship follows ... 

While in Fig. 16 selected results are plotted against the average energy density e = P/V9, in Fig. 17 all of the essential results for stirred tanks and bubble... 

Fig. 31. Maximum pressures produced throughout the bursting process plotted against bubble radius [118]...

Fig. 32. Maximum energy dissipation rates produced throughout the bursting process, plotted against bubble radius. The logarithmic scale indicates an exponential dependence of maximum stress on bubble radius for large bubbles. The slight drop in the data point for the smallest bubble as compared to the next smallest may be because of the difficulty in locating the exact place and time of the peak, due to large spatial and temporal gradients beneath the forming jet [113]...

Solution To determine the location of the azeotrope for a specified pressure, the liquid composition has to be varied and a bubble-point calculation performed at each liquid composition until a composition is identified, whereby X = y,-. Alternatively, the vapor composition could be varied and a dew-point calculation performed at each vapor composition. Either way, this requires iteration. Figure 4.5 shows the x—y diagram for the 2-propanol-water system. This was obtained by carrying out a bubble-point calculation at different values of the liquid composition. The point where the x—y plot crosses the diagonal line gives the azeotropic composition. A more direct search for the azeotropic composition can be carried out for such a binary system in a spreadsheet by varying T and x simultaneously and by solving the objective function (see Section 3.9) ... 

The system methanol-cyclohexane can be modeled using the NRTL equation. Vapor pressure coefficients for the Antoine equation for pressure in bar and temperature in Kelvin are given in Table 4.176. Data for the NRTL equation at 1 atm are given in Table 4.186. Assume the gas constant R = 8.3145 kIkmol 1-K 1. Set up a spreadsheet to calculate the bubble point of liquid mixtures and plot the x-y diagram. 

Figure 3.21 is a plot of bubble-to-slug transition lines for various test pressures ... 

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