High Surface Viscosity Research Articles

CFD simulation of a small bubble motion in 3D flow domain: effect of liquid density, viscosity and surface tension

The motion of spherical and slightly deformed bubbles rising rectilinearly in a stagnant liquid was numerically simulated in a fully three-dimensional domain using the CFD solver COMSOL Multiphysics. The interface was tracked by the built-in conservative Level set method on a fixed numerical grid. The purpose of this work was to study the single bubble motion in three industrially used liquids that differ significantly in surface tension, density, and viscosity. The motion of bubbles with diameters up to 1.6 mm was also studied experimentally using a high-speed camera. The data obtained together with the results of theoretical models for bubble motion were used for the validation of the simulation data. Using a 3D domain, very good agreement was obtained in both bubble shape deformations and bubble terminal velocity. The best results were achieved for propanol with low surface tension and low viscosity. In the case of high surface tension and low viscosity liquid (water), both the bubble deformation and the bubble velocity were slightly underestimated. In the case of glycerol (high surface tension and viscosity), the negligible bubble deformation is correctly calculated, but the velocity is again slightly underestimated.Graphical abstract

Sprayability Analysis of Pristine and Enhanced PEDOT:PSS Inks via Electrohydrodynamic Spray Deposition

Poly (3,4-ethylene dioxythiophene) polystyrene sulfonate (PEDOT:PSS) is a conductive polymer and versatile material to fabricate numerous organic electronic devices. PEDOT:PSS inks were studied and analyzed for their sprayability via Electrohydrodynamic (EHD) printing. Commercially obtained pristine PEDOT:PSS ink could not produce any decent cone-jet mode due to its high surface tension and viscosity. Two different surfactants – acetone and ethanol were then dispersed into PEDOT:PSS at different concentrations to enhance the sprayability of the PEDOT:PSS ink. Both modified PEDOT:PSS inks could produce a cone-jet mode of spraying, which is essential for EHD printing. The flow rates were tested between 10 - 20 μl/hr. These limits were established to prevent the splashing effect at a higher flow rate (>20μl/hr) and inks disintegrating at a lower flow rate 5μl/hr. PEDOT:PSS:Acetone and PEDOT:PSS:Ethanol with 50:50 and 75:25 ratios, respectively, produced the best performance in their respective categories.

Mechanism of Hexane Displaced by Supercritical Carbon Dioxide: Insights from Molecular Simulations

Supercritical carbon dioxide (sCO2) has great potential for displacing shale oil as a result of its high solubility and low surface tension and viscosity, but the underlying mechanisms have remained unclear up to now. By conducting equilibrium molecular dynamics (EMD) simulations, we found that the displacing process could be divided into three steps: the CO2 molecules were firstly injected in the central region of shale slit, then tended to adsorb on the SiO2-OH wall surface and mix with hexane, resulting in loose hexane layer on the shale surface, and finally displaced hexane from the wall due to strong interactions between CO2 and wall. In that process, the displacing velocity and efficiency of hexane exhibit parabolic and increased trends with pressure, respectively. To gain deep insights into this phenomenon, we further performed non-equilibrium molecular dynamics (NEMD) simulations and found that both the Onsager coefficients of CO2 and hexane were correlated to increase with pressure, until the diffusion rate of hexane being suppressed by the highly dense distribution of CO2 molecules at 12 MPa. The rapid transportation of CO2 molecules in the binary components (CO2 and hexane) actually promoted the hexane diffusion, which facilitated hexane flowing out of the nanochannel and subsequently enhanced oil recovery efficiency. The displacing process could occur effectively at pressures higher than 7.5 MPa, after which the interaction energies of the CO2-wall were stronger than that of the hexane-wall. Taking displacing velocity and efficiency and hexane diffusion rate into consideration, the optimal injection pressure was found at 10.5 MPa in this work. This study provides detailed insights into CO2 displacing shale oil and is in favor of deepening the understanding of shale oil exploitation and utilization.

Green synthesis of a hydrophobic metal-organic gel for the capture of trace odorous hexanal from humid air

The development of superhydrophobic adsorbents for the capture of trace volatile organic compounds (VOCs) from humid indoor air is still a challenge. Herein, we reported the formation of a granular zinc-based metal-organic gel, i.e., ZIF-412(gel) by optimizing the synthesis conditions. The thermally stable xerogel exhibited high surface area (1008 m2/g), hydrophobicity, and viscosity for self-depositing on the substrate such as non-woven fibers. Dynamic adsorption experiments under various humidity conditions demonstrated as-synthesized ZIF-412(gel) owned excellent VOC (hexanal) adsorption performance with adsorption capacity higher than commercial activated carbon and some water-stable MOFs including ZIF-8, ZIF-67, MIL-101(Cr) and ZIF-414. ZIF-412(gel) could be regenerated at temperature as low as 358 K without obvious loss in adsorption capacity. The adsorption mechanism of hexanal over ZIF-412(gel) is also simulated by Grand canonical Monte Carlo (GCMC).

Preparation of ethanol and palm oil/palm kernel oil alternative biofuels based on property improvement and particle size analysis

With the continuous rise in fuel prices and the depletion of fossil fuel resources, the alternative biofuel which has good stability and is suitable for engine combustion is the focus of scientists' research. In this study, the method of mixing ethanol with palm oil (PO) and palm kernel oil (PKO) was used to improve the shortcomings of PO/PKO, such as high surface tension, high density and viscosity. Five co-solvents with a biological production background are selected: tetrahydrofuran (THF), polyoxymethylene dimethyl ether (PODE) and three butanol isomers to aid solubility. The results show that with the continuous dripping of the co-solvent, the PO/PKO and the ethanol gradually dissolve each other until the emergence of a single-phase liquid. Among the five co-solvents, the order of solubilization is THF > PODE > n-butanol > 2-butanol > iso-butanol. Also, with the increase in temperature, the solubility-assisting ability increases. When the particle size of the ternary blended fuel microemulsion system reaches the maximum value of 59.65 nm, the composition ratio of ethanol in the basic system is 50%. In addition, PKO has a stronger affinity with ethanol than PO; PKO can be completely miscible with ethanol when the experimental temperature is 35 °C. As the proportion of ethanol increases, the surface tension of the ternary system decreases by 36.2% at most. In terms of fuel property adjustment, THF has the best adjustment effect on solubility and viscosity. Butanol has the best adjustment effect on the density of blended fuel. PODE will corrode copper strips due to high oxygen content. In the future, according to the fuel demand in different scenarios, the proportion of each component in the blended fuel can be adjusted to achieve the optimum in practical applications.

Enhanced stability of free viscous films due to surface viscosity

The stability of a thin liquid film bounded by two free surfaces is examined in the presence of insoluble surface-active agents. This study is broadly aimed at understanding enhanced stability of emulsions with the increasing surface concentration of surface-active agents. Surface-active agents not only cause gradients in surface tension but could also render surface viscosity to be significant, which could vary with surface concentration. We employ two phenomenological models for surface viscosity, a linear viscosity model and a nonlinear viscosity model. In the latter, surface viscosity diverges at a critical concentration, which is termed the “jamming” limit. We show that rupture can be significantly delayed with high surface viscosity. An analysis of the “jamming” limit reveals that Γi(nl)>3D/M provides a simple criterion for enhanced stability, where Γi(nl), D, and M are the normalized initial surfactant concentration, disjoining pressure number, and Marangoni number, respectively. Nonlinear simulations suggest that high surface viscosity renders free films remarkably stable in the jamming limit, and their free surfaces behave like immobile interfaces consistent with experimental observations. Furthermore, it is shown that rupture times can be arbitrarily increased by tuning the initial surfactant concentration, offering a fluid dynamical route to stabilization of thin films.

On the role of the surface rheology in film drainage between fluid particles

Coalescence in the presence of low surfactant concentrations is investigated via a film drainage model, where the interface is a Boussinesq surface fluid with surfactant concentration dependent physical properties. Three cases are considered representing the systems where water is the continuous phase and the dispersed phase is either high viscosity droplets, droplets of comparable viscosity to water or gas bubbles. In the former, the immobilization of the interface is due to high dispersed phase viscosity and surface viscosities, whereas in the latter two, the Marangoni flow plays an important role, too. When droplets of comparable viscosity to water or gas bubbles are considered, it is seen that both the Marangoni flow and the surface viscosities can change the coalescence time significantly for the experimentally encountered values of the initial surfactant concentration, and the Boussinesq and surface Péclet numbers. In all cases, the impact of the surface phenomena amplifies with the approach velocity, especially for the dimpled interfaces. A complete immobilization criterion that is independent of the dispersed phase viscosity is proposed as a function of the continuous phase and surface viscosities, and the particle radii.

Surface rheological measurements of isolated food foam systems

Liquid foams represent a key component to a vast range of food industry products, from ice creams to the crema on coffee. Longevity of these foams is a highly desirable attribute; however, in order for foam stability to be effectively controlled, a better understanding of the interdependence of the bulk liquid and air-liquid interfacial rheologies is required. This study follows an increasing trend in experimental investigations made of isolated foam structures at the microscale, where the bulk and surface dynamics of a single foam liquid channel can be accurately assessed. Isolated foam channels with adjoining nodes were studied for aqueous solutions of four food grade surfactants. Existing observations of distortions to sodium dodecyl sulphate channel geometries were confirmed for solutions of Tween 20 (T20) and Tween 80 (T80) and were well described by the theory presented here. Moreover, previously unseen distortions to liquid channels were observed for polymeric surfactant systems (hydroxypropyl methylcellulose and hydrolyzed pea protein blend), which were proposed to result from their high surface viscosities. The apparent surface viscosities, μs, of surfactants tested here ranged from high (10 g/s < μs < 10−3 g/s) for polymeric surfactants to very low (10−10 g/s < μs < 10−8 g/s) for Tweens, clearly demarking the regimes of viscous and inertial dominant flows, respectively. It is recommended that further work seeks to investigate the finding of a strong correlation between μs and channel surface tension, γ, for soluble surfactant systems, which could explain the apparent non-Newtonian values of μs that were consistently measured here.

A Review: Non-Evaporating Spray Characteristics of Biodiesel Jatropha and Palm Oil and Its Blends

The study on the Non-evaporating spray characteristics in biodiesel is imperative to comprehend the conduct of the spray in different biodiesel. Non evaporating spray characteristics give some parameters, such as spray cone (plume) angle, spray (tip) penetration and droplet size. This paper reviews that methyl ester or biodiesel fuel from Jatropha (BDFJ) and biodiesel fuel from palm oil (BDFP) have similar characteristics of Diesel Fuel (DF). Biodiesel derived from palm oil and Jatropha oil have longer cone angle and spray (tip) penetration than DF. In biodiesel, high surface tension and viscosity, caused by the slower separation, can lead to shorter cone angle and higher penetration. Spray tip penetration will increment with the increasing of mixing proportion in biodiesel blends. In the cone angle, palm methyl ester gives a smaller angle than DF. The characteristic of cone angle is decreased when the percentage of the proportion of biodiesel is expanded. In Sauter Mean Diameter (SMD), diesel fuel sprays are smaller than the biodiesel spray. The SMD diminishes when the injection pressure is expanded. It happens because of the biodiesel has high viscosity that can expand the friction among the fuels to the surface of the nozzle. Hence, a study of biodiesel is needed before conducting the experiment of non-evaporating spray. Mainly, the fuel properties such as surface tension, viscosity and density play critical parts in the conduction of non-evaporating spray characteristics of biodiesel and its blends.

Facile preparation of polymer microspheres and fibers with a hollow core and porous shell for oil adsorption and oil/water separation

Non-solvent assisted electrospinning was proposed for fabricating Polymethylmethacrylate (PMMA) microspheres and fibers with a hollow core and porous shell, which could be used for oil adsorption and oil/water separation. Propanediol was chosen as the non-solvent because of its high surface tension and viscosity as well as large phase separation tendency with polymer, which was beneficial to the formation of both the hollow core and porous shell during the electrospinning. With the increase of the polymer solution concentration, the microsphere gradually evolved to the bead-on-string geometry and finally to a continuous fiber form, indicating the transition from electro-spraying to electrospinning. The hollow core and dense surface pores enhanced the hydrophobicity, oleophilicity, permeability, and specific surface area of the fibers, and hence imparted the fibrous mat a high oil adsorption capacity. When the porous hollow microspheres were electro-sprayed onto the stainless steel mesh followed by the PDMS modification, the modified mesh became super-hydrophobic and super-oleophilic with the contact angle of 153° and sliding angle of 4°. The as-prepared mesh showed rapid oil/water separation with high efficiency and excellent recycling performance. The flux for separation of oil/water mixture could reach as high as 11,000 L m−2 h−1. This facile non-solvent assisted electrospinning method provides a new avenue for preparation of multifunctional porous materials which possess potential applications in large-scale oil/water separation.

Self-Assembly of Escin Molecules at the Air-Water Interface as Studied by Molecular Dynamics.

Escin belongs to a large class of natural biosurfactants, called saponins, that are present in more than 500 plant species. Saponins are applied in the pharmaceutical, cosmetics, and food and beverage industries due to their variously expressed bioactivity and surface activity. In particular, escin adsorption layers at the air-water interface exhibit an unusually high surface elastic modulus (>1100 mN/m) and a high surface viscosity (ca. 130 N·s/m). The molecular origin of these unusual surface rheological properties is still unclear. We performed classical atomistic dynamics simulations of adsorbed neutral and ionized escin molecules to clarify their orientation and interactions on the water surface. The orientation and position of the escin molecules with respect to the interface, the intermolecular interactions, and the kinetics of molecular aggregation into surface clusters are characterized in detail. Significant differences in the behavior of the neutral and the charged escin molecules are observed. The neutral escin rapidly assembles in a compact and stable surface cluster. This process is explained by the action of long-range attraction between the hydrophobic aglycones, combined with intermediate dipole-dipole attraction and short-range hydrogen bonds between the sugar residues in escin molecules. The same interactions are expected to control the viscoelastic properties of escin adsorption layers.

Influence of surface viscosity on droplets in shear flow

The behaviour of a single droplet in an immiscible external fluid, submitted to shear flow is investigated using numerical simulations. The surface of the droplet is modelled by a Boussinesq–Scriven constitutive law involving the interfacial viscosities and a constant surface tension. A numerical method using Loop subdivision surfaces to represent droplet interface is introduced. This method couples boundary element method for fluid flows and finite element method to take into account the stresses due to the surface dilational and shear viscosities and surface tension. Validation of the numerical scheme with respect to previous analytic and computational work is provided, with particular attention to the viscosity contrast and the shear and dilational viscosities characterized both by a Boussinesq number$B_{q}$. Then, influence of equal surface viscosities on steady-state characteristics of a droplet in shear flow are studied, considering both small and large deformations and for a large range of bulk viscosity contrast. We find that small deformation analysis is surprisingly predictive at moderate and high surface viscosities. Equal surface viscosities decrease the Taylor deformation parameter and tank-treading angle and also strongly modify the dynamics of the droplet: when the Boussinesq number (surface viscosity) is large relative to the capillary number (surface tension), the droplet displays damped oscillations prior to steady-state tank-treading, reminiscent from the behaviour at large viscosity contrast. In the limit of infinite capillary number$Ca$, such oscillations are permanent. The influence of surface viscosities on breakup is also investigated, and results show that the critical capillary number is increased. A diagram$(B_{q};Ca)$of breakup is established with the same inner and outer bulk viscosities. Additionally, the separate roles of shear and dilational surface viscosity are also elucidated, extending results from small deformation analysis. Indeed, shear (dilational) surface viscosity increases (decreases) the stability of drops to breakup under shear flow. The steady-state deformation (Taylor parameter) varies nonlinearly with each Boussinesq number or a linear combination of both Boussinesq numbers. Finally, the study shows that for certain combinations of shear and dilational viscosities, drop deformation for a given capillary number is the same as in the case of a clean surface while the inclination angle varies.

Surfactant transport onto a foam film in the presence of surface viscous stress

Surfactant transport onto a foam film in the presence of surface viscosity has been simulated as a model for processes occurring during foam fractionation with reflux. A boundary condition is specified determining the velocity at the end of the film where it joins up with a Plateau border containing surfactant rich reflux material. The evolutions of surface velocity and surfactant surface concentration on the film are computed numerically using a finite difference method coupled with the material point method. Results are analysed both for low and high surface viscosities. Evolution is comparatively rapid when surface viscosity is low, but the larger the surface viscosity becomes, the slower the surface flow, and the lower the surfactant surface concentration on the film at any given time. For a large surface viscosity, the surface concentration of surfactant is maintained nearly uniform except at positions near the Plateau border where the velocity and surfactant concentration fields need to adjust to satisfy the boundary condition at the end of the film. The boundary condition imposed at the end of the film implies also that a drier foam (i.e. smaller radius of curvature of the Plateau border) leads to less surfactant transport onto the films. Moreover, the shorter the film length is, also the shorter the characteristic time for surfactant transport onto the film surface. Thinner films however give longer characteristic times for surfactant transport.

From spin coating to doctor blading: A systematic study on the photovoltaic performance of an isoindigo-based polymer

Doctor blading is suitable to roll-to-roll process with much little solution wasting and is less studied compared with the mainstream spin coating. In this work, we used a novel polymer blended with two common fullerene derivatives as active solutions. To systemically understand the different coating methods and the different fullerene acceptors on the effect of polymer solar cells (PSCs) photovoltaic performance, the wet active solution physic-chemical properties and variations of the dried active layer characterizations were investigated. It was observed that it is much easier to obtain a homogeneous film from doctor blading compared with spin coating for the polymer: PC71BM solution due to the high surface tension and viscosity. Moreover, the high boiling point additive plays an important role in inhibiting the wet film shrinkage and forming a uniform film. The longer film drying time for the doctor-blading films leads to larger domains than spin coating, thus increases the geminate recombination and results in lower mobilities as well as power conversion efficiencies (PCE). Doctor-blading-processed PSCs with PCE of 4.46% were achieved for P3TI:PC71BM devices, which were comparable to those of spin-coating devices. This work provided valuable suggestions and solutions for the doctor-blading process, especially for crystalline D-A polymer-based devices.

The role of the hydrophobic phase in the unique rheological properties of saponin adsorption layers.

Saponins are a diverse class of natural, plant derived surfactants, with peculiar molecular structure consisting of a hydrophobic scaffold and one or several hydrophilic oligosaccharide chains. Saponins have strong surface activity and are used as natural emulsifiers and foaming agents in food and beverage, pharmaceutical, ore processing, and other industries. Many saponins form adsorption layers at the air-water interface with extremely high surface elasticity and viscosity. The molecular origin of the observed unique interfacial visco-elasticity of saponin adsorption layers is of great interest from both scientific and application viewpoints. In the current study we demonstrate that the hydrophobic phase in contact with water has a very strong effect on the interfacial properties of saponins and that the interfacial elasticity and viscosity of the saponin adsorption layers decrease in the order: air > hexadecane ≫ tricaprylin. The molecular mechanisms behind these trends are analyzed and discussed in the context of the general structure of the surfactant adsorption layers at various nonpolar phase-water interfaces.

On the Addition of Protein (Casein) to Aqueous Lactose as a Drying Aid in Spray Drying—Theoretical Surface Composition

Spray drying is the primary process for the formation of dairy powders. In multistage drying operations, the post-spray-drying stage—for example, a fluidized bed drying stage—may not alter much of the surface composition formed earlier due to the extremely high surface viscosity. Spray drying of high-sugar-content product without a retardant on the surface to prevent sticky powder deposition in drying chamber may produce very low yields due to drying chamber wall deposition or cyclone deposition. The powder products are not flow able. A functional spray-dried product begins with its efficient incorporation into water; hence, surface composition plays a key role. This study is an attempt to explore the solid formation around the outermost layer of a single droplet of protein–sugar solution during the drying process using a continuum approach (diffusion–convection equations). The main feature of this model is that the multicomponent effect is lumped into the viscosity of the fluid at the surface, which inversely affects the diffusivities of individual components in the solution droplets or suspension droplets. The trend (and the order of magnitudes) of surface composition development of the caseinate/lactose system (from a 20/80 ratio down to 0.01/99.99) has been explored and the phenomeno has been explained with the aid of the continuum model, coupled with a simplified, geometrical, molecular-level interpretation. Based on the current study, we were able to make some useful conclusions.

Tracking the interfacial dynamics of PNiPAM soft microgels particles adsorbed at the air–water interface and in thin liquid films

We report the behavior of thermosensitive soft microgel particles adsorbed at the air–water interface. We study the effect of temperature on the adsorption, interfacial diffusion, and surface rheology of pure N-isopropylacrylamide (NiPAM) microgel particles at the air–water interface. We find that the surface tensions of the solutions are the same as those of polyNiPAM solution; hence, their adsorption properties are dominated by the surface activity of the NiPAM repeat units of the particles. Particle-tracking experiments show that the particles adsorb irreversibly at the interface and form stable clusters at very low concentrations, e.g., 5.10-3 wt%. We suggest that attractions between dangling arms or capillary interaction may be responsible for the formation of these clusters. For concentrations above 10-2 wt%, the interface is filled with particles, and their Brownian diffusivity is arrested. The compression elastic moduli—measured using the pendant drop method—are one or two orders of magnitude below those obtained for hard particles and NiPAM chains, and their value is probably dominated by the intrinsic compressibility of the particles. The thin liquid films made from microgels exhibit a symmetric drainage, consistent with a high surface viscosity, but their lifetime is surprisingly short, illustrating the fragility of the films. We observed the formation of a monolayer of microgels bridging the two interfaces of the film outside the dimple. This zone grows and thins over time to a point where the microgels are highly compressed and stretched, resulting in the rupture of the film.

Fabrication of micro-pin array with high aspect ratio on stainless steel using nanosecond laser beam machining

In this paper, a micro-pin array with a high aspect ratio was fabricated on AISI 304 using laser beam ablation for attachment to a vertical wall. In recent times, there has been research in various fields, including robotics and bio-MEMS, regarding attachment to vertical walls, and micro-pin arrays may offer the best solution. For vertical wall attachment, the micro-pin should have a high aspect ratio, long length, and sharp tip. The recast layer could be piled due to the chromium oxide with high surface tension and viscosity of chromium oxide, and it composed the micro-pins with high aspect ratio. X-ray photoelectron spectroscopy (XPS) was used to identify the characteristics of the piled recast layer. The machining characteristics for a high aspect ratio micro-pin array were investigated according to laser beam machining parameters. In addition, experiments for attaching force relative to the surface roughness of the subject plane were carried out.

Solid Character of Membrane Ceramides: A Surface Rheology Study of Their Mixtures with Sphingomyelin

The compression and shear viscoelasticities of egg-ceramide and its mixtures with sphingomyelin were investigated using oscillatory surface rheology performed on Langmuir monolayers. We found high values for the compression and shear moduli for ceramide, compatible with a solid-state membrane, and extremely high surface viscosities when compared to typical fluid lipids. A fluidlike rheological behavior was found for sphingomyelin. Lateral mobilities, measured from particle tracking experiments, were correlated with the monolayer viscosities through the usual hydrodynamic relationships. In conclusion, ceramide increases the solid character of sphingomyelin-based membranes and decreases their fluidity, thus drastically decreasing the lateral mobilities of embedded objects. This mechanical behavior may involve important physiological consequences in biological membranes containing ceramides.

WITNESSING THE BIRTH OF A QUASAR

The coalescence of a supermassive black hole binary (SMBHB) is thought to be accompanied by an electromagnetic (EM) afterglow, produced by the viscous infall of the surrounding circumbinary gas disk after the merger. It has been proposed that once the merger has been detected in gravitational waves (GWs) by LISA, follow-up EM searches for this afterglow can help identify the EM counterpart of the LISA source. Here we study whether the afterglows may be sufficiently bright and numerous to be detectable in EM surveys alone. The viscous afterglow, which lasts for years to decades for SMBHBs in LISA's sensitivity window, is characterized by rapid increases in both the bolometric luminosity and in the spectral hardness of the source. If quasar activity is triggered by the same major galaxy mergers that produce SMBHBs, then the afterglow could be interpreted as a signature of the birth of a quasar. Using an idealized model for the post-merger viscous spreading of the circumbinary disk and the resulting light curve, and using the observed luminosity function of quasars as a proxy for the SMBHB merger rate, we delineate the survey requirements for identifying such birthing quasars. If circumbinary disks have a high disk surface density and viscosity, an all-sky soft X-ray survey with a sensitivity of ~<3x10^-14 erg s^-1 cm^-2 and a time resolution of ~months could identify dozens of birthing quasars with sustained brightening rates of >10%/yr. If >1% of the X-ray emission is reprocessed into optical frequencies, birthing quasars could also be identified in optical transient surveys such as the LSST. Distinguishing a birthing quasar from other variable sources may be facilitated by the monotonic hardening of its spectrum, but will likely remain challenging. This reinforces the notion that joint EM-plus-GW observations offer the best prospects for identifying the EM signatures of SMBHB mergers.