Foam drainage equation in fractal dimensions: breaking and instabilities.

This paper is concerned with the construction of a phenomenological model for drainage of a liquid in foam in fractal dimensions. Our model is based on the concepts of "product-like fractal measure" introduced to model dynamics in porous media and "complex fractional transform" which converts a fractal space on a small scale to a smooth space with a large scale. The solution of the fractal foam drainage equation has been approximated using the He's homotopy perturbation method. Qualitative analysis shows that the behavior of the solitonic wave in fractal dimensions differ from the behavior in integer dimensions. This deformation generates instabilities in the foam dynamics, dispersion and spontaneous breaking of the solitonic wave.

Numerical Analysis of an Unsteady, Electroviscous, Ternary Hybrid Nanofluid Flow with Chemical Reaction and Activation Energy across Parallel Plates.

Despite the recycling challenges in ionic fluids, they have a significant advantage over traditional solvents. Ionic liquids make it easier to separate the end product and recycle old catalysts, particularly when the reaction media is a two-phase system. In the current analysis, the properties of transient, electroviscous, ternary hybrid nanofluid flow through squeezing parallel infinite plates is reported. The ternary hybrid nanofluid is synthesized by dissolving the titanium dioxide (TiO2), aluminum oxide (Al2O3), and silicon dioxide (SiO2) nanoparticles in the carrier fluid glycol/water. The purpose of the current study is to maximize the energy and mass transfer rate for industrial and engineering applications. The phenomena of fluid flow is studied, with the additional effects of the magnetic field, heat absorption/generation, chemical reaction, and activation energy. The ternary hybrid nanofluid flow is modeled in the form of a system of partial differential equations, which are subsequently simplified to a set of ordinary differential equations through resemblance substitution. The obtained nonlinear set of dimensionless ordinary differential equations is further solved, via the parametric continuation method. For validity purposes, the outcomes are statistically compared to an existing study. The results are physically illustrated through figures and tables. It is noticed that the mass transfer rate accelerates with the rising values of Lewis number, activation energy, and chemical reaction. The velocity and energy transfer rate boost the addition of ternary NPs to the base fluid.

High-precision grating period measurement.

We introduce a method for measuring a periodic structure, particularly a grating period. The method is based on the high-precision laser Talbot effect. The combination of a rubidium-locked external cavity diode laser and the Talbot interferometer provides an excellent and simple tool for this purpose. Some experimental results are provided to demonstrate the approach.