Directional property abscissas

The terminal velocity of liquid drops is the same as solid spheres when the diameter is small. The drag coefficient versus Reynold s number can be recalculated to provide a diameter-free ordinate versus a velocity-free abscissa to facilitate direct solution, as shown in Fig. 15. With drops, a maximum velocity is attained, and this maximum has been correlated with a parameter based on physical properties of the system. 

The major goal of The direct quadrature method of moments (DQMOM) was to derive transport equations for the weights w and abscissas that can be solved directly and which yield the same moments nk without resorting to the ill-conditioned PD algorithm. Another novel concept imposed is that each phase can be characterized by a weight w and a property vector )i, thus the DQMOM can be employed solving the multi-fluid model describing multi-phase systems. Moreover, since each phase has its own momentum balance in the multi-fluid model, the nodes of the DQMOM quadrature approximation are convected with their own velocities. The DQMOM was proposed by Marchisio and Fox [143] and Fan et al. [53] in order to handle poly-dispersed multi-variate systems. 

In determining creep properties, a series of specimens are subjected to static loads at different levels and their increase in strain over time is measured. Data may be either presented directly as creep strain on a logarithmic time scale, as creep modulus c(t)= isochronous stress—strain diagrams where the relation between stress on the axis of ordinates over strain on the axis of abscissa is presented for different time levels. The schematic approach to converting creep data into an isochronous stress-strain diagram is illustrated in Fig. 34.7. 

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