Based on the biochemical theory of multiple ligand-receptor complexes (Klotz (1946)) a sigmoidal proceeding adsorption isotherm is derived. The special case of an arbitrarily large number of equal interaction sites and a separate one yields an equation which corresponds to the ζ-isotherm, disparately derived by Ward et al. (2007) for surface tension of solid-fluid interfaces. From the mathematical point of view it is analogous to the BET-isotherm for a limited number of adsorption layers (1938). It is shown that the isotherm maps type IV and V isotherms. The isotherm is compared with others including the type IV isotherm of Do and Do (2009). The present isotherm is unified in contrast to existing hybrid models. It is successfully applied to numerous literature data concerning the adsorption of water on microporous carbon and aluminophosphate molecular sieves.

https://pubs.rsc.org/en/content/articlepdf/2019/cp/c8cp07751g

Modeling of type IV and V sigmoidal adsorption isotherms

The flow in a completely filled rotating cylinder driven by the counter-rotation of the top endwall is investigated both numerically and experimentally. The basic state of this system is steady and axisymmetric, but has a rich structure in the radial and axial directions. The most striking feature, when the counter-rotation is sufficiently large, is the separation of the Ekman layer on the top endwall, producing a free shear layer that separates regions of flow with opposite senses of azimuthal velocity. This shear layer is unstable to azimuthal disturbances and a supercritical symmetry-breaking Hopf bifurcation to a rotating wave state results. For height-to-radius ratio of 0.5 and Reynolds number (based on cylinder radius and base rotation) of 1000, rotating waves with azimuthal wavenumbers 4 and 5 co-exist and are stable over an extensive range of the ratio of top to base rotation. Mixed modes and period doublings are also found, and a bifurcation diagram is determined. The agreement between the Navier–Stokes computations and the experimental measurements is excellent. The simulations not only capture the qualitative features of the multiple states observed in the laboratory, but also quantitatively replicate the parameter values over which they are stable, and produce accurate precession frequencies of the various rotating waves.

Instability and mode interactions in a differentially-driven rotating cylinder

Numerical study on combined buoyancy–Marangoni convection heat and mass transfer of power-law nanofluids in a cubic cavity filled with a heterogeneous porous medium

Entropy generation and natural convection of nanoparticle-water mixture (nanofluid) near water density inversion in an enclosure with various patterns of vertical wavy walls

Review article: Microscale evaporative cooling technologies for high heat flux microelectronics devices: Background and recent advances

Three-dimensional thermocapillary–buoyancy flow of a binary mixture with Soret effect in a shallow annular pool

Flow pattern transition of thermal–solutal capillary convection with the capillary ratio of −1 in a shallow annular pool

We use the Zeta adsorption isotherm and propose a method for determining the conditions at which an adsorbed vapour becomes an adsorbed liquid. This isotherm does not have a singularity when vapour phase pressure, PV, is equal to the saturation-vapour pressure, Ps, and is empirically supported by earlier studies for PV < Ps. We illustrate the method using water and three hydrocarbon vapours adsorbing on silica. When the Zeta isotherm is combined with Gibbsian thermodynamics, an expression for γSV, the surface tension of the solid–vapour interface as a function of xV(≡PV/Ps) is obtained, and it is predicted that adsorption lowers γSV from the surface tension of the substrate in the absence of adsorption, γS0, to that at the wetting condition. The wetting hypothesis indicates that γSV at wetting, xVw, is equal γLV, the surface tension of the liquid–vapour interface. For water vapour adsorbing on silica, adsorption lowers γSV to γLV at xVw equal unity, but for the hydrocarbons heptane, octane and toluene adsorbing on silica xVw is found to be 1.40, 1.30 and 1.32 respectively.

Chun-Mei Wu

Papers

Three-dimensional thermocapillary–buoyancy flow of a binary mixture with Soret effect in a shallow annular pool

Flow pattern transition of thermal–solutal capillary convection with the capillary ratio of −1 in a shallow annular pool

Prediction of the wetting condition from the Zeta adsorption isotherm.

Experimental investigation on the effect of crystal and crucible rotation on thermocapillary convection in a Czochralski configuration

Flow state multiplicity in Rayleigh–Bénard convection of cold water with density maximum in a cylinder of aspect ratio 2