Extended law of corresponding states: square-well oblates

The vapour-liquid coexistence collapse in the reduced temperature, Tr=T/Tc, reduced density, ρr= ρ/ρc, plane is known as a principle of corresponding states, and Noro and Frenkel have extended it for pair potentials of variable range. Here, we provide a theoretical basis supporting this extension and show that it can also be applied to short-range pair potentials where both repulsive and attractive parts can be anisotropic. We observe that the binodals of oblate hard ellipsoids for a given aspect ratio (κ=1/3) with varying short-range square-well interactions collapse into a single master curve in the Δ B*2--ρr plane, where Δ B*2= (B2(T)-B*2(Tc))/v0, B2 is the second virial coefficient, and v0 is the volume of the hard body. This finding is confirmed by both REMC simulation and second virial perturbation theory for varying square-well shells, mimicking uniform, equator, and pole attractions. Our simulation results reveal that the extended law of corresponding states is not related to the local structure of the fluid.

New corresponding states correlation for the temperature-dependent surface tension of refrigerant liquids

We collected data of the surface tension versus the temperature of 28 saturated refrigerant fluids available in the NIST database. These data are used to build a new corresponding state-based correlation. Compared with other previously proposed correlations, the current one has the advantages of both simplicity and accuracy. To check the ability of correlations, we compared the numerically calculated/predicted results with the data in the NIST database. It is found that the average absolute deviations are less than 10% for 26 refrigerants and less than 1% for 8 refrigerants.

Synchronization of N-Non-Linear Slave Systems with Master System Using Non-Adaptive and Adaptive Coupled Observers

Synchronization of N-slave chaotic systems with a master system is a challenging task, particularly in recent times. In this paper, a novel methodology is proposed for synchronizing the N number of slave systems with a master system. The proposed methodology is based on coupled adaptive synchronous observers. The difference between the corresponding states of master and slave systems is converged to the origin by means of a novel feedback control scheme to achieve synchronization between the master and slave systems. The efficacy of the proposed methodology is verified through a simulation of FitzHugh–Nagumo non-linear systems in MATLAB. The simulation results validate and prove claims, and these systems are successfully synchronized by CCS and CCAS observer-based control.

A Two-Parameter Corresponding States Method for Calculating the Steady-State Evaporation Rate of C2–C9 n-Alkane Droplets in Air for Elevated Pressures and Temperatures

Advanced gas turbine and internal combustion engine combustion chambers operate at highly elevated pressures and temperatures. Therefore, spray vaporization analysis cannot be limited to the atmospheric environment since evaporation strongly depends on ambient conditions. Presently, the effect of air pressure and temperature on droplet evaporation rate was investigated by using both a transient and a steady-state approach. A corresponding states model was derived for the steady-state evaporation rate for n-alkanes in the range of C2–C9 with an excellent fit quality and < 1% model uncertainty, considering the thermophysical data uncertainties. The model was tested for C1, C10, and C12 n-alkanes as well with low success. The ambient conditions were evaluated in terms of reduced pressures and temperatures, covering the range of 0.02–0.5 and 1.2–1.5, respectively. However, the applicability of the model was limited to reduced temperature of 1.3–1.5, as higher discrepancy was observed between the trends of the different n-alkanes at lower temperatures. Since the heat-up phase of practical sprays in combustion chambers is often short, the present model might significantly reduce the computational effort required for liquid evaporation calculations.