Surface Tension Parameters Research Articles

Numerical Simulation of Droplet Coalescence Using Meshless Radial Basis Function and Domain Decomposition Method

The present investigation of the dynamic two-binary droplet interactions has gained attention since its use to expand and improve several numerical methods. Generally, its interactions are classified into coalescence, bouncing, reflective, and stretching separation. This study simulated droplet coalescence using the meshless radial basis function (RBF) method. These methods are used to solve the Navier-Stokes equations combined with the Cahn-Hilliard equations to track the interface between two fluids. This work uses the fractional step method to calculate the pressure-velocity coupling in the Navier-Stokes equations. The numerical results were compared with the available data in the literature to validate the proposed method. Based on the validation, the proposed method conforms well with the literature. To identify further coalescence characteristics, the model considered different values in viscosity (2, 4, and 8 cP), collision velocity (1.5 m/s and 3 m/s), and surface tension (0.014, 0.028, and 0.056 N/m) parameters. The increasing viscosity was linearly proportional to the collision time, whereas increased surface tension and collision velocity shortened the collision time.

Thin film development on a double layer of fluids over a stretching sheet

Abstract The thin film development on a double layer of fluids in which the first layer is Newtonian and the second layer is of second-grade fluid on a stretching sheet is analyzed in this paper. The governing equations describing the flow are solved using the Long-wave perturbation method. The coupled partial differential equations thus obtained are solved numerically by the finite volume approach where the spatial derivatives are approximated using the upwind difference scheme and the time derivatives are by forward difference. The study focuses on analyzing the impact of surface tension parameters, viscosity ratio parameters, and Reynolds numbers on the flow dynamics. From the analysis, it is observed that the film height decreases for higher surface tension parameters and Reynolds numbers of both fluid layers and the viscosity ratio parameter $m>1$.

EVALUATION OF THE GRAPHENE DISPERSIONS FOR KEVLAR FABRICS FUNCTIONALIZATION OBTAINED BY THE LIQUID-EXFOLIATION OF GRAPHITE

The process where pristine graphite is subjected to a solvent treatment seems simple and scalable and has attracted the attention of researchers over many years. However, for successful exfoliation, overcoming the van der Waals attractions between the adjacent layers of graphite is necessary. Over time, several methods have been created to overcome the attraction between layers. Graphene’s liquid phase exfoliation (LPE) occurs due to the strong interactions between the solvent molecules and the basal planes of graphite, overcoming the energetic resistance to exfoliation and subsequent dispersion. Ultra sonication used for exfoliation can produce single or few layered graphene flakes. During sonication the sound waves propagate through liquid medium in alternating high- and low-pressure cycles, strong mechanical and thermal energy released by acoustic cavitation results in splitting up large particles into fine ones and dispersing them. Simultaneous insertion of solvent and/or intercalation molecules in between the graphite layers takes place supporting graphite separation into graphene layers. ; The dispersion capacity of graphene flakes depends on how appropriate the solvent properties are to the corresponding properties of graphene, such as surface tension, Hildebrand, and Hansen solubility parameters. Only certain solvents can disperse graphene well and form a dispersion appropriate for specific future applications. In addition, after exfoliation by ultra sonication graphene flakes aggregation due to the van der Waals attractions must be overcome to prepare in long-term stable dispersions of nanometres-size graphene sheets. ; The research has focused on the preparation of stable dispersion ready for transfer without intermediate processes to the Kevlar fabrics. An experimental comparison of the potentials of the 4 solvents for the application resulted in three corresponding to the intended use, two of them examined in detail, supplementing the composition of the LPE liquid medium with triethanolamine to obtain sufficient performance graphene coverage on Kevlar textile fibres.

Some physicochemical properties of ethyl oleate mixtures with ethanol and n-hexane

Due to the wide use of ethyl oleate (EO) in agriculture, medicine and automotive fuels, measurements of the surface tension, density, viscosity and contact angle of a mixture of ethyl oleate with ethanol (ET) and/or n-hexane (HEX) were made. The contact angle was measured on polytetrafluoroethylene (PTFE), poly(methyl methacrylate) (PMMA), glass and steel. The measurement results for the mixtures of EO + ET and EO + HEX were analyzed based on the properties of individual components of the mixtures. When considering the changes in the surface tension and contact angle on PTFE for the EO + ET and EO + HEX mixtures as a function of the mixture composition there were taken into account, not only the values of the total surface tension of the mixture components, but also the components and parameters of this tension. Based on the surface tension components and parameters of EO, ET, HEX, PTFE, PMMA, glass and steel, it was possible to predict changes in the surface tension of tested mixtures and the contact angle as a function of the mixture composition.

Experimental and model research on judging liquid accumulation in pipelines under the action of surfactant

Foam drainage gas extraction is applied in various natural gas extraction scenarios, such as water-bearing gas wells, gas fields with high water content, and wet natural gas pipeline transport, with the goal of enhancing extraction efficiency and lowering production costs. A common issue in foam-carrying liquid gas wells and wet natural gas pipelines is the large errors observed in the prediction model for liquid accumulation onset, derived using ellipsoidal droplets. Additionally, this model is only applicable to a single surfactant type and concentration. To investigate the effects of different types and concentrations of surfactants on the onset of liquid accumulation. This paper re-establishes the critical foam-carrying flow rate model for spherical cap-shaped foam droplets using Newton's laws of motion, through an analysis of their motion state within the air core. Through the critical foam-carrying flow rate test experiments and foam droplet deformation test experiments to obtain critical foam-carrying flow rate model in the surface tension, foam density, Weber number, drag coefficient and other parameters of the change rule and calculation method. The model's validity was further confirmed using field-measured production data from foam-carrying liquid gas wells, demonstrating accurate validation results. Compared to the previous model, this new model treats foam droplets as spherical cap-shape and introduces a dimensionless scaling factor and foaming capacity to quantify the impact of surfactant types and concentrations on foam droplet surface tension and density. This enhances the model's applicability across different types and concentrations of surfactants with greater accuracy. This offers an efficient, precise, and versatile method for predicting liquid accumulation in foam-carrying liquid gas fields, thereby enhancing the efficiency and safety of gas extraction.

Synergistic effects of nonionic surfactants ethoxylated alkylamines and sodium dodecyl sulfate in mixed systems

HypothesisIn general, the performance of surfactant hybrid systems is better than that of single surfactants, so surfactant hybrid systems are widely used in various industries. As a very important class of nonionic surfactants, ethoxylated alkylamines have been widely used in industries such as washing, coating, and pesticide, but little research has been conducted on their mixed systems. In order to improve the utilization efficiency of surfactants and reduce wastage, the surface properties and aggregation behavior of ethoxylated alkylamine mixed systems should be further explored. ExperimentIn this study, the nonionic surfactant ethoxylated dodecylamine (AC-1202) and the anionic surfactant sodium dodecyl sulfate (SDS) were used to form a mixed system. The static surface tension and interaction parameters of the mixed system under the influence of inorganic salt ions were investigated using a KRÜSS K12 surface tensiometer. The diffusion process of the mixed system was investigated using a KRÜSS bubble pressure tensiometer. At the same time, the aggregate behavior of the mixed system was studied by particle size analyzer. In addition, the contact angle and rheological properties of the mixed solution were also investigated. FindingsThe SDS/AC-1202 mixture system formed a synergistic effect that could reduce the CMC value to 24.20 mN/m and the CMC value was as low as 22.89 mN/m after the addition of inorganic salts. The mixed system conforms to the kinetic mechanism of mixing and diffusion and the Ostwald de model for non-Newtonian fluids. Finally, there is a good aggregation pattern in the mixed system, and the stronger synergistic effect will lead to the reduction of the average particle size of the mixture to 45.41 nm.

Evolution of Surface Tension and Hansen Parameters of a Homologous Series of Imidazolium-Based Ionic Liquids.

In this study, we systematically analyze the surface tension and Hansen solubility parameters (HSPs) of imidazolium-based ionic liquids (ILs) with different anions ([NTf2]-, [PF6]-, [I]-, and [Br]-). These anions are combined with the classical 1-alkyl-3-methyl-substituted imidazolium cations ([CnC1Im]+) and a group of oligoether-functionalized imidazolium cations ([(mPEGn)2Im]+) based on methylated polyethylene glycol (mPEGn). In detail, the influences of the length of the alkyl- and the mPEGn-chain, the anion size, and the water content are investigated experimentally. For [CnC1Im]+-based ILs, the surface tension decreases with increasing alkyl chain length in all cases, but the magnitude of this decrease depends on the size of the anion ([NTf2]- < [PF6]- < [Br]- ≤ [I]-). Molecular dynamics (MD) simulations on [CnC1Im]+-based ILs indicate that these differences are caused by the interplay of charged and uncharged domains, in particular in the different anions, which affects the ability of the alkyl chains of the cation to orient toward the liquid-gas interface. An increase in the mPEGn-chain length of the [(mPEGn)2Im][A] ILs does not significantly influence the surface tension. These changes upon variation of the cation/anion combination do not correlate with the evolution of the HSPs for the two sets of ILs. Finally, our data suggest that significant water contents up to water mole fractions of x(H2O) = 0.25 do not significantly affect the surface tension of the studied binary IL-water mixtures.

Synthesis, self-assembly and surface-active properties of alkyl halide mediated imidazolium monomeric surfactants

Two imidazolium monomeric surfactants, that is, 1-tetradecyl-1H-imidazole [14IM] and 1-hexadecyl-1H-imidazole [16IM] has been synthesized and characterized by 1H NMR,13C NMR, FTIR, HRMS spectroscopies and thermogravimetric analysis (TGA) for number and types of protons and carbon, functional groups, estimation of molecular weight and thermal stability of these compounds. The conductivity was measured in double distilled water at four different temperatures, 288, 293, 298, and 303 K. The results showed that these surfactants behave as weak electrolytes. The density and viscosity data have shown the existence of strong interactions between imidazolium surfactants and solvent (water) molecules. The results obtained from Root’s equation indicate that surfactant–solvent interactions are important than surfactant–surfactant interactions in dilute solutions, that is, below critical micellar concentration. The values of constants obtained from Einstein and Moulik equations have revealed that there was stronger and significant interaction between imidazolium surfactants and water molecules below critical micellar region. The surface tension parameters have indicated that these surfactants are good contenders to lower the surface tension of air/water interface. The results obtained from surface tension data have shown that standard change in free energy of micellization (ΔG°mic) and adsorption (ΔG°ads) were negative, indicating that these surfactants molecules have spontaneous tendencies to form micelles in solution at higher concentration and to get adsorb at the air/water interface at lower concentration. The TGA has indicated good thermally stability and activation energy for thermal decomposition was found in the range of 37.26.26–98.20.20 kJ/mol.

Development and test of highly accurate endpoint free energy methods. 3: partition coefficient prediction using a Poisson-Boltzmann method combined with a solvent accessible surface area model for SAMPL challenges.

Accurately predicting solvation free energy is the key to predict protein-ligand binding free energy. In addition, the partition coefficient (log P), which is an important physicochemical property that determines the distribution of a drug in vivo, can be derived directly from transfer free energies, i.e., the difference between solvation free energies (SFEs) in different solvents. Within the Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL) 9 challenge, we applied the Poisson-Boltzmann (PB) surface area (SA) approach to predict the toluene/water transfer free energy and partition coefficient (log Ptoluene/water) from SFEs. For each solute, only a single conformation automatically generated by the free software Open Babel was used. The PB calculation directly adopts our previously optimized boundary definition - a set of general AMBER force field 2 (GAFF2) atom-type based sphere radii for solute atoms. For the non-polar SA model, we newly developed the solvent-related molecular surface tension parameters γ and offset b for toluene and cyclohexane targeting experimental SFEs. This approach yielded the highest predictive accuracy in terms of root mean square error (RMSE) of 1.52 kcal mol-1 in transfer free energy for 16 small drug molecules among all 18 submissions in the SAMPL9 blind prediction challenge. The re-evaluation of the challenge set using multi-conformation strategies based on molecular dynamics (MD) simulations further reduces the prediction RMSE to 1.33 kcal mol-1. At the same time, an additional evaluation of our PBSA method on the SAMPL5 cyclohexane/water distribution coefficient (log Dcyclohexane/water) prediction revealed that our model outperformed COSMO-RS, the best submission model with RMSEPBSA = 1.88 versus RMSECOSMO-RS = 2.11 log units. Two external log Ptoluene/water and log Pcyclohexane/water datasets that contain 110 and 87 data points, respectively, are collected for extra validation and provide an in-depth insight into the error source of the PBSA method.

Wettability of Quartz by Ethanol, Rhamnolipid and Triton X-165 Aqueous Solutions with Regard to Its Surface Tension

The wettability of quartz by different liquids and solutions plays a very important role in practical applications. Hence, the wetting behaviour of ethanol (ET), rhamnolipid (RL) and Triton X-165 (TX165) aqueous solutions with regard to the quartz surface tension was investigated. The investigations were based on the contact angle measurements of water (W), formamide (F) and diiodomethane (D) as well as ET, RL and TX165 solutions on the quartz surface. The obtained results of the contact angle for W, F and D were used for the determination of quartz surface tension as well as its components and parameters using different approaches, whereas the results obtained for the aqueous solution of ET, RL and TX165 were considered with regard to their adsorption at the quartz–air, quartz–solution and solution–air interfaces as well as the solution interactions across the quartz–solution interface. The considerations of the relations between the contact angle and adsorption of solution components at different interfaces were based on the components and parameters of the quartz surface tension. They allow us to, among other things, establish the mechanism of the adsorption of individual components of the solution at the interfaces and standard Gibbs surface free energy of this adsorption.

Connecting Structural Characteristics and Material Properties in Phase-Separating Polymer Solutions: Phase-Field Modeling and Physics-Informed Neural Networks.

The formed morphology during phase separation is crucial for determining the properties of the resulting product, e.g., a functional membrane. However, an accurate morphology prediction is challenging due to the inherent complexity of molecular interactions. In this study, the phase separation of a two-dimensional model polymer solution is investigated. The spinodal decomposition during the formation of polymer-rich domains is described by the Cahn-Hilliard equation incorporating the Flory-Huggins free energy description between the polymer and solvent. We circumvent the heavy burden of precise morphology prediction through two aspects. First, we systematically analyze the degree of impact of the parameters (initial polymer volume fraction, polymer mobility, degree of polymerization, surface tension parameter, and Flory-Huggins interaction parameter) in a phase-separating system on morphological evolution characterized by geometrical fingerprints to determine the most influential factor. The sensitivity analysis provides an estimate for the error tolerance of each parameter in determining the transition time, the spinodal decomposition length, and the domain growth rate. Secondly, we devise a set of physics-informed neural networks (PINN) comprising two coupled feedforward neural networks to represent the phase-field equations and inversely discover the value of the embedded parameter for a given morphological evolution. Among the five parameters considered, the polymer-solvent affinity is key in determining the phase transition time and the growth law of the polymer-rich domains. We demonstrate that the unknown parameter can be accurately determined by renormalizing the PINN-predicted parameter by the change of characteristic domain size in time. Our results suggest that certain degrees of error are tolerable and do not significantly affect the morphology properties during the domain growth. Moreover, reliable inverse prediction of the unknown parameter can be pursued by merely two separate snapshots during morphological evolution. The latter largely reduces the computational load in the standard data-driven predictive methods, and the approach may prove beneficial to the inverse design for specific needs.

Numerical investigation of highly viscous droplet generation based on level set method

Piezo-driven needle valves are widely used in electronic packaging due to their fast response, high resolution and good dispensing consistency. However, the stable generation of high-viscosity droplets is one of the key issues to its packaging quality. To investigate the formation mechanism of the high-viscosity droplet. In this paper, a 2D finite element model of the drop-on-demand injection process of the high-viscosity droplet is established based on the level set method, the droplet formation and separation processes are numerically simulated, and the reliability of the simulation results is checked by comparing the outcomes with published data. Specifically, the detailed evolution of the high-viscosity droplet formation and separation process is gained by coupling the two-phase flow-level set method and the dynamic grid technique, and the pressure distribution in the injection chamber is further discussed and the effects of operating parameters on the droplet formation volume are examined. The results of the study show that the needle motion is the main factor of pressure fluctuations in the injection chamber. Moreover, we also found that among the parameters of needle stroke, nozzle diameter, supply pressure, fluid viscosity, and surface tension, the nozzle diameter has the most significant effect on droplet volume, while surface tension has the least effect on droplet formation.

On the structure of parasitic gravity-capillary standing waves in the small surface tension limit

We present new numerical solutions for nonlinear standing water waves when the effects of both gravity and surface tension are considered. For small values of the surface tension parameter, solutions are shown to exhibit highly oscillatory capillary waves (parasitic ripples), which are both time- and space-periodic, and which lie on the surface of an underlying gravity-driven standing wave. Our numerical scheme combines a time-dependent conformal mapping together with a shooting method, for which the residual is minimised by Newton iteration. Previous numerical investigations typically clustered gridpoints near the wave crest, and thus lacked the fine detail across the domain required to capture this phenomenon of small-scale parasitic ripples. The amplitude of these ripples is shown to be exponentially small in the zero surface tension limit, and their behaviour is linked to (or explains) the generation of an elaborate bifurcation structure.

THE ROLE OF FIBRINOGEN IN SERUM AND PLASMA BLOOD TENSIO- AND RIOMETRY IN CORONARY HEART DISEASE AND VALVE LESIONS PATIENTS

Background. Insight into blood viscosity in terms of its physical and biochemical properties carries significant clinical value. By understanding the relationship between the physical properties of blood and physiology, a potentially powerful tool for diagnosing early signs of many diseases can be discovered.&#x0D; Purpose. To identify the effect of fibrinogen on tensio- and rheometric characteristics of blood plasma and serum in patients with coronary heart disease and with mitral and/or aortic valve disease.&#x0D; Materials and methods. Prospective non-randomized study. The study of dynamic, equilibrium surface tension and viscoelastic modulus was performed by the pendant drop method using a PAT-1 device (Sinterface Technologies, Germany). We measured parameters characterizing the surface tension and dilatation rheology of blood serum such as: dynamic surface tension at an adsorption time of 100 s (γ), equilibrium surface tension (γ ∞) (adsorption time 2500 s), viscoelastic modulus |E|, and phase angle (φ) at frequencies of 0.1 and 0.01 Hz.&#x0D; All patients under study were divided into 3 groups. The healthy volunteers (30 subjects) without chronic diseases and active complaints aged 49 to 78 years (mean age, 61.1±1.1 years) comprised the comparison group (group 1).&#x0D; Group 2 - 40 patients with coronary heart disease (CHD) aged 49 to 77 years (mean age 62.2±1.3 years) who underwent bypass surgery to treat atherosclerotic coronary vessels (2 to 5 bypasses).&#x0D; Group 3 - 30 patients with cardiac mitral and/or aortic valve lesions aged 52 to 78 years (mean age 61.3±1.2 years). They underwent mitral and/or aortic valve replacement with mechanical prostheses.&#x0D; The most common pathophysiological syndrome in patients due to coronary artery or heart valve lesions was chronic heart failure (CHF) (stage 2A-2B according to Vasilenko-Strazhesko classification).&#x0D; Results. Characteristic γ100s of blood serum and plasma had significant difference in both patients’ groups, possibly due to the role of coagulation and anti-coagulation system proteins’ role in dynamic surface tension of plasma in a shorter timeframe (up to 100 s.). The increase in Δγ100s in both patients’ groups by day 7 of the postoperative period indicates an increasing dynamic surface tension of serum compared to plasma. Plasma of perioperative patients does not differ from the comparison group by its surface-equilibrium properties. Accordingly, the Δγ∞s values in groups 1 and 2 both before surgery and on days 1 and 7 of the postoperative period are almost identical, pointing to no difference in the amount of surfactants tending to adsorb on the droplet surface. Alterations of viscoelastic modulus |E| and phase angle (φ) at 0.1 and 0.01 Hz in the perioperative period indicate changes in qualitative and quantitative characteristics of circulating blood with variation in individual homeostasis characteristics, resulting in an increase in surface elasticity combined with an almost unchanged surface viscosity.&#x0D; Conclusion. Dynamic and equilibrium surface tension parameters in patients’ plasma differ from those in serum due to the presence of fibrinogen and other proteins of the blood coagulation system.

Role of Membrane-Solute Affinity Interactions in Carbamazepine Rejection and Resistance to Organic Fouling by Nano-Engineered UF/PES Membranes.

In this study, polyethersulfone (PES) ultrafiltration (UF) membranes were modified with GO, Ag, ZnO, Ag-GO and ZnO-GO nanoparticles to improve carbamazepine removal and fouling prevention by making membrane surfaces more hydrophilic. The fabricated membranes were characterized for surface and cross-sectional morphology, surface roughness and zeta potential, as well as hydrophilicity, functional groups, surface tension parameters and water permeability Thereafter, the membranes were evaluated for their efficiency in removing MgSO4 and carbamazepine as well as antifouling properties. To understand the role of affinity interactions in rejection and fouling, membrane-solute adhesion energies (∆Gslm) were quantified based on the Lifshitz-van der Waals/acid-base method. Unlike previous studies, which have generalized fouling prevention to be due to improvements in hydrophilicity upon adding nanoparticles, this work further explored the role of surface tension components on rejection and fouling prevention. The addition of nanoparticles improved membrane hydrophilicity (77-62°), water permeability (11.9-17.7 Lm-2 h-1 bar-1), mechanical strength (3.46-4.11 N/mm2), carbamazepine rejection (30-85%) and fouling prevention (60-23% flux decline). Rejection and antifouling properties increased as ∆Gslm became more repulsive (i.e., less negative). Membrane modification reduced irreversible fouling, and the fouled membranes were cleaned by flushing with water. Fouling related more to membrane electron donor components (γ-), while the roles of electron acceptor (γ+) and Lifshitz-van der Waals components (γLW) were less important. This work provides more insights into the role of affinity interactions in rejection and fouling and how rejection and fouling mechanisms change with nanoparticle addition.

Bubble-assisted matte transportation into slag phase: A numerical investigation

Copper loss into the slag phase during the smelting process can be minimized by controlling gas bubble size and hydrodynamics. Here, bubble rising characteristics from copper matte to slag phase were investigated using the volume-of-fluid modelling approach, in which the continuous surface force model was adopted to define the surface tension parameters. The simulated results for bubble terminal velocities in bulk water and the literature data showed relative errors up to 4.51 %. The obtained qualitative and quantitative data from simulation at the liquid–liquid interface agreed well with the literature experimental results. The simulation setup was applied to investigate three different sizes of bubble rising dynamics from matte to slag phase with the bubble Reynolds number (Re) up to 1734 and the Eotvos number (Eo) up to 3.2. For low Re and Eo, the bubble rising velocity decreased before the matte film rupture and the bubble required a long time to complete that film drainage due to the balance of interfacial tension force and bubble buoyancy. No matte residue associated with the bubble rise in the slag phase was obtained because of restoring initial, non-deformed shape of bubbles. For the higher Re and Eo, quicker matte film drainage was obtained around the upper bubble surface while the entrained matte contribution to the slag phase was strongly dependent on the bubble-shape deformation, which was discussed with the well-known Grace diagram. The decreasing viscosity and increasing surface tension of the slag phase significantly affected the matte film height more than the film rupture time. The film height and rupture time increased and decreased with increasing Eo, respectively. The outcomes of our studies are useful for the design and operation of smetling furnaces in pyrometallurgical purification of metal concentrates.

Flow instabilities of second-grade fluid over a stretching sheet

The work at hand studies thin-film flow instabilities in a non-Newtonian second-grade fluid moving over a stretching sheet. The analysis considers the free surface evolution equation of the thin second-grade viscoelastic fluid model based on the long-wave approximation method. We undertook a linear stability analysis using a normal mode approach and obtained expressions for the linear time growth rate, linear phase speed, and critical wavenumber, which illustrates the linear stability structure of the flow system. Furthermore, the multi-scale analysis of the fluid’s weakly non-linear stability characteristics reveals the presence of subcritical instability in the linear stability zone. The study shows that the varying flow parameters affect the threshold amplitude, which influences the stable and unstable zones in the subcritical region. The outcomes show a stabilizing effect spanning the range of non-dimensional parameters, such as the second-grade parameter ranging from 0 to 100 in values, the surface tension parameter ranging from 0 to 100 in values, and the modified Froude number from 0 to 100 in values.

A new elastic instability in gravity-driven viscoelastic film flow

We examine the linear stability of the gravity-driven flow of a viscoelastic fluid film down an inclined plane. The viscoelastic fluid is modeled using the Oldroyd-B constitutive equation and, therefore, exhibits a constant shear viscosity and a positive first normal stress difference in viscometric shearing flows; the latter class of flows includes the aforesaid film-flow configuration. We show that the film-flow configuration is susceptible to two distinct purely elastic instabilities in the inertialess limit. The first instability owes its origin entirely to the existence of a free surface and has been examined earlier [Shaqfeh et al., “The stability of gravity driven viscoelastic film-flow at low to moderate Reynolds number,” J. Non-Newtonian Fluid Mech. 31, 87–113 (1989)]. The second one is the analog of the centermode instability recently discovered in plane Poiseuille flow [Khalid et al., “Continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow,” Phys. Rev. Lett. 127, 134502 (2021)] and owes its origin to the base-state shear; it is an example of a purely elastic instability of shearing flows with rectilinear streamlines. One may draw an analogy of the aforesaid pair of unstable elastic modes with the inertial free-surface and shear-driven instabilities known for the analogous flow configuration of a Newtonian fluid. While surface tension has the expected stabilizing effect on the Newtonian and elastic free-surface modes, its effect on the corresponding shear modes is, surprisingly, more complicated. For both the Newtonian shear mode and the elastic centermode, surface tension plays a dual role, with there being parameter regimes where it acts as a stabilizing and destabilizing influence. While the Newtonian shear mode remains unstable in the limit of vanishing surface tension, the elastic centermode becomes unstable only when the appropriate non-dimensional surface tension parameter exceeds a threshold. In the limit of surface tension being infinitely dominant, the free-surface boundary conditions for the film-flow configuration reduce to the centerline symmetry conditions satisfied by the elastic centermode in plane Poiseuille flow. As a result, the regime of instability of the film-flow centermode becomes identical to that of the original channel-flow centermode. At intermediate values of the surface tension parameter, however, there exist regimes where the film-flow centermode is unstable even when its channel-flow counterpart is stable. We end with a discussion of the added role of inertia on the aforementioned elastic instabilities.

Thermodynamic Consideration of the Solid Saponin Extract Drop-Air System.

The aim of this research was to elucidate the surface active properties of Saponaria officinalis (soapwort) extract containing the plant surfactants saponins. To this end, the advancing contact angle (θ) of water, formamide and diiodomethane on the glass, as well as θ of the aqueous solution of S. officinalis extract fractions on PTFE, PMMA and glass, were studied. Based on the obtained results, the wetting behaviour of saponins was considered with regard to the surface tension components and parameters of the solutions and solids. The investigations also involved the description of the θ isotherms, the dependences between the cosine of contact angle and/or the adhesion of the solution to the solid surfaces and solution surface tension, as well as the critical surface tension of PTFE, PMMA and glass wetting. These dependences were studied based on the saponin adsorption at the different interfaces, which was deduced from the dependence between the adhesion and surface tension of the solution, as well as using the Gibbs and Frumkin isotherm equations. This proved that the saponins are poor wetting agents and that the contact angle isotherm can be described by the exponential function of the second order as well as the Szyszkowski equation, but only for PTFE.

A numerical method for two-phase flow with its application to the Kelvin–Helmholtz instability problem

This article uses the artificial compressibility-based high-order finite difference method to simulate the two-phase Kelvin–Helmholtz (KH) instability problem. The equations are based on the mass-conserving Allen–Cahn equation coupled with the incompressible Navier–Stokes equations. One of the advantages of the artificial compressibility approach is that many high-order numerical schemes based on hyperbolic conservation law can be applied. A fifth-order weighted essentially non-oscillatory (WENO) scheme is used for discretizing the convective terms while a standard central finite difference scheme is used for the viscous and surface tension terms. The system of equations is then solved using the Beam-Warming approximate factorization technique. For validation, the effects of both single- and double-mode sinusoidal perturbations on the Kelvin–Helmholtz instability dynamics are analyzed. When there is a single-mode sinusoidal perturbation, the interface roll-up at the center of the domain. Additionally, the role of the surface tension parameter in the instability’s dynamics is investigated. The development of Kelvin–Helmholtz instability is shown to be sensitive to the surface tension value. The analysis of grid convergence is also performed to capture the interface dynamics at varying resolutions. The comparison of the computed results is in good agreement with those from the literature. It is observed that the proposed technique effectively resolves the dynamics of the chaotically distorted interfaces of the Kelvin–Helmholtz instability in two-phase flow.