Linear stability of a rotating liquid column revisited

We revisit the somewhat classical problem of the linear stability of a rigidly rotating liquid column in this article. Although the literature pertaining to this problem dates back to 1959, the relation between inviscid and viscous stability criteria has not yet been clarified. While the viscous criterion for stability, given by $We < n^2 + k^2 -1$ , is both necessary and sufficient, this relation has only been shown to be sufficient in the inviscid case. Here, $We = \rho \varOmega ^2 a^3 / \gamma$ is the Weber number and measures the relative magnitudes of the centrifugal and surface tension forces, with $\varOmega$ being the angular velocity of the rigidly rotating column, $a$ the column radius, $\rho$ the density of the fluid and $\gamma$ the surface tension coefficient; $k$ and $n$ denote the axial and azimuthal wavenumbers of the imposed perturbation. We show that the subtle difference between the inviscid and viscous criteria arises from the surprisingly complicated picture of inviscid stability in the $We$ – $k$ plane. For all $n > 1$ , the viscously unstable region, corresponding to $We > n^2 + k^2-1$ , contains an infinite hierarchy of inviscidly stable islands ending in cusps, with a dominant leading island. Only the dominant island, now infinite in extent along the $We$ axis, persists for $n=1$ . This picture may be understood, based on the underlying eigenspectrum, as arising from the cascade of coalescences between a retrograde mode, that is the continuation of the cograde surface-tension-driven mode across the zero Doppler frequency point, and successive retrograde Coriolis modes constituting an infinite hierarchy.

Calculation of evaporation length of a liquid bridge flowing between inclined hot tubes

The bridge consists of liquid held by surface tension forces between two inclined tubes in an LNG heat exchanger. The shape of the bridge is calculated by the hydrostatic equation, which is reduced to a nonlinear integral equation and resolved by the Newton method. The velocity and temperature fields in the bridge are described by the Navier-Stokes and energy equations, respectively. They are reduced to the boundary integral equations and calculated by the method of boundary elements. Heat transfer coefficient is calculated for evaporating bridge and the length of total bridge evaporation is estimated.

Rapid Direct Laser Writing of Microoptical Components on A Meltable Biocompatible Gel

Microoptical components are coming of age in a wide range of applications: lab-on-a-chip, imaging, detection... There are a large number of fabrication technologies capable of producing high quality individual components and their arrays. However, most of them require high-end and costly equipment, complex and time-consuming fabrication, harmful chemicals, resulting in expensive final products. Here we present a technology capable of producing high quality microoptical components, using low-end direct laser writing on a biocompatible, environmentally friendly hydrogel, without any waste substances. Gel is locally and controllably melted while surface tension forces shape the optical component, following the laser beam profile. Process is so quick that a single microlens is fabricated in less than a second, and can be used instantly without any further processing. The technology is neither subtractive nor additive, and the base material is simply displaced producing a smooth surface. We have been able to fabricate individual microlenses and their arrays (positive, negative, aspheric), gratings and diffractive components. The technology is tested by generating unique, difficult to counterfeit QR-codes. Turnaround time is fast and makes the technology suitable both for rapid prototyping and serial production.

ACCOUNTING FOR THE INFLUENCE OF HUMIDITY PROPERTIES OF AUTOCLAVE- CURED CELLULAR CONCRETE IN THE DESIGN AND CONSTRUCTION OF ENCLOSING STRUCTURES

The results of studies of porosity, water absorption, moisture shrinkage and frost resistance of cellular concrete, which are some of the main factors determining the durability of cellular concrete enclosing structures manufactured using autoclave hardening technology, are considered. Methods for determining water absorption, moisture shrinkage and frost resistance are presented. The relationship between the moisture shrinkage and the capillary forces (the sum of the surface tension forces on the micromeniscs of liquid in the capillaries of cellular concrete), as well as the dependence of the shrinkage on the size (radius) of the capillary and gas pores of cellular concreteand on the water-solid ratio (W/S-factor) of cellular concrete, is established. In the field of frost resistance of cellular concrete, the relationship between the structure of the pore space of concrete and its deformation characteristics under the action of negative temperatures is studied. The effect of the presence of gas pores in cellular concrete on the reduction of frost expansion deformations is described.

Influence of temperature dependent physical properties on liquid metal droplet impact dynamics

The dynamics of a metal droplet impacting on a substrate surface has been studied in the paper numerically. Numerical solutions of the Navier-Stokes and Energy equations show the evolution of the droplet as it spreads upon impact with the substrate while simultaneously undergoing solidification. The interplay of the different forces including inertia, viscous and surface tension, coupled with solidification of the molten material in layers lead to complex flow dynamics. The change in density and viscosity owing to change in temperature resulting from the cooling process, is found to influence the spreading of the droplet significantly. The model was exercised for three different materials viz. aluminium, copper and nickel to determine the final splat radius as well as spreading time. The surface tension forces as well as solidification rates were found to be the dominant factors in determining the above parameters as well as the shape of the splat during spreading. The results were found to be in good agreement with existing analytical model.

Numerical simulation of water film edge dynamics

&lt;p&gt;Fundamental contribution to the formation of sea spray under strong winds is provided by the bag-breakup phenomenon - rupture of film in the form of parachute [1]. Breaking of water film into droplets is caused, among other factors, by processes occurring on the free edge of the film moving under action of surface tension forces. The study of these processes will help to understand how characteristics of the film and the drops appearing after its rupture are related.&lt;/p&gt;&lt;p&gt;Using the Basilisk software package with Volume of Fluid advection scheme for interfacial flows, numerical simulation of three-dimensional water film placed in domain filled with air was carried out. The water film was placed into domain filled with air. One of the edges of the film is free, and the second is fixed on the left boundary of the domain; along the third coordinate, the boundary conditions are periodic. At the initial moment of time, the film is defined by a sheet with variable thickness - the upper boundary has the form of a cosine. The change in the shape of the film over time was recorded. It is revealed that the inhomogeneity of the film thickness leads to the appearance of a significant curvature of the edge of the film as it moves under the action of surface tension forces.&lt;/p&gt;&lt;p&gt;This work was supported by the RFBR grants (20-05-00322, 21-55-50005, 21-55-52005) and RSF grant 19-17-00209.&lt;/p&gt;&lt;p&gt;[1] Troitskaya, Y. et al. Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds. Sci. Rep. 7, 1614 (2017).&lt;/p&gt;

Developing a heap leaching technology for floating gold ores

The features of the technology of heap leaching with floating gold are disclosed. It was found that significant technological losses of gold in the processes of enrichment of gold-bearing ores, as a rule, are associated with its natural fine mineralization or technogenic transformation to such a state. It has been shown that flat gold flakes (even with a gold grain size of more than 1 mm) are quite well retained on the surface of technological solutions, i.e., have a certain buoyancy. The wettability of gold particles is explained by the manifestation of the surface tension forces of aqueous solutions, the mechanisms of which are determined by the van der Waals interaction. In addition, the wettability of gold grains is affected by their electric charge, which, accumulating on a convex surface, creates a negative charge that prevents the formation of a double electric field around the gold particle, which is an additional reason for the non-wettability of gold. The mechanism of the formation of gold films, which are formed at a high value of surface tension, with the formation of floating "islands" covered with a hydrophilic shell, is explained. It was revealed that the energy of interaction of a gold nanoparticle with water can serve as a quantitative indicator of the buoyancy of gold grains and "islands" of nanogold, at a value of which of 0.05427 eV, clearly pronounced hydrophilic properties appear. The theoretical substantiation of the buoyancy of gold grains and "islands" of nanogold is the van der Waals interaction. On this basis, heap leaching technology was developed, with the targeted deposition of floating gold in the most suitable places. As a result of a decrease in the surface tension of leaching solutions, nanogold loses their initial buoyancy and sink from them to the bottom, where they will be subjected to the processes of their disembarkation (collection and extraction).

Determination of the surface tension coefficient of ferrites 600NN upon sintering

The manufacturing process of ferrite production consists in a chain of structural and phase transformations resulted in formation of ferrite ceramics from disperse systems (their solid phase is represented by metal oxides). The forces of surface tension play a crucial role at all stages of the technological process. A decrease in surface tension forces during grinding due to the use of surfactants (surface active substances) leads to better disaggregation of the components (both original and ferritized). The use of surfactants reduces interparticle friction and provides manufacturing of more dense workpieces at the stage of pressing. Microadditives promote faster formation of contact isthmuses. The goal of the study is to develop a method for determining the surface tension coefficient of 600NN ferrite material during sintering. The proposed approach is based on measurements of the shrinkage of various fragments of a vertically sintered ferrite rod, which are used to determine the values of the coefficient. It is shown that the surface tension coefficient of the studied ferrite material during sintering was σ = 65.2 ± 13.0 N/m with a confidence probability of 95%. The results obtained can be used to study the effect of the sintering temperature, the size of sintered particles, the amount and quality of alloying additives on the forces of surface tension. Moreover, the data can be used in the study of the relationship between the value of the surface tension coefficient and the parameters of the microstructure.

Theoretical Underpinnings of the Parameters of Device for Cleaning Grain from Ergot Sclerotia

Introduction. The grain collected by a combine contains not only full-weight grain, but also weeds, including harmful ones, which include toxic ergot sclerotia. Existing grain cleaning machines cannot provide complete separation of toxic ergot sclerotia during a single technological process, because of the similarity of physical properties. A complete separation of ergot from grain in one technological process is possible by density using aqueous solutions of inorganic salts. Therefore, an urgent issue is the development of a machine for separating harmful impurities in a wet way. Materials and Methods. We consider the fall of grains of rye, wheat, barley and oats, which have a shape close to ellipsoidal, from the outlet of the loading hopper into a liquid with a density of 1.0; 1.05; 1.10 and 1.15 ∙ 103 kg/m3. Theoretical explorations were undertaken for grain density (1.2...1.5) ∙ 103 kg/m3, a length (5.0...10.0) ∙ 10–3 m, a width (1.4...3.6) ∙ 10–3 m and thickness (1.2...3.5) ∙ 10–3 m by mathematical modeling methods using the laws of mechanics and hydrodynamics. Results. For the development of a machine for a wet separation of harmful impurities, the height of the location of the outlet of the loading hopper relative to the surface of an aqueous salt solution was estimated. The formulas are obtained for determining the minimum height required to overcome the Archimedean ellipsoid grain force, surface tension forces and fluid hydrodynamic resistance, taking into account the law of conservation of energy. Discussion and Conclusion. It was found that the minimum height of the loading hopper outlet location relative to the liquid surface depends on the orientation of the grains at the moment of entering it, their linear dimensions and density, as well as the density of an aqueous salt solution. The height of the outlet of the loading hopper, necessary for guaranteed overcoming of the surface tension of the liquid by all grains, is 57.1 ∙ 10–3 m.