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The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\\epsilon \\leq c_0\\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \\rightarrow \\infty $. For times $t \\gtrsim \\mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of \"2.5 dimensional\" streamwise-independent solutions referred to as streaks.

This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number

A relatively complete continuous relaxation spectrum H ( τ ) of poly(styrene- b -isoprene- b -styrene) (SIS) two-phase system was divided into five regions based on the variation of H ( τ ) strength, which corresponded to: (1) glass transition of PI phase, (2) high elastic state of PI phase, (3) glass transition of PS phase, (4) high elastic state of PS phase, and (5) viscous flow state of the entire SIS molecular chain. Five regions only appeared in SIS1105, because the molecular of SIS1105 experienced glass transition of PI block, PS block, and viscous flow of the whole molecular chain. The stress relaxation of SIS was influenced by the S/I ratios, because the PS microdomains ultimately determined the relaxation characteristics. The stress relaxation of SIS system was also closely related to the viscous flow transition temperature ( T f ). When the S/I ratio was low (15/85), forced stress relaxation occurred; when the S/I ratio was high (29/71 and 45/55), the SIS system did not show stress relaxation below the T f . When the temperature was higher than the T f , the S/I ratio did not affect the stress relaxation. The relaxation information obtained from the Cole–Cole diagram further verified the analysis of the continuous relaxation spectrum H ( τ ) and stress relaxation. Graphical abstract

In this study, a novel meshless collocation method based on the Gaussian–cubic hybrid kernel function in conjunction with the ghost-points method and the general Newton–Raphson method is proposed for solving the four-order stream function formulation of Navier–Stokes equations. The decrease of variables and equations results in better computational efficiency of stream function formulation than primitive variable formulations of 2D incompressible viscous flow. The original Naiver–Stokes equations can be transformed into a four-order stream function partial differential equation by introducing the vorticity and stream function. The new proposed Gaussian–cubic backward substitution method is used to solve the corresponding system of equations where the nonlinear stream function formulation is linearized by the general Newton–Raphson method. The ghost-points method is applied as the layout scheme of center points, which can effectively improve the accuracy without requiring more computational resources. Several examples are provided and the results demonstrate the feasibility of the proposed novel approach.

In this note we investigate the initial-boundary value problem for a Stokes system arising in a free surface viscous flow of a horizontally periodic fluid with fractional boundary operators. We derive an integral representation of solutions by making use of the multiple Fourier series. Moreover, we demonstrate a unique solvability in the framework of the Sobolev space of L 2 -type.

Feasibility has been demonstrated for the use of electron phenomenological spectroscopy (EPS) for the rapid determination of the physicochemical properties of heavy oil residues serving as raw material for the production of carbon materials, pitch, and coke. EPS was used to obtain several relationships, in particular, the dependence of the coking number (Conradson carbon residue) on the viscous flow activation energy for high‑molecular‑weight multifunctional systems. Using EPS methods, the time required for the simultaneous determination of the physicochemical properties of this raw material was shortened to 20‑25 min instead of tens of hours when using traditional methods. EPS does not replace the standard analytical methods for quality control but can be used to monitor the change in the quality of the residual raw material upon change in the technological conditions employed for the preparation of carbon materials in research and industrial laboratories and can be readily adapted for automation.

Variational formulations for viscous flows which lead to the Navier–Stokes equation are examined. Since viscosity leads to dissipation and, therefore, to the irreversible transfer of mechanical energy to heat, thermal degrees of freedom have been included in the construction of viscous dissipative Lagrangians, by embedding of thermodynamics aspects of the flow, such as thermasy and flow exergy. Another approach is based on the presumption that the pressure gradient force is a constrained force, whose sole role is to maintain the continuity constraint, with a magnitude that is minimum at every instant. From these considerations, Lagrangians based on the minimal energy dissipation principal have been constructed from which the application of the Euler–Lagrange equation leads to the standard form of the Navier–Stokes equation directly, or at least they are capable of generating the same equations of motion for simple steady and unsteady one-dimensional viscous flows. These efforts show that there is equivalence between Lagrangian, Hamiltonian, and Newtonian mechanics as far as the derivation of the Navier–Stokes equation is concerned. However, one of the conclusions is that the attractiveness of the variational approach in more complex situations is still an open question for the applied fluid mechanician.

In this paper, the rheological properties of bio-based semi-aromatic high temperature polyamide PA5T/56 were studied by melt index meter and rotational rheometer, and the effect of PA5T content on the rheological properties was discussed. The results showed that the melt index of PA5T/56 decreased with the increase in PA5T content; The bio-based semi-aromatic high temperature polyamide PA5T/56 with different ratios was pseudoplastic fluids, and its non-Newtonian index increased with the increase in temperature, the increase in PA5T content can improve the sensitivity of apparent viscosity to shear stress and shear rate; The apparent viscosity reduced with the increase in shear stress or shear rate; With the increase in shear rate, the viscous flow activation energy decreased, and the apparent viscosity was less sensitive to temperature; With the increase in PA5T content, the viscous flow activation energy of PA5T/56 increased gradually, indicated that the increase in PA5T content can improve the temperature sensitivity of PA5T/56 apparent viscosity; Therefore, in the synthesis and post-treatment of PA5T/56 material, in order to improve its processing properties, make the operation easier and reduce the economic cost, it can be improved by adjusting the processes such as shear stress, shear rate and the ratio of PA5T/56 components.

Ion irradiation can cause burrowing of nanoparticles in substrates, strongly depending on the material properties and irradiation parameters. In this study, it is demonstrated that the sinking process can be accomplished with ion irradiation of cube‐shaped Ag nanoparticles on top of silicon; how ion channeling affects the sinking rate; and underline the importance of the amorphous state of the substrate upon ion irradiation. Based on these experimental findings, the sinking process is described as being driven by capillary forces enabled by ion‐induced plastic flow of the substrate. Ion irradiation causes nanoparticles to sink into substrates, influenced by material properties and irradiation specifics. This study reveals nanoparticle shape doesn't dictate sinking. Ion channeling and substrate's amorphous state play crucial roles. Sinking is driven by capillary forces, facilitated by ion‐induced substrate plasticity.

The effect of alloying elements Nb and Mo on the viscosity of the 84KKhSR Co alloy melt is investigated using the oscillating crucible method. The temperature dependences of the viscosities of the melts are shown to coincide upon heating and cooling, to be monotonic, and to be described by Arrhenius-type dependences. Alloying with 3 wt % Mo or Nb is found to increase the viscosity of the base Co–Cr–Fe–Si–B alloy, with Nb alloying having a more pronounced effect. Alloying with niobium from 1 to 3 wt % is shown to be accompanied by a pronounced linear increase in the viscosity and the activation energy of viscous flow; for alloying with molybdenum, the concentration-induced change in the viscosity and the activation energy depends on its content in the alloy. For an alloy with 1 wt % Mo, the viscosity remains virtually unchanged compared to the Co–Cr–Fe–Si–B matrix alloy, and the activation energy of viscous flow even slightly decreases. A further increase in the molybdenum concentration in the alloy is also accompanied by a monotonic increase in both the viscosity and the activation energy of viscous flow. The minimum threshold values of temperature (T = 1080°C), drawing speed (V = 4 m/min), and viscosity (ν = 27 × 10–7 m2/s) that ensure the production of amorphous wires from the 84KKhSR alloy by the Ulitovskii–Taylor method are determined. When analyzing data on the concentration and temperature dependences of viscosity, we have determined the optimum Co alloy compositions and quenching conditions: alloys with 2 wt % Nb and 3 wt % Mo have the same viscosity (27 × 10–7 m2/s), and the drawing temperature of microwires is 1100°C. Amorphous wires 130–150 μm in diameter and more than 50 m in length with a high level of mechanical properties are fabricated. The obtained results indicate a high glass-forming ability of Co–Cr–Fe–Si–B (84KKhSR) alloys additionally alloyed with 2 wt % Nb or 3 wt % Mo.