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One of the major issues with Extreme ultraviolet lithography (EUVL) is mask defects, which can occur by particle contamination. Gaussian Diffusion Sphere Model (GDSM) was developed to predict particle deposition velocity considering electrophoresis in addition to Brownian diffusion and gravitational settling of particles. For the validation of GDSM, the particle deposition velocities predicted using GDSM were compared with the computational fluid dynamics (CFD) simulation data. The improved GDSM predicted the particle deposition velocity correctly and had fast calculation time. Using the improved GDSM, in an electric field ranging from 0 V/cm to 1000 V/cm, the effects of both attractive electrophoresis and repulsive electrophoresis were evaluated. For the case considering electrophoresis, not only diffusion but also electrophoresis was dominant for the deposition velocity for submicron particles. Repulsive electrophoresis caused the deposition velocity to decrease. However, when the electric field strength was less than 100 V/cm, deposition was not small enough to be ignored. The deposition velocity was analyzed according to free-stream velocity. The effect of free-stream velocity was noticeable under repulsive electrophoresis, whereas it was suppressed under attractive electrophoresis.

The application of nanofluids has exploded in recent decades to improve the local number, mean Nusselt number, and rate of heat transfer. However, boundary layer equations of nanofluid across a flat plate with radiation have not been studied, and therefore this paper studies them mathematically for the first time. For water-based copper and aluminum oxide nanofluids, a similarity solution is presented in this study, and the subsequent system of the ordinary differential equation (ODE) is numerically solved by the Runge–Kutta method in MATLAB. Two different hydraulic boundary conditions are used in the simulations. In the first, the flow across a moving plate and the direction of the flow are analyzed, while in the second, the flow over a nonlinearly moving plate in a still fluid is investigated. The nanoparticle’s boundary layer thickness is found less than the thermal and hydraulics boundary layers. The local Nusselt number and friction factor of both the nanofluids are calculated and compared with the base fluid. The results demonstrate that the friction coefficient is high and the Nusselt number is low for nanoparticles with a high volume fraction. It also revealed that the friction factor for water–aluminum oxide is 16% greater than that for the water–CuO whereas the local Nusselt number for water–aluminum oxide is only 5% more than that for the water–CuO.

This research captures nonlinear thermo-solutal buoyancy (i.e., nonlinear mixed convection) impact in nanofluid flow based on magnetized Casson model. The generalized porosity concept (i.e., Darcy–Forchheimer relationship) is employed by considering incompressible liquid that saturates the porous space. Effects of thermophoresis, Robin conditions, thermo-solutal stratifications and Brownian diffusion are accounted. Consideration of transpiration phenomenon captures suction/injection aspects. Fluid mechanics basic laws are depleted to simplify the governing rheological expressions. A transformation procedure is then employed to convert the nonlinear governing partial systems into differential systems. Homotopy methodology is used to obtain analytical solutions and convergence is ensured. Graphical and tabular outcomes are presented to address the importance of emerging variables.

We examine the kinetics of relaxation processes in dynamical models with the fixed number of Brownian particles and with the constant source of the particles. The former evolves to the zero equilibrium distribution, while the latter develops to the stationary state with non-equilibrium distribution and non-zero stationary flow. We show that the relaxation times in the both systems coincide. This is valid for an arbitrary noise intensity and shape of potential profile. In addition we propose to modify the well-known Kramers' approach for the determination of relaxation time. The modified approach is valid for an arbitrary height of potential barriers.