Synchronization of low Reynolds number plane Couette turbulence

We demonstrate that in plane Couette turbulence a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition allows us to identify an active subspace comprising a small number of the gravest streamwise components of the flow that can synchronize all the remaining streamwise flow components. The critical streamwise wavelength, $\ell _{x c}$ , that separates the active from the synchronized passive subspace is identified as the streamwise wavelength at which perturbations to the time-dependent turbulent flow with streamwise wavelengths $\ell _x<\ell _{xc}$ have negative characteristic Lyapunov exponents. The critical wavelength is found to be approximately 130 wall units and obeys viscous scaling at these Reynolds numbers.

A vortex–wave interaction theory describing the effect of boundary forcing on shear flows

A strongly nonlinear theory describing the effect of small amplitude boundary forcing in the form of waves on high Reynolds number shear flows is given. The interaction leads to an $O(1)$ change in the unperturbed flow and is relevant to a number of forcing mechanisms. The cases of the shear flow being bounded or unbounded are both considered and the results for the unbounded case apply to quite arbitrary flows. The instability criterion for unbounded flows is expressed in terms of the wall forcing and the friction Reynolds number. As particular examples we investigate wall transpiration or surface undulations as sources of the forcing and both propagating and stationary waves are considered. Results are given for propagating waves with crests perpendicular to the flow direction and for stationary waves with crests no longer perpendicular to the flow direction. In the first of those situations we find the instability induced by transpiration waves is independent of the propagation speed. For wavy walls downstream propagation completely stabilises the flow at a critical speed whereas upstream propagation greatly destabilises the flow. For stationary oblique waves we find that the instability is enhanced and a much wider range of unstable wavenumbers exists. For the bounded case with a wall of fixed wavelength we identify a critical wavelength where the most dangerous mode switches from the aligned to the oblique configuration. For the transpiration problem in the oblique configuration a strong resonance occurs when the vortex wavelength coincides with the spanwise wavelength of the forcing.

Dynamics and instabilities of the free boundary of a two-dimensional dry active nematic aggregate

The dynamics of of the free boundary of a two-dimensional aggregate of active rod-shaped particles in the nematic phase is considered theoretically. The aggregate is in contact with a hard boundary at $y=0$, a free boundary at $y=H(x,t)$, and in the $x$-direction the aggregate is of infinite size. The analysis shows that the behavior for an aggregate with steady-state particle density $\rho _s$, strength of active stress $\chi$, bulk modulus $\rho_s \beta$, and particles aligned perpendicular to the boundaries can be mapped to one with active stress strength $- \chi$, bulk modulus $\rho_s(\beta - \chi)$, and particles aligned parallel to the boundaries. For a contractile aggregate, when the particles are aligned parallel to the boundaries, the system is unstable in long wavelengths at any strength of contractility for any $H$, and the critical wavelength increases as $H$ increases; when the particles are aligned perpendicular to the boundaries, the system acquires a finite-wavelength instability at a critical active stress whose strength decreases as $H$ increases. The stability of an extensile aggregate can be obtained from the analysis for contractile aggregates and the aforementioned mapping, even though the corresponding physical mechanisms for the instabilities are different. Finally, in the limit $H \rightarrow \infty$, the free boundary is unstable for any contractile or extensile systems in the long wavelength limit.

A Novel Quality Control Method for the Determination of the Refractive Index of Oil-in-Water Creams and Its Correlation with Skin Hydration

The sensory properties of cosmetic products can influence consumers’ choice. The accurate correlation of sensory properties, such as skin hydration, with the material properties of the formulation could be desirable. In this study, we aimed to demonstrate a new method for the in vitro measurement of the refractive indices (RIs) of turbid creams. The critical wavelength of each cream was obtained through direct measurement using a sun protection factor (SPF) meter; the wavelength value was then applied in the Sellmeier equation to determine the RI. The results obtained from the in vitro skin hydration measurement for each cream correlated with their RI values. This suggests that RI measurements could be a useful predictive tool for the ranking of creams in terms of their skin hydration effects.

Simplified, Cost Effective, and Accurate Calculation of Critical Wavelength via the MATLAB Software

The use of sunscreens in our daily lives to reduce UV exposure on our skin is a good measure against photoaging. However, the current active ingredients in the market are not able to cover the entire spectrum range of UVA and UVB. Therefore, broader spectrum compounds are constantly being searched by cosmetic companies to replace the commercially available UV filters. In this study, an experimental model utilizing the MATLAB software was developed to measure a compound’s critical wavelength (λc). The purpose of this research was to ease the cost and speed up the screening of bioactive compounds for photoprotective properties while maintaining accuracy in the process. In this paper, the measurement of caffeic acid, gallic acid, and pinocembrin’s critical wavelength in the MATLAB software was explained in a step-by-step guide. This was done to create an understandable and executable procedure for future researchers to utilize. Subsequently, from the results, the critical wavelength of caffeic acid, gallic acid, and pinocembrin was 378.2nm, 324.6nm, and 364.8nm, respectively. This shows that caffeic acid has the broadest absorbance spectrum, followed by pinocembrin, and finally gallic acid. Thus, it may be possible that caffeic acid might have stronger photoprotective abilities as compared to pinocembrin and gallic acid, based on its critical wavelength.

Development of Sunscreen Products Containing Titanium Dioxide and Aloe vera Gel

This study aimed to develop sunscreen emulsion from natural sunscreening agents, titanium dioxide and Aloe vera gel extract that have good sun protection efficacy. The effects of formulation variables i.e., particle size and amount of titanium dioxide, amount of Aloe vera gel extract (spray dried powder) and combination of sunscreening agents (titanium dioxide and Aloe vera gel extract) on physical properties and sun protection efficacy (e.g., SPF, UVA/UVB ratio, critical wavelength) of sunscreen products were evaluated. The results showed that the smaller particle size of titanium dioxide improved the sun protection efficacy and increased the UVB absorption edge of the products. SPF of the formulations could be ranked as Nanofine TiO2 (particle size 25–30 nm) > Kingruti T-01 TiO2 (particle size 200 nm) > Pigment TiO2 (particle size < 45,000 nm) and UVA/UVB ratio and critical wavelength of the formulations could be arranged in order as follows: Nanofine TiO2 < Kingruti T-01 TiO2 < Pigment TiO2. Increasing amount of titanium dioxide from 5 to 15 %w/w increased significantly viscosity and SPF of formulations. Aloe vera gel extract itself did not significantly affect SPF, however, combination of Aloe vera gel extract and titanium dioxide seemed to have synergistic effect on sun protection efficacy and decreased viscosity of the formulation. According to the results, the good sunscreen formulation consisted of 15 %w/w Nanofine TiO2, 5 %w/w Aloe vera gel spray dried powder in emulsion base because it was broad spectrum sunscreen and showed high SPF (27.53±1.92), high UVA/UVB ratio with critical wavelength higher than 370 nm.

Dielectric characteristics of epoxy resin modified with tetraethoxysilane in the millimeter range

In this work, the influence of alkoxysilanes introduced into the epoxy resin was studied. That was done in order to study the possibility of using the obtained binders in composite materials with increased radio transparency in the millimetre microwave radio band. Determination of the modified epoxy resin dielectric characteristics in the millimetre microwave radio transparency was carried out by the waveguide method. The measuring complex consisted of a precision measuring line P1-31, a tunable generator on a Gann diode (30-38 GHz), a ferrite gate, and a section of a standard-section waveguide. Based on measurements of the minimum position displacement of the standing wave coefficient by known propagation constants, the free-space wavelength λ0 for a given operating frequency, and the critical wavelength in the waveguide λcr, the loss angle tangent tg(δ) and the permittivity ε were calculated. Calculations of the permittivity ε, the angle of the dielectric loss tg(δ) and the radio transparency loss-ΔР were performed in the MathСad. Moisture absorption of samples was determined by holding them in a desiccator with a humidity of 98 %. The samples were kept in a tightly closed desiccator for 24 hours at a temperature of 25 oC. In addition, the relative moisture absorption was determined using the increase in mass. It was found that the introduction of tetraethoxysilane in the composition in an amount of 1.5-3.5% leads to a decrease in the tangent of the dielectric loss angle. The optimum is observed in the range of the modifier concentration of 2.5-3.5%. This fact confirms that at these concentrations there is a complete interaction of TEOS alkoxygroups with epoxy resin epoxygroups.