Path Processes

Path-dependent properties are a function of the sequencing of the transition steps from an initial to a final state, and it is only when each event is enacted in an identical way that the integrals of path-dependent functions are themselves identical. 

Different polysaccharide variable-path processes were observed in a pectin-sugar-water-acid mixture dispersed at 105°C then cooled to 25°C, and a mixture dispersed at 50°C then cooled to 25°C. The higher-temperature gel was relatively stable, but the lower-temperature gel was unstable (Walter and Sherman, 1986). Heated agar sols gel when cooled to approximately 30°C, and they remain dimensionally stable to a reheating temperature of 85°C due to relatively permanent physical crosslinks below Tm (Lips et al., 1988). The reheated gels follow a hysteretic pathway to melting at the 

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FIG. 22-75 Air fractionation by membrane. O2 in retentate as a function of feed fraction passed tbrougb tbe membrane (stage cut) showing tbe different result with changing process paths. Process has shell-side feed at 690 kPa (abs) and 298 K. Module comprised of hollow fibers, diameter 370 im od X 145 im id X 1500 mm long. Membrane properties (X = 5.7 (O2/N2), permeance for O2 = 3.75 X 10 Barrer/cm. Coutiesy Innovative Membrane Systems/ Fraxair)... 

Figure 6.12. p-V diagram showing actuai and assumed path process for a bursting sphere (Adamczyk 1976). 

When separating volatile components such as a single stream from low-volatility bottoms, use a molecular or unobstructed path process, either thin film or batch. 

If one or all of the intermediate states of a path, process, or reaction are not equihbrium states, then the path is regarded as irreversible. See Nonequilibrium Thermodynamics (A Primer)... 

Short-path process from raw material to final product... 

Moving from long to short lead-times - Overall lead-time is composed of individual cycle-times for multiple processes. This step involves shortening the cycle-time at each step in the critical path processes from the point of purchase to the start of production for the entire supply chain. 

The critical-path processes "Procurement Part 1395" and "Sawing" are scheduled in the past. 

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