GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

Viscosity and structure relationship with equimolar substitution of CaO with MgO in the CaO–MgO–Al_(2)O_(3)–SiO_(2)slag melts

Currently,the Al_(2)O_(3)content in the high-alumina slag systems within blast furnaces is generally limited to 16wt%–18.5wt%,making it challenging to overcome this limitation.Unlike most studies that concentrated on managing the MgO/Al_(2)O_(3)ratio or basicity,this paper explored the effect of equimolar substitution of MgO for CaO on the viscosity and structure of a high-alumina CaO-MgO-Al_(2)O_(3)-SiO_(2)slag system,providing theoretical guidance and data to facilitate the application of high-alumina ores.The results revealed that the viscosity first decreased and then increased with higher MgO substitution,reaching a minimum at 15mol%MgO concentration.Fourier transform infrared spectroscopy(FTIR)results found that the depths of the troughs representing[SiO_(4)]tetrahedra,[AlO_(4)]tetrahedra,and Si-O-Al bending became progressively deeper with increased MgO substitution.Deconvolution of the Raman spectra showed that the average number of bridging oxygens per Si atom and the X_(Q^(3))/X_(Q^(2))(X_(Q^(i))is the molar fraction of Q^(i) unit,and i is the number of bridging oxygens in a[SiO_(4)]tetrahedral unit)ratio increased from 2.30 and 1.02 to 2.52 and 2.14,respectively,indicating a progressive polymerization of the silicate structure.X-ray photoelectron spectroscopy(XPS)results highlighted that non-bridging oxygen content decreased from 77.97mol% to 63.41mol% with increasing MgO concentration,whereas bridging oxygen and free oxygen contents increased.Structural analysis demonstrated a gradual increase in the polymerization degree of the tetrahedral structure with the increase in MgO substitution.However,bond strength is another important factor affecting the slag viscosity.The occurrence of a viscosity minimum can be attributed to the complex evolution of bond strengths of non-bridging oxygens generated during depolymerization of the[SiO_(4)]and[AlO_(4)]tetrahedral structures by CaO and MgO.

Study of the Viscosity and Specific Gravity of the Ternary Used Frying Oil (UFO)-Bioethanol-Diesel System

Fossil fuels cover around 80% of global energy consumption. However, the problems linked to their use justify the choice of using biofuel. In order to reduce as much as possible, diesel rate, an increase in the number of additives may be considered. Thus, in this work, the study of the used frying oil (UFO), bioethanol and diesel ternary system was undertaken. It emerges from this study that the addition of bioethanol reduces the viscosity and the density of the ternary system and permits a 90% substitution rate for diesel between the UFO and bioethanol. Finally, the percentage of oil becomes 40% after adding alcohol compared to the binary diesel crude vegetable oil mixture where this rate is 30%.

Effects of basicity and MgO content on the viscosity of the SiO_2-CaO-MgO-9wt%Al_2O_3 slag system

The effects of basicity and MgO content on the viscosity of SiO2-CaO-MgO-9wt%Al2O3 slags with basicity from 0.4 to 1.0 and MgO content from 13wt%to 19wt%were investigated using the rotating cylinder method. A correlation between the viscosity and the slag structure was determined by Fourier transform infrared （FTIR） spectroscopy. It is indicated that the complex network structure of the slag melt is depolymerized into simpler network units with increasing basicity or MgO content, resulting in a continuous decrease in viscosity of the slag. The viscosity is strongly dependent on the combined action of basic oxide components in the slag. Under the present experimental conditions, increasing the basicity is found to be more effective than increasing the MgO content in decreasing the viscosity of the slag. At higher temperatures, the increase of basicity or MgO content does not appreciably decrease the viscosity of the slag, as it does at lower tem-peratures. The calculated activation energy of viscous flow is between 154 and 200 kJ＆#183;mol-1, which decreases with an increase in basicity from 0.4 to 1.0 at a fixed MgO content in the range of 13wt%to 19wt%.

Investigations on methane hydrate formation,dissociation,and viscosity in gas-water-sand system

Understanding the kinetics and viscosity of hydrate slurry in gas-water-sand system is of great significance for the high-efficiency and high-safety development of natural gas hydrates.The effect of micronsized sands with various concentrations and particle sizes on the hydrate formation,dissociation,and viscosity in gas-water-sand system are investigated in this work.The experimental results show that the hydrate induction time in the sandy system is slightly prolonged compared to the pure gas-water system,and the inhibition effect first strengthens and then weakens as the sand concentration increases from0 wt%to 5 wt%.Besides,the difference of hydrate formation amount in various cases is not obvious.The concentration and particle size of sand have little effect on the kinetics of hydrate formation.Both promoting and inhibiting effects on hydrate formation have been found in the sandy multiphase fluid.For the viscosity characteristics,there are three variations of hydrate slurry viscosity during the formation process:Steep drop type,S-type and Fluctuation type.Moreover,appropriate sand size is helpful to reduce the randomness of slurry viscosity change.Meanwhile,even at the same hydrate volume fraction,the slurry viscosity in the formation process is significantly higher than that in dissociation process,which needs further research.This work provides further insights of hydrate formation,dissociation,and viscosity in gas-water-sand system,which is of great significance for safe and economic development of natural gas hydrates.

Measurement and Correlation on Viscosity and Apparent Molar Volume of Ternary System for L-ascorbic Acid in Aqueous D-Glucose and Sucrose Solutions

Viscosities and densities at several temperatures from 293.15 K to 313.15K are reported for L-ascorbic acid in aqueous glucose and sucrose solutions at different concentrations. The parameters of density, viscosity coefficient B and partial molar volume are calculated by regression. The experimental results show that densities and viscosities decrease as temperature increases at the same solute and solvent (glucose and sucrose aqueous solution) concentrations, and increase with concentration of glucose and sucrose at the same solute concentration and temperature. B increases with concentration of glucose and sucrose and temperature. L-ascorbic acid is structure-breaker or structure-making for the glucose and sucrose aqueous solutions. Furthermore, the solute-solvent interactions in ternary systems of water-glucose-electrolyte and water-sucrose-electrolyte are discussed.

Modeling of Surface Tension and Viscosity for Non-electrolyte Systems by Means of the Equation of State for Square-well Chain Fluids with Variable Interaction Range

The equation of state(EOS)for square-well chain fluid with variable range(SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids(ILs).A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures.The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation(AAD)of 0.36%.A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring’s rate theory of viscosity and the SWCF-VR EOS.The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases.The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT,vapor-liquid equilibrium,caloric properties,surface tension,and viscosity.

CONVERGENCE OF THE VISCOSITY METHOD FOR A NONSTRICTLY HYPERBOLIC SYSTEM

A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves.

Experimental study on viscosity characteristic of sewage in urban untreated sewage source heat pump system

To confirm the rheological characteristic of sewage in the research and application of urban sewage source heat pump system, the viscosity of sewage was investigated. The tube-type rheometer was used in this experimental study, and the sewage was treated as homogeneous non-Newtonian fluid. In addition, the relational expression between viscosity parameters was developed, and the function of apparent viscosity was obtained. It is concluded that the viscosity characteristic of sewage is influenced largely by complex mixture in sewage, and the sewage has the characteristic of sheared densification fluid.

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

Viscosity model of high-viscosity dispersing system

High-viscosity dispersing system is formed by dispersing the solid particles in the high-viscosity continuous medium.It is very easy to form the three-dimensional network structure for solid particles in the system and the rheology behavior becomes complicated.The apparent viscosity of this dispersing system always has the connection with the volume ratio and the shear rate.In order to discuss the rheology behavior and put up the viscosity model,the suspension of silicon dioxide and silicon oil were prepared.Through testing the viscosity,the solid concentration and the shear rate,the effects of the ratio and the shear rate on viscosity was analyzed,the model of the high-viscosity dispersing system was designed and the model with the printing ink were validated.The experiment results show that the model is applicable to the high-viscosity dispersing systems.

Density and Viscosity of Ternary Systems(Poloxamer 188+Ethanol/ Acetone+Water)at Temperatures from 288.15 K to 308.15 K

The densities and viscosities of ternary systems(Poloxamer 188+ethanol/acetone+water)were meas- ured at 288.15,293.15,298.15,303.15,308.15 K and atmospheric pressure for different mass fractions of Poloxamer 188(0 to 0.02)in aqueous solution and different solvent volume fractions of ethanol/acetone(0 to 0.3)in Poloxamer 188 aqueous solution.The densities were measured by a pycnometer,while the viscosities were measured using two Ubbelohde capillary viscometers.The correlations of density and viscosity of these ternary systems are obtained by fitting the experimental data at different temperatures,mass fractions and volume fractions.

Evaluation of Feed and Feeding Regime on Growth Performance, Flesh Quality and Fecal Viscosity of Atlantic Salmon(Salmo salar L.) in Recirculating Aquaculture Systems

The effects of different feeds and feeding regimes on growth performance, flesh quality and fecal viscosity of Atlantic salmon （Salmo salar L.） in recirculating aquaculture systems （R.AS） were investigated. Fish （initial body weight of 1677 g＋ 157 g） were fed with four commercial feeds （Nosan salmon-NS, Aller gold-AG, Skretting salmon-SS and Hart ye-HY） in two feeding regimes （80% and 100% satiation） for 78 d. The results showed that salmon specific growth ratio （SGR） and weight gain ratio （WGR） were significantly affected by feed type and feeding regime （P〈0.05）. Feed conversion ratio （FCR） varied between 0.93 and 3.40, which was significantly affected by feed type （P〈0.05）, and slightly improved with increased satiation degree. The activities of digestive enzymes including protease, lipase and amylase were also significantly affected by feed type and feeding regime （P〈0.05）, increasing with satiation degree. Flesh qualities for vitamin E, hydroxyproline （HYP）, liquid loss and muscle pH among all groups showed significant differences （P〈0.05）, ranging from 26.67 to 29.67, while no obvious difference was found in flesh color. Fecal viscosity for different treatments showed no significant difference, though improvement was found in 100% satiation group. From present experiment, it was concluded that both feed type and feeding regime can affect the important quality attributes of Atlantic salmon.

Prediction of density and viscosity of ternary systems [C_2q]Br+[C_4q]Br+H_2O, [C_2q]Br+[C_6q]Br +H_2O, and [C_4q]Br+[C_6q]Br+H_2O at different temperatures using their binary subsystems data

The simple equations for prediction of the density and viscosity of mixed electrolyte solutions were extended to the related properties of mixed ionic liquid solutions. The density and viscosity were measured for ternary solutions [C2q]Br（N-ethylquinolinium bromide）＋[C4q]Br （N-butylquinolinium bromide）＋H2O, [C2q]Br＋[C6q]Br（N-hexylquinolinium bromide）＋H2O, and [C4q]Br＋[C6q]Br＋H2O and their binary subsystems [C2q]Br＋H2O, [C4q]Br＋H2O, and [C6q]Br＋H2O at 15, 20 and 25 °C, respectively. The results were used to test the predictability of the extended equations. The comparison results show that these simple equations can be used to predict the density and viscosity of the mixed ionic liquid solutions from the properties of their binary subsystems of equal ionic strength.

Intradiffusion, density and viscosity studies in binary liquid systems of acetylacetone + DMF/DMSO/benzene at 303.15 K and 333.15 K

Intradiffusion coefficients of acetylacetone(AcAc) and DMF/DMSO/benzene in binary systems over the entire concentration range at 303.15 K were determined by 1H diffusion-order spectroscopy(DOSY) nuclear magnetic resonance(NMR) method based pulse field gradient(PFG).The densities and viscosities of the above three binary systems at 303.15 K were also studied and employed to calculate the excess molar volumes(V^E) and deviations in viscosity(△η).Besides,experiments were carried out at 333.15 K for the system of AcAc+DMF.The solvent and temperature effect upon the difference in D between enol and keto tautomers,the tautomeric equilibrium and excess properties(V^E and △η) were discussed as well.Isotherms of V^E as a function of mole fraction of AcAc(χ_1) show positive deviations in benzene but negative deviations in DMF and DMSO,whereas isotherms of △ηas a function of χ_1 record positive deviations in DMF but negative in benzene and DMSO.V^E values show more negative and △η values are less positive in the system of AcAc+DMF at 333.15 K compared to 303.15 K.The V^E and △η were fitted to a Redlich-Kister type equation and the measured results were interpreted concerning molecular interactions in the solutions.

GLOBAL WELLPOSEDNESS OF MAGNETOHYDRODYNAMICS SYSTEM WITH TEMPERATURE-DEPENDENT VISCOSITY

The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is considered in this article. A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1.

Construction of coal pitch-based HA-K grafted poly condensates and their excellent anti-temperature and viscosity-reducing properties

Humic acids(HAs)are widely used as filtrate and viscosity reducers in drilling fluids.However,their practical utility is limited due to poor stability in salt resistance and high-temperature resistance.Hightemperature coal pitch(CP)is a by-product from coal pyrolysis above 650℃.The substance's molecular structure is characterized by a dense arrangement of aromatic hydrocarbon and alkyl substituents.This unique structure gives it unique chemical properties and excellent drilling performance,surpassing traditional humic acids in drilling operations.Potassium humate is prepared from CP(CP-HA-K)by thermal catalysis.A new type of high-quality humic acid temperature-resistant viscosity-reducer(Graft CP-HA-K polymer)is synthesized with CP-HA-K,hydrolyzed polyacrylonitrile sodium salt(Na-HPAN),urea,formaldehyde,phenol and acrylamide(AAM)as raw materials.The experimental results demonstrate that the most favorable conditions for the catalytic preparation of CP-HA-K are 1 wt%catalyst dosage,30 wt%KOH dosage,a reaction temperature of 250℃,and a reaction time of 2 h,resulting in a maximum yield of CP-HA-K of 39.58%.The temperature resistance of the Graft CP-HA-K polymer is measured to be 177.39℃,which is 55.39℃ higher than that of commercial HA-K.This is due to the abundant presence of amide,hydroxyl,and amine functional groups in the Graft CP-HA-K polymer,which increase the length of the carbon chains,enhance the electrostatic repulsion on the surface of solid particles.After being aged to 120℃ for a specified duration,the Graft CP-HA-K polymer demonstrates significantly higher viscosity reduction(42.12%)compared to commercial HA-K(C-HA-K).Furthermore,the Graft CP-HA-K polymer can tolerate a high salt concentration of 8000 mg.L-1,measured after the addition of optimum amount of 3 wt%Graft CP-HA-K polymer.The action mechanism of Graft CP-HA-K polymer on high-temperature drilling fluid is that the Graft CP-HA-K polymer can increase the repulsive force between solid particles and disrupt bentonite's reticulation structure.Overall,this research provides novelty insights into the synthesis of artificial humic acid materials and the development of temperature-resistant viscosity reducers,offering a new avenue for the utilization of CP resources.

Hybrid data-driven and physics-based modeling for viscosity prediction of ionic liquids

Viscosity is one of the most important fundamental properties of fluids.However,accurate acquisition of viscosity for ionic liquids(ILs)remains a critical challenge.In this study,an approach integrating prior physical knowledge into the machine learning(ML)model was proposed to predict the viscosity reliably.The method was based on 16 quantum chemical descriptors determined from the first principles calculations and used as the input of the ML models to represent the size,structure,and interactions of the ILs.Three strategies based on the residuals of the COSMO-RS model were created as the output of ML,where the strategy directly using experimental data was also studied for comparison.The performance of six ML algorithms was compared in all strategies,and the CatBoost model was identified as the optimal one.The strategies employing the relative deviations were superior to that using the absolute deviation,and the relative ratio revealed the systematic prediction error of the COSMO-RS model.The CatBoost model based on the relative ratio achieved the highest prediction accuracy on the test set(R^(2)=0.9999,MAE=0.0325),reducing the average absolute relative deviation(AARD)in modeling from 52.45% to 1.54%.Features importance analysis indicated the average energy correction,solvation-free energy,and polarity moment were the key influencing the systematic deviation.

Influences of clean fracturing fluid viscosity and horizontal in-situ stress difference on hydraulic fracture propagation and morphology in coal seam

The viscosity of fracturing fluid and in-situ stress difference are the two important factors that affect the hydraulic fracturing pressure and propagation morphology. In this study, raw coal was used to prepare coal samples for experiments, and clean fracturing fluid samples were prepared using CTAB surfactant. A series of hydraulic fracturing tests were conducted with an in-house developed triaxial hydraulic fracturing simulator and the fracturing process was monitored with an acoustic emission instrument to analyze the influences of fracturing fluid viscosity and horizontal in-situ stress difference on coal fracture propagation. The results show that the number of branched fractures decreased, the fracture pattern became simpler, the fractures width increased obviously, and the distribution of AE event points was concentrated with the increase of the fracturing fluid viscosity or the horizontal in-situ stress difference. The acoustic emission energy decreases with the increase of fracturing fluid viscosity and increases with the increase of horizontal in situ stress difference. The low viscosity clean fracturing fluid has strong elasticity and is easy to be compressed into the tip of fractures, resulting in complex fractures. The high viscosity clean fracturing fluids are the opposite. Our experimental results provide a reference and scientific basis for the design and optimization of field hydraulic fracturing parameters.

Nuclear magnetic resonance experiments on the time-varying law of oil viscosity and wettability in high-multiple waterflooding sandstone cores

A simulated oil viscosity prediction model is established according to the relationship between simulated oil viscosity and geometric mean value of T2spectrum,and the time-varying law of simulated oil viscosity in porous media is quantitatively characterized by nuclear magnetic resonance(NMR)experiments of high multiple waterflooding.A new NMR wettability index formula is derived based on NMR relaxation theory to quantitatively characterize the time-varying law of rock wettability during waterflooding combined with high-multiple waterflooding experiment in sandstone cores.The remaining oil viscosity in the core is positively correlated with the displacing water multiple.The remaining oil viscosity increases rapidly when the displacing water multiple is low,and increases slowly when the displacing water multiple is high.The variation of remaining oil viscosity is related to the reservoir heterogeneity.The stronger the reservoir homogeneity,the higher the content of heavy components in the remaining oil and the higher the viscosity.The reservoir wettability changes after water injection:the oil-wet reservoir changes into water-wet reservoir,while the water-wet reservoir becomes more hydrophilic;the degree of change enhances with the increase of displacing water multiple.There is a high correlation between the time-varying oil viscosity and the time-varying wettability,and the change of oil viscosity cannot be ignored.The NMR wettability index calculated by considering the change of oil viscosity is more consistent with the tested Amott(spontaneous imbibition)wettability index,which agrees more with the time-varying law of reservoir wettability.