Water pollution remains a critical concern, one necessitated by rapidly increasing industrialization and urbanization. Among the various strategies for water purification, membrane technology stands out, with polyethersulfone (PES) often being the material of choice due to its robust mechanical properties, thermal stability, and chemical resistance. However, PES-based membranes tend to exhibit low hydrophilicity, leading to reduced flux and poor anti-fouling performance. This study addresses these limitations by incorporating titanium dioxide nanotubes (TiO₂NTs) into PES nanofiltration membranes to enhance their hydrophilic properties. The TiO₂NTs, characterized through FTIR, XRD, BET, and SEM, were embedded in PES at varying concentrations using a non-solvent induced phase inversion (NIPS) method. The fabricated mixed matrix membranes (MMMs) were subjected to testing for water permeability and solute rejection capabilities. Remarkably, membranes with a 1 wt% TiO₂NT loading displayed a significant increase in pure water flux, from 36 to 72 L m² h⁻¹ bar⁻¹, a 300-fold increase in selectivity compared to the pristine sample, and a dye rejection of 99%. Furthermore, long-term stability tests showed only a slight reduction in permeate flux over a time of 36 h, while dye removal efficiency was maintained, thus confirming the membrane’s stability. Anti-fouling tests revealed a 93% flux recovery ratio, indicating excellent resistance to fouling. These results suggest that the inclusion of TiO₂ NTs offers a promising avenue for the development of efficient and stable anti-fouling PES-based membranes for water purification.

In this article, the attenuation of fluid–structure coupled modes of non-planar waveguide involving cavities is discussed. The physical problem is modeled to illustrate the scattering behavior of acoustic waves in a flexible waveguide composed of thin elastic elements having edges or joints and structural discontinuities. The fluid–structure coupled waveforms scatter after interacting with the discontinuities and edges of the underlying structure. An appropriate choice of edges offers scattering or resonance processes, which also guide fluid–structure coupled waves. The mode-matching technique, together with low-frequency approximation, is used to determine velocity potentials. The guiding structure is then analyzed and validated through scattering energy functionals by varying the dimensions of the cavities and the wave frequency. The results are formulated and analyzed by tuning the device using an appropriate choice of edge conditions, dimension of cavities, and wave frequencies, thereby validating the obtained solutions. These descriptions are very useful for the active control measure of structural vibrations.

This article discusses the modal behavior of elastically constrained beams under various types of foundations and provides insights into the effects of different factors on the eigenfrequencies of beams. Numerical and analytical techniques, specifically the Galerkin finite element method (GFM) and the separation of variables, are utilized to determine the eigenfrequencies and mode shapes of beams. Modal analysis of Timoshenko, shear, Rayleigh, and Euler-Bernoulli beams that are elastically constrained and resting on Winkler, Pasternak, and Hetényi foundations, considering non-classical boundary conditions, is included in the study. The effects of factors such as flexural rigidity, transverse modulus, and Winkler foundation constant on natural frequencies of different beam models are investigated. The proposed method efficiently converges to the exact solution without shear locking in the stiffness element. The results demonstrate that the natural frequencies of the beam rise because of the shear layer, flexural rigidity, and foundation constant. Furthermore, the Hetényi elastic foundation affects the natural frequency of the beam, depending on the relative values of beam stiffness and foundation stiffness. Additionally, incorporating both shear deformation and rotary inertia has a greater impact on the eigenfrequencies of Euler-Bernoulli beams compared to incorporating only one of these effects. The findings of this work provide valuable insights into the behavior of beams under different foundation conditions and have potential applications in the design and optimization of structures incorporating beams, thereby enhancing the understanding of beam analysis.

Steady and unsteady flow of a second grade MHD fluid in a porous medium with Hall current effects is studied. Assuming an à priori known vorticity proportional to the stream function up to an additive uniform stream, exact solutions for velocity field are obtained corresponding to different choices of pertinent flow parameters. Graphical results are presented to depict the influence of pertinent flow parameters on the considered MHD flow.

The present article highlights the acoustic waves scattering in a trifurcated waveguide containing compressible fluid together with step discontinuities and change of bounding material properties. The study is important because of its applications in active noise control measures, especially used to control the low-frequency noise and related vibrations. The governing boundary value problem is solved by using the mode-matching technique. The solution is developed for the analysis of symmetric, uniform, and non-uniform cross-sections. The solution procedure begins by determining the expanded form of field potentials in various duct regions of the waveguide. Then, the pressures and the normal velocity modes across the waveguide regions are matched at interface. The energy flux against frequency and various duct configurations is plotted. The solution is validated altogether through the apposite analytical and numerical results.