This study uses the singular perturbation method to analyze the streaming flow around a pulsating bubble at the velocity antinode of a standing wave. The bubble radially and laterally oscillates with small nondimensional amplitudes of $\stackrel{`}{\epsilon }$ and $\epsilon ,$ respectively. The momentum equation is expanded using $\epsilon$ . The frequency parameter $\left|M\right|$ , which is the ratio of the bubble radius to the viscous length, is included in the expanded equations as $O\left({\left|M\right|}^{-1}\right)$ . Four boundary conditions are solved: non-pulsating and pulsating assuming no-slip and shear-free boundaries. For the non-pulsating bubble, the streaming is on the order of $O\left({\left|M\right|}^{-1}\right)$ for the shear-free boundary. The flow has a quadrupole pattern, with direction from the equator to the poles. However, for the non-pulsating bubble with the no-slip boundary, the flow pattern is from the poles to the equator and the direction reverses after a critical value of $\left|M\right|=13.3$ . When bubble pulsation is introduced, the intensity of the streaming increases and is proportional to $\left|M\right|$ . The flow pattern is dipole with a direction from the south to the north pole for the shear-free boundary. For the non-slip boundary, the flow is quadrupole for small values of $\left|M\right|$ and varies with the phase shift $\varphi$ . As $\left|M\right|$ increases, the flow intensifies and becomes dipole. For both cases, the maximum velocity is at the phase shift angle $\varphi =135°$ and $\left|M\right|=10$ .

The lack of freshwater in the world requires a paradigm shift from linear water consumption to resilient and low-energy desalination technologies. Although reverse osmosis (RO) is the standard in the industry, its usefulness is essentially constrained by concentration polarization (CP) and non-useful hydraulic pressure losses. This paper applies a high-fidelity computational model in ANSYS Fluent 2022 R1 to conduct a comparative parametric evaluation of hexagonal and sinusoidal feed-spacer geometries relative to a baseline grid configuration. The solute concentration gradients at the fluid–membrane interface were solved using a 3D species transport model, which was optimized using one-micron near-wall inflation layers. The hexagonal configuration produced the lowest maximum membrane-surface salt mass fraction, decreasing it from 0.1127 kg/kg for the baseline grid to 0.0429 kg/kg, corresponding to a 61.9% reduction. Although the hexagonal design required an inlet pressure of 205.7 Pa, it produced a more favorable normalized mass-transfer–friction trade-off than the sinusoidal configuration (447.8 Pa), with a System Performance Index (η) of 2.53. These results demonstrate comparative micro-scale improvements in concentration polarization control and hydraulic performance under the simulated conditions. Experimental testing and system-level modeling are required before conclusions can be drawn regarding full-module energy consumption, photovoltaic integration, long-term fouling behavior, or economic feasibility. This study is consistent with the emerging Concepts and design for sustainability, whereby a circular and energy-efficient water economy is facilitated through an innovative mechanical design.

A modified compartmental epidemic model was developed to simulate the state of Kuwait protocol in fighting COVID-19 pandemic. The next generation matrix method was used to drive an expression for the basic reproduction number, R₀. Basic and effective reproduction numbers were calculated using data from the intrinsic growth rate of the confirmed COVID-19 cases. R₀ was found to be 2.18. Three scenarios that varied by effective reproduction number were used to estimate the future course of the disease: a high value of R = 1.98, a middle value of R = 1.62, and a low value of R = 1.2. The maximum number of beds required in general hospitals in each scenario were estimated at 141 184, 85 341, and 16 412, respectively. For intensive care units, the estimated numbers of beds required were 16 461, 9 645, and 1788. Maximum deaths also varied and were estimated to be 29 202, 23 973, and 11 565. For the maximum value of R, it is estimated to peak on August 27, 2020. For the middle value of R, it is estimated to peak on September 20, 2020. For the minimum value of R, it is estimated to peak on December 21, 2020.