Viscous Liquid Research Articles

On the mechanics of droplet surface crater during impact on immiscible viscous liquid pool

We study drop impacts on an immiscible viscous liquid pool and investigate the formation of droplet surface craters using experimental and theoretical analyses. We attribute the formation of air craters to the rapid deceleration of the droplet due to viscous drag force. The droplet response to the external impulsive decelerating force induces oscillatory modes on the surface exposed to the air forming capillary waves that superimpose to form air craters of various shapes and sizes. We introduce a non-dimensional parameter (${\varGamma }$), that is, the ratio of the drag force to the capillary force acting on the droplet. We show that${\varGamma }$is directly proportional to the capillary number. We show that droplets forming air craters of significant depths have${\varGamma }>1$. Further, we demonstrate that Legendre polynomials can locally approximate the central air crater jet profile. We also decipher that the air crater response time scale ($T$) varies as the square root of impact Weber number ($T\sim We^{1/2}$). Further, we generalize the local droplet response with a global response model for low impact energies based on an eigenvalue problem. We represent the penetrating drop as a constrained Rayleigh drop problem with a dynamic contact line. The air–water interface dynamics is analysed using an inviscid droplet deformation model for small deformation amplitudes. The local and global droplet response theories conform with each other and depict that the deformation profiles could be represented as a linear superposition of eigenmodes in Legendre polynomial basis. We unearth that the droplet response in an immiscible impact system differs from the miscible impact systems due to the presence of such a dynamic contact line.

Lagrangian modelling of nonlinear viscous waves generated by moving seabed deformation

A Lagrangian flow model is used to investigate highly nonlinear, dispersive waves generated by moving seabed deformation (MSD) of an otherwise horizontal seabed. Applications include free surface wave responses to horizontal co-seismic displacements and to novel bed-driven wave making systems used in surfing competitions. This paper considers gravity waves in viscous liquid, without restrictions on wave steepness, dispersion coefficient, and flow regime. Numerical computations are carried out using a Moving Particle Explicit method, which provides a Lagrangian flow description with far fewer particles than existing meshless methods. We show that the MSD speed has different effects in shallow and intermediate water depths. In shallow water, raising the MSD speed to a transcritical value promotes generation of leading solitary waves as expected. In supercritical flow, the highly nonlinear dynamics promotes breaking of the precursor soliton. In intermediate depth, wave dynamics is dominated by nonlinearity and dispersion, which act concurrently to generate a large leading wave that travels faster than predicted by linear theory, followed by a train of dispersive, short, steep waves. These waves break, even at subcritical values of MSD speed. We show that strongly nonlinear viscous dynamics occurs in the presence of a steep seabed deformation. This triggers flow separation, linked to strong amplification of wave steepness. Finally, we show that an oscillating MSD is capable of generating higher harmonics by means of nonlinear wave–wave interactions. The model is validated and verified by comparison to previously published experimental data and approximate analytical solutions.

Surface instability of static liquid metal in magnetized fusion plasma

Understanding surface instability in magnetized fusion plasma supports the appropriate implementation and handling of liquid metal as plasma facing components (PFCs) in future fusion reactors. A Lagrange equation describing a viscous liquid surface deformation in a magnetized plasma is derived using Rayleigh’s method. Its solution justifies the general instability criterion and helps in characterizing the key interactions driving such instability under fusion conditions. Surface tension and gravity, especially with the poloidal angles of the lower part of a plasma chamber, mainly stabilize the liquid surface at small and large disturbance wavelengths, respectively. The sheath electric field and the external tangential magnetic field cause the liquid surface to disintegrate at an intermediate wavelength. Practically, a magnetic confinement fusion (MCF) device requires a strong magnetic field for confinement. The study suggests that such a strong field dominates the rest and governs instability. In addition, this implies that the configuration of a static planar free liquid surface is difficult to adopt as a candidate for handling the liquid metal as PFCs in next step MCF devices.

Characterization of Air Entrainment Using a Pair of Vertically Aligned Revolving Rollers

The present study reports the characterization of air entrainment within a viscous liquid pool using a pair of revolving rollers. The rollers are aligned vertically. The top roller (first roller) is partially submerged with a fixed submergence ratio of 0.5 (equally submerged in the gas and liquid); however, the bottom roller (second roller) is fully immersed inside the liquid pool. The present computational work is carried out using open-source Gerris Solver, which discretizes the working domain adaptively based on the gradient of volume fraction. The influence of the rotational speed (described by the capillary number, Ca) and depth of immersion of the second roller (W/D) on the length and width of the entrained cusp is analyzed thoroughly. A scattered regime plot is provided to describe the different patterns of entrainment with the effect of both Ca and W/D. In addition, we have also elucidated the instantaneous (Y*) and maximum (Ymax*) vertical shift of the cusp tip by varying Ca and W/D. An interesting bubble pinch-off mechanism at the cusp tip after achieving the steady length is elucidated by characterizing the frequency and volume accumulation of the detached gaseous masses. The influence of the gravitational pull and viscous drag on the pattern of entrainment is also investigated. They play important roles in controlling the behavior of cusp entrainment. Lastly, an analytical formulation is established to predict the bent thickness of the cusp by employing a balance of the relevant influencing forces acting on the cusp. It provides an excellent agreement between the analytical solutions and computational results.

Illustration of chemical reaction on the flow of viscous fluid in a deformable permeable layer: A numerical approach

In this article, analysis is carried out for the flow of viscous liquid in a deformable permeable layer. Influence of chemical reaction is considered that will affect the flow behavior. The governing equation describes the coupling between the solid deformation, fluid movement and concentration in the porous layer. However, these complex transformed designed problems are numerically examined retaining “Runge-Kutta fourth-order” in coordination with shooting method. Computational results for the numerous parameters on the flow phenomena such as solid displacement profiles are presented graphically. Moreover, the significant finding of the results is; increasing viscous drag retards the momentum within the permeable stratum whereas increasing particle concentration has opposite impact on the solid displacement within the domain.

Output-feedback control of viscous liquid–tank system and its numerical approximation

We solve the output-feedback stabilization problem for a tank with a liquid modeled by the viscous Saint-Venant PDE system. The control input is the acceleration of the tank and a Control Lyapunov Functional methodology is used. The measurements are the tank position and the liquid level at the tank walls. The control scheme is a combination of a state feedback law with functional observers for the tank velocity and the liquid momentum. Four different types of output feedback stabilizers are proposed. A full-order observer and a reduced-order observer are used in order to estimate the tank velocity while the unmeasured liquid momentum is either estimated by using an appropriate scalar filter or is ignored. The reduced order observer differs from the full order observer because it omits the estimation of the measured tank position. Exponential convergence of the closed-loop system to the desired equilibrium point is achieved in each case. An algorithm is provided that guarantees that a robotic arm can move a glass of water to a pre-specified position no matter how full the glass is, without spilling water out of the glass, without residual end point sloshing and without measuring the water momentum and the glass velocity. Finally, the efficiency of the proposed output feedback laws is validated by numerical examples, obtained by using a simple finite-difference numerical scheme. The properties of the proposed, explicit, finite-difference scheme are determined.

NUMERICAL SIMULATION OF MULTIPHASE FLOW IN A POROUS MEDIUM IN THE PRESENCE OF HEAT AND MASS TRANSFER BETWEEN PHASES

The work is focused on unstable displacement of a viscous liquid from a porous medium in the presence of chemical interactions between phases. When a viscous liquid is displaced by a less viscous liquid or gas, the Saffman−Taylor instability develops at the displacement front: the less viscous liquid breaks through the layer of the more viscous liquid being displaced, forming "viscous finger" channels in it. With the development of instability, the initially flat interface is perturbed, and the area of contact between the phases increases. This phenomenon must be taken into account when modeling the displacement process with chemical reactions between phases, since the extension of the contact line between the reacting phases leads to an increase in the rate of the chemical reaction. The article provides a mathematical model for describing the process of oil displacement by the thermogas method: when oil is displaced by a mixture of heated water vapor and gas, which enters into an exothermic chemical reaction with oil, resulting in a decrease in oil viscosity and formation CO2, which leads to better displacement. Also, the mathematical model implies the possibility of accounting for subgrid instability by including additional flow terms into the equations. The results of computational experiments based on the described mathematical model are presented.

Two-dimensional wave motion in a viscous homogeneous liquid

The propagation of two-dimensional periodic capillary-gravitational waves in a viscous homogeneous liquid with a free surface in the frequency range from \(5 \cdot {{10}^{{ - 2}}}\) to \(5 \cdot {{10}^{4}}\) Hz is investigated. Dispersion relations are obtained, as well as expressions for phase and group velocities for surface waves in physically observable variables. It is shown that there is another class of solutions that is not observed in the ideal fluid model.

Theoretical essentials for designing viscous liquid pumping systems in the conditions of the Arctic region

The purpose is the creation of a scientifically based solution for the design of hermetic electromechanical converters adapted to existing pipelines, as well as those under construction and development. These pipelines meet the energy efficiency requirements and operate in the conditions of the Arctic region. Methods: methods of mathematical analysis, numerical methods, and methods of mathematical programming were used as the main mathematical means. The CFD design package of Ansys Maxwell was used. Research results: we showed that an increase of the efficiency of the system of technological transportation of petroleum products at low temperatures is possible through the use of electromechanical devices that combine the functions of heating and pumping the working liquid. We solved the field problem based on the analytical calculations carried out by a computer. This allowed us to determine the distribution of eddy current density in the structural elements of these devices responsible for creating pressure and heating the pumped petroleum products. The importance of the electrical parameters of the secondary windings has been confirmed numerically and experimentally. The hydraulic characteristics, mechanical losses, volumetric losses and efficiency are determined. Taking into account the outcomes of theoretical studies the experimental sample of the sealed electromechanical converter with the specified physical and chemical characteristics was created at Emperor Alexander I St. Petersburg State Transport University. Practical relevance: the obtained analytical formulas can be used at the development of the systems for pumping viscous liquids at low temperatures using the sealed electromechanical converters which helps to reduce the installed power of energy equipment without degrading the values of technological indicators.

Calculated model of a lubricant in a bearing with a non-standard support profile of a sleeve and a metal-coated shaft

In this work, on the basis of the flow equation of a truly viscous liquid, the continuity equation, and the equation describing the radius of the molten contour of the shaft coating, taking into account the dissipation rate of mechanical energy, an asymptotic and exact self-similar solution was found for the zero (without taking into account the melt) and the first (taking into account the melt) approximation of a radial bearing with a non-standard support profile adapted to friction conditions in hydrodynamic mode when the metal coating lubricates the shaft surface, taking into account the dependence of viscosity on pressure. An analytical dependence is obtained for the radius of the molten surface of the metal coating, as well as for the field of velocities and pressures at zero and first approximations. In addition, the main operating characteristics of the friction pair under consideration, the load capacity and the friction force are determined. The influence of the parameters characterizing the melt of the coating, the support profile adapted to the friction conditions, the dependence of the viscosity on the pressure on the load capacity and the friction force is estimated.

Study of annular flow wave characteristics in a rectangular microchannel for gas-liquid flow with a viscous liquid

Study of annular flow wave characteristics in a rectangular microchannel for gas-liquid flow with a viscous liquid

Experimental study of effect of the surfactant type on dynamics of monodispersed bubble cluster rising in a viscous liquid

Experimental study of effect of the surfactant type on dynamics of monodispersed bubble cluster rising in a viscous liquid

Benzophenone glass, supercooled liquid, and crystals: elastic properties and phase transitions.

The elastic properties of glass α- and β-modifications of benzophenone (C6H5)2CO are determined for the first time by the ultrasonic method at high pressures up to 1 GPa and in the temperature range of 77 K< T < 293 K. Four states of benzophenone are experimentally observed in the investigated temperature range of 77-293 K: glass, supercooled liquid, and α- and β-crystalline phases. The boundaries of phase transitions during isobaric heating are determined. The bulk and shear moduli B and G, Poisson's ratio σ, and density ρ are calculated. Glassy benzophenone has much lower elastic moduli than the α-modification at 77 K (the shear modulus G of glass is about half the value for the crystal). The crystalline α-modification demonstrates a strong softening of both moduli with an increase in the temperature in the range of 77-293 K. Heating of glass leads to the formation of a very viscous supercooled liquid, which crystallizes into the metastable β-modification. A further increase in the temperature leads to a monotropic phase transition β → α.

Семейство математических моделей для описания движения металлических проводников в электромагнитном поле

The modeling of metal conductors acceleration in an electromagnetic field in a two-dimensional approximation is executed. A family of mathematical models for describing the motion of a body is presented: a model of a thermoelastoplastic body (for the case of large deformations), a model of a viscous compressible liquid and a mixed model that includes two previous models for different phase states of matter. A mathematical model of electromagnetic processes is presented, which allows to ensure the flow of total currents along the cross-sections of conductors. Numerical algorithms based on the finite element method are presented. The described models are used to solve the problem of accelerating the aluminum cylindrical shell to a speed of about 8 km/s. The results obtained for different models were compared with each other, as well as with known calculated and experimental results published in the literature.

MODIFICATION OF α- GLYCEROL MONO CAPRATE SYNTHESIS FROM CAPRIC ACID

A three-step procedure has been employed to synthesize monoglycerides, namely α-glycerol mono caprate, using capric acid as the raw material. The esterification of capric acid with methanol generated a viscous yellow liquid of methyl caprate with a yield of 85% and a purity of 99.14%. The reaction of methyl caprate and 1,2-O-isopropylidene glycerol (1:4) using a green catalyst from lipozyme TL IM produced a yellowish liquid of isopropylidene glycerol caprate with a yield of 70.3% and 93.13% purity. The ring opening of the acetal group from isopropylidene glycerol caprate with amberlyst-15 in ethanol and followed by simple recrystallization in n-hexane produced α-glycerol mono caprate as a white solid with 64% yield, 100% purity, and a melting point of 51 ⁰C.

Решение обратной задачи, описывающей медленную тепловую конвекцию во вращающемся слое

The linear inverse initial-boundary value problem arising when modeling the rotational motion of a viscous heat-conducting liquid in a flat layer is solved. It is shown that the problem has two different integral identities. Based on these identities, a priori estimates of the solution in a uniform metric are obtained and its uniqueness is proved. The conditions for the input data are also determined, under which this solution goes to the stationary mode with increasing time according to the exponential law. In the final part, the existence of a unique classical solution of the inverse problem is proved. To do this, differentiating the problem by a spatial variable, we come to a direct non-classical problem with two integral conditions instead of the usual boundary conditions. The new problem is solved by the method of separation of variables, which makes it possible to find a solution in the form of rapidly converging series on a special basis.

Accelerated lithium-ion diffusion via a ligand 'hopping' mechanism in lithium enriched solvate ionic liquids.

Solvate ionic liquids (SILs), equimolar amounts of lithium salts and polyether glymes, are well studied highly customisable "designer solvents". Herein the physical, thermal and ion mobility properties of SILs with increased LiTFSI (LiTFSA) concentration, with ligand 1 : >1 LiTFSI stoichiometric ratios, are presented. It was found that between 60-80 °C, the lithium cation diffuses up to 4 times faster than the corresponding anion or ligand (glyme). These systems varied from viscous liquids to self-supporting gels, though were found to thin exponentially when heated to mild temperatures (50-60 °C). They were also found to be thermally stable, up to 200 °C, well in excess of normal operating temperatures. Ion mobility, assessed under an electric potential via ionic conductivity, showed the benefit of SIL optimisation for attaining greater concentrations of Li+ cations to store charge during supercapacitor charging and discharging. Molecular dynamics simulations interrogate the mechanism of enhanced diffusion at high temperatures, revealing a lithium hopping mechanism that implicates the glyme in bridging two lithiums through changes in the denticity.

A revisit of Rayleigh capillary jet breakup at low Ohnesorge number

The average Rayleigh capillary breakup length of a cylindrical Newtonian viscous liquid jet moving with homogeneous velocity must be determined by the selection of normal modes with time-independent amplitude and wavelength. Invariant modes (IMs) with both positive and negative group and phase velocities exist in ample ranges of the parameter domain (Weber and Ohnesorge), which explains (i) the self-sustained average breakup length (long-term resonance) and (ii) the governing role on breakup of both spatial growth rate and wave number of the dominant positive group velocity IM. Published experimental results at low Ohnesorge numbers confirm our proposal.

Simulation of self-induced capillary break up of a viscous liquid jet

The aim of the study is to reveal the patterns of self-induced disintegration of a viscous liquid jet flowing out at low speed from a capillary hole under microgravity conditions. The research method is numerical modeling of the regularities of self-induced capillary decay using the methods of Lagrange mechanics. Results. A verified technique for numerical simulation of a capillary jet of a viscous liquid based on the methods of Lagrange mechanics. Identified patterns of self-induced decay of a viscous jet under microgravity conditions. Dependence of the length of the undisintegrated part of the jet on the viscosity of the liquid and the velocity of its outflow from the capillary nozzle. Conclusion. The developed numerical simulation technique allows one to correctly and efficiently (from the point of view of the computing resource used) simulate the dynamics of a capillary jet, taking into account complex nonlinear and boundary effects. A pronounced effect of viscosity on the regularities of the disintegration of a jet moving at low speed has been established. The obtained spectral characteristics of perturbations in the jet make it possible to raise the question of the possibility of developing an asymptotic theory of the self-induced decay of a viscous jet.

Моделирование кинетики отверждения композиционного материала в условиях открытого космоса при высоких скоростях испарения молекул

The paper proposes a mathematical model necessary for computational modeling of the features of the formation of mechanical properties during the transition of an epoxy resin from a viscous liquid to solid state during curing. We consider a problem in which the transition to a deformable state occurs under conditions close to those of outer space. An important role is played by the vacuum near the surface of the material and the high temperature resulting from the heating of the material under the influence of solar radiation. Computational modeling was carried out up to the moment of the transitionof the medium from the state of a viscous fluid to that of a deformable body. Theoret-ical calculations are compared with experimental data. Within the proposed model, the formation of the material structure at the molecular level is studied and the viscosity of the medium is calculated. The material is inhomogeneous. The presence of vacuum near the boundary of the material leads to diffusion processes. The low-mass components present in the material begin to leave the material into the surrounding vacuum. The proposed model makes it possible to trace, in time and by volume of the material, the transformation of the initial low-mass components into deformable fragments formed from them and having a larger mass. The model uses parameters that have a specific physical meaning. Information about them was obtained from the analysis of available experimental data. The experiments were carried out under laboratory vacuum conditions. The temperature in the vac-uum cabinet varied from 20 to 80 °C. Numerical modeling of the technological process was carried out using the finite element method. The material was presented in the form of a semi-infinite plate. One boundary of the plate was considered to be in contact with vacuum. Through it, the low-mass components escaped into the surrounding space. The boundary conditions were derived from the assumption that the evaporation of these components only occurs when the value of the kinetic en-ergy of diffusing molecules exceeds the amount of work necessary to overcome the energy barrier. The opposite side of the plate was considered impermeable to the material components.