Critical isotherms from virial series using asymptotically consistent approximants

The low‐density equation of state of a fluid along its critical isotherm is considered. An asymptotically consistent approximant is formed having the correct leading‐order scaling behavior near the vapor‐liquid critical point, while retaining the correct low‐density behavior as expressed by the virial equation of state. The formulation is demonstrated for the Lennard–Jones fluid, and models for helium, water, and n‐alkanes. The ability of the approximant to augment virial series predictions of critical properties is explored, both in conjunction with and in the absence of critical‐property data obtained by other means. Given estimates of the critical point from molecular simulation or experiment, the approximant can refine the critical pressure or density by ensuring that the critical isotherm remains well‐behaved from low density to the critical region. Alternatively, when applied in the absence of other data, the approximant remedies a consistent underestimation of the critical density when computed from the virial series alone. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3336–3349, 2014     

Model for the outer cavity of a dual‐cavity die with parameters determined by two‐dimensional finite‐element analysis

A coating die forms liquid layers of uniform thickness for application to a substrate. In a dual‐cavity coating die an outer cavity and slot improves flow distribution from an inner cavity and slot. A model for axial flow in the outer cavity must consider the ever‐present cross flow. A 1‐D equation for the pressure gradient for a power‐law liquid is obtained as a small departure from a uniform flow distribution and no axial flow. The equation contains a shape factor dependent on cavity shape, Reynolds number, and power‐law index. The shape factor for five triangular cavity shapes is obtained by finite‐element analysis and correlated for application to die design up to the onset of flow recirculation which arises at the junction of the cavity and outer slot. The performance of the combined cavity and slot is considered and the most effective design determined. © 2017 American Institute of Chemical Engineers AIChE J, 64: 708–716, 2018