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.

Determination of liquid viscosity based on dual-frequency-bandparticle tracking

An optical-tweezers-based dual-frequency-band particle tracking system was designed and fabricated for liquid viscositydetection. On the basis of the liquid viscosity dependent model of the particle’s restricted Brownian motion with theFax´en correction taken into account, the liquid viscosity and optical trap stiffness were determined by fitting the theoreticalprediction with the measured power spectral densities of the particle’s displacement and velocity that were derived from thedual-frequency-band particle tracking data. When the SiO2 beads were employed as probe particles in the measurements ofdifferent kinds of liquids, the measurement results exhibit a good agreement with the reported results, as well as a detectionuncertainty better than 4.6%. This kind of noninvasive economical technique can be applied in diverse environments forboth in situ and ex situ viscosity detection of liquids.

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.

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.

Numerical Simulation of Slurry Diffusion in Fractured Rocks Considering a Time-Varying Viscosity

To analyze the effects of a time-varying viscosity on the penetration length of grouting,in this study cement slur-ries with varying water-cement ratios have been investigated using the Bingham’sfluidflow equation and a dis-crete element method.Afluid-solid coupling numerical model has been introduced accordingly,and its accuracy has been validated through comparison of theoretical and numerical solutions.For different fracture forms(a single fracture,a branch fracture,and a fracture network),the influence of the time-varying viscosity on the slurry length range has been investigated,considering the change in the fracture aperture.The results show that under different fracture forms and the same grouting process conditions,the influence of the time-varying viscosity on the seepage length is 0.350 m.

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.

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%.

Molecular composition of naphthenic acids in a Chinese heavy crude oil and their impacts on oil viscosity

Most heavy crude oils underwent biodegradation and generated a significant amount of naphthenic acids. Naphthenic acids are polar compounds with the carboxylic group and are considered as a major factor affecting the oil viscosity. However, the relationship between the molecular composition of naphthenic acids and oil viscosity is not well understood. This study examined a “clean” heavy oil with low contents of heteroatoms but had a high content of naphthenic acids. Naphthenic acids were fractionated by distillation and caustic extraction. The molecular composition was characterized by high-resolution Orbitrap mass spectrometry. It was found that the 2- and 3-ring naphthenic monoacids with 15–35 carbon atoms are dominant components of the acid fractions;the caustic extraction is capable of isolating naphthenic acids with less than 35 carbons, which is equivalent to the upper limit of the distillable components, but not those in the residue fraction;the total acid number of the heavy distillates is higher than that of the residue fraction;the viscosity of the distillation fraction increases exponentially with an increased boiling point of the distillates. Blending experiments indicates that there is a strong correlation between the oil viscosity and acids content, although the acid content is only a few percent of the total oil.

Prediction of the viscosity of natural gas at high temperature and high pressure using free-volume theory and entropy scaling

Eighteen models based on two equations of state(EoS),three viscosity models,and four mixing rules were constructed to predict the viscosities of natural gases at high temperature and high pressure(HTHP)conditions.For pure substances,the parameters of free volume(FV)and entropy scaling(ES)models were found to scale with molecular weight,which indicates that the ordered behavior of parameters of Peng-Robinson(PR)and Perturbed-Chain Statistical Associating Fluid Theory(PC-SAFT)propagates to the behavior of parameters of viscosity model.Predicting the viscosities of natural gases showed that the FV and ES models respectively combined with MIX4 and MIX2 mixing rules produced the best accuracy.Moreover,the FV models were more accurate for predicting the viscosities of natural gases than ES models at HTHP conditions,while the ES models were superior to PRFT models.The average absolute relative deviations of the best accurate three models,i.e.,PC-SAFT-FV-MIX4,tPR-FVMIX4,and PC-SAFT-ES-MIX2,were 5.66%,6.27%,and 6.50%,respectively,which was available for industrial production.Compared with the existing industrial models(corresponding states theory and LBC),the proposed three models were more accurate for modeling the viscosity of natural gas,including gas condensate.

Influence of substituting B_(2)O_(3) with Li_(2)O on the viscosity,structure and crystalline phase of low-reactivity mold flux

The low-reactivity mold flux with low SiO_(2)content is considered suitable for the continuous casting of high-aluminum steel since it can significantly reduce the reaction between Al in steel and SiO_(2)in mold flux.However,the traditional low-reactivity mold flux still presents some problems such as high viscosity and strong crystallization tendency.In this study,the co-addition of Li_(2)O and B_(2)O_(3)in CaO–Al_(2)O_(3)–10wt%Si O_(2)based low-reactivity mold flux was proposed to improve properties of mold flux for high-aluminum steel,and the effect of Li_(2)O replacing B_(2)O_(3)on properties of mold flux was investigated.The viscosity of the mold flux with 2wt%Li_(2)O and 6wt%B_(2)O_(3)reached a minimum value of 0.07 Pa·s.The break temperature and melting point showed a similar trend with the viscosity.Besides,the melt structure and precipitation of the crystalline phase were studied using Raman and X-ray diffraction spectra to better understand the evolution of viscosity.It demonstrated that with increasing Li_(2)O content in the mold flux from 0 to 6 wt%,the degree of polymerization of aluminate and the aluminosilicate network structure increased because of increasing Li+released by Li_(2)O,indicating the added Li_(2)O was preferentially associated with Al^(3+)as a charge compensator.The precipitation of LiAlO_(2)crystalline phase gradually increased with the replacement of B_(2)O_(3)by Li_(2)O.Therefore,Li_(2)O content should be controlled below 2wt%to avoid LiAlO_(2)precipitation,which was harmful to the continuous casting of highaluminum steels.

Lipschitz Regularity of Viscosity Solutions to the Infinity Laplace Equation

In this paper, we study the viscosity solutions of the Neumann problem in a bounded C2 domain Ω, where ΔN∞ is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory. .

Incompressible Limit of the Oldroyd-B Model with Density-Dependent Viscosity

This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ Rd, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.

Enhancing Heavy Crude Oil Flow in Pipelines through Heating-Induced Viscosity Reduction in the Petroleum Industry

The process of transporting crude oil across pipelines is one of the most critical aspects of the midstream petroleum industry.In the present experimental work,the effect of temperature,pressure drop,and pipe diameter on the flow rate of heavy crude oil have been assessed.Moreover,the total discharge and energy losses have been evaluated in order to demonstrate the improvements potentially achievable by using solar heating method replacing pipe,and adjusting the value of the initial pressure difference.Crude oil of API=20 has been used for the experiments,with the studied pipelines sections connecting the separator unit to the storage tank operating at a temperature of 25℃-100℃,pressure drop of 3,4,5,and 6 kg/cm^(2),and with pipe diameter of 4,6,and 8 in.The results show that on increasing the temperature and/or the pressure drop,the flow rate through the pipeline becomes higher,thus raising the total pumping energy(as the pipe diameter increase),while energy losses increase from the last separator to the storage tank in the field.A pipe diameter increase can also produce a growth of the total pumping energy(i.e.,energy losses increase).The results of the present analysis suggest that employing an optimal temperature(50℃)is needed to ensure good performance.

An artificial viscosity augmented physics-informed neural network for incompressible flow

Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or interior data.However,the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported.The present paper proposes an artificial viscosity(AV)-based PINN for solving the forward and inverse flow problems.Specifically,the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics(CFD)to stabilize the simulation of flow at high Reynolds numbers.The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re=1000 and the inverse problem derived from two-dimensional film boiling.The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.

Influences of across-strike heterogeneous viscosity on the earthquake cycle in a three-dimensional strike-slip fault model

Geodetic observations have shown that there exist large differences in the viscosity of the deep lithosphere across many large strike-slip faults.Heterogeneity in lithospheric viscosity structure can influence the efficiency of stress transfer and thus may have a significant effect on the earthquake cycle.Until now,how the lateral viscosity variation across strike-slip faults affects the earthquake cycles is still not well understood.Here,we investigate the effects of across-strike viscosity variation on long-term earthquake behaviors with a three-dimensional strike-slip fault model.Our model is a quasi-static model which is controlled by the slip-weakening friction law and powerlaw rheology.By comparing with the reference case,we find that low viscosity on one side of the fault results in a smaller rupture area but with a higher Coulomb stress drop on the ruptured fault region.In addition,low viscosity also leads to a small Coulomb stress accumulation rate.These combined effects increase the earthquake recurrence interval by approximately 10%and the earthquake moments by about 30%when the low viscosity is related to a geothermal gradient of 30 K/km.In addition,across-strike viscosity variation causes asymmetric interseismic ground surface deformation rate.As the viscosity contrast increases,the difference in the interseismic ground surface deformation rate between the two sides of the fault gradually increases,although the asymmetric feature is not pronounced.This asymmetry of interseismic ground deformation rate across a strike-slip fault is supposed to result in asymmetric coseismic deformation if the long-term plate motion velocity is invariant.As a result,this kind of asymmetry of interseismic deformation may influence the evaluation of potential earthquake hazards along large strike-slip faults with lateral viscosity contrast.

Study on the in situ desulfurization and viscosity reduction of heavy oil over MoO_(3)–ZrO_(2)/HZSM-5 catalyst

Heavy oil is characterized by high viscosity.High viscosity makes it challenging to recover and transport.HZSM-5,MoO_(3)/HZSM-5,ZrO_(2)/HZSM-5 and MoO_(3)–ZrO_(2)/HZSM-5 catalysts were developed to promote in situ desulfurization and viscosity reduction of heavy oil.The physical and chemical properties of catalysts were characterized by XPS,XRD,TEM,NH3-TPD,etc.The effects of temperature,catalyst type and addition amount on viscosity and composition of heavy oil were evaluated.The results showed that the presence of MoO_(3)–ZrO_(2)/HZSM-5 nanoparticles during aquathermolysis could improve the oil quality by reducing the heavy fractions.It reduced viscosity by 82.56%after the reaction at 280℃ and catalyst addition of 1 wt%.The contents of resins and asphaltic in the oil samples were 5.69%lower than that in the crude oil.Sulfur content decreased from 1.45%to 1.03%.The concentration of H2S produced by the reaction was 2225 ppm.The contents of sulfur-containing functional groups sulfoxide and sulfone sulfur in the oil samples decreased by 19.92%after the catalytic reaction.The content of stable thiophene sulfur increased by 5.71%.This study provided a basis for understanding the mechanism of heavy oil desulfurization and viscosity reduction.

Efficient and reversible separation of NH_(3) by deep eutectic solvents with multiple active sites and low viscosities

The efficient separation and collection of ammonia(NH_(3))during NH_(3) synthesis process is essential to improve the economic efficiency and protect the environment.In this work,ethanolammonium hydrochloride(EtOHACl)and phenol(PhOH)were used to prepare a novel class of deep eutectic solvents(DESs)with multiple active sites and low viscosities.The NH_(3) separation performance of EtOHACl+PhOH DESs was analyzed completely.It is figured out that the NH_(3) absorption rates in EtOHACl+PhOH DESs are very fast.The NH_(3) absorption capacities are very high and reach up to 5.52 and 10.74 mol·kg1 at 11.2 and 100.4 kPa under 298.2 K,respectively.In addition,the EtOHACl+PhOH DESs present highly selective absorption of NH_(3) over N_(2) and H_(2) and good regenerative properties after seven cycles of absorption/desorption.The intrinsic separation mechanism of NH_(3) by EtOHACl+PhOH DESs was further revealed by spectroscopic analysis and quantum chemistry calculations.

Laboratory study of fluid viscosity induced ultrasonic velocity dispersion in reservoir sandstones

Ultrasonic velocities of a set of saturated sandstone samples were measured at simulated in-situ pressures in the laboratory.The samples were obtained from the W formation of the WXS Depression and covered low to nearly high porosity and permeability ranges.The brine and four different density oils were used as pore fluids,which provided a good chance to investigate fluid viscosity-induced velocity dispersion.The analysis of experimental observations of velocity dispersion indicates that（1）the Biot model can explain most of the small discrepancy（about 2–3%）between ultrasonic measurements and zero frequency Gassmann predictions for high porosity and permeability samples saturated by all the fluids used in this experiment and is also valid for medium porosity and permeability samples saturated with low viscosity fluids（less than approximately 3 mP·S）and（2）the squirt flow mechanism dominates the low to medium porosity and permeability samples when fluid viscosity increases and produces large velocity dispersions as high as about 8%. The microfracture aspect ratios were also estimated for the reservoir sandstones and applied to calculate the characteristic frequency of the squirt flow model,above which the Gassmann’ s assumptions are violated and the measured high frequency velocities cannot be directly used for Gassmann’s fluid replacement at the exploration seismic frequency band for W formation sandstones.

Effects of melt viscosity on enrichment and separation of primary silicon from Al-Si melt

The effects of melt viscosity on the enrichment and separation of Si crystals from Al–Si melt during an electromagnetic solidification process were investigated. Both the enrichment efficiency and the separation were found to be strongly dependent on the melt viscosity. A high melt viscosity was beneficial to the enrichment of primary silicon, whereas a low melt viscosity facilitated the separation process. A new enrichment mechanism was proposed in order to clarify the influence of melt viscosity, and an improved process for achieving high-efficiency enrichment of Si crystals via control of the melt viscosity was also proposed. Additionally, the morphology of Si crystals was found to change from spheroidal to plate-like in shape owing to the difference in viscosities in different regions.

VISCOSITY BEHAVIOR OF AQUEOUS SOLUTION OF CMC PRODUCED IN TWO PHASE MEDIUM C 6H 6 C 2H 5OH

This study is focused on the viscosity behavior of the aqueous solution of the CMC prepared in a two phase medium C 6H 6 C 2H 5OH H 2O.The effects of properties such as the degree of substitution,molecular weight,distribution of substituent along the molecular chain or at positions C 2,C 3 and C 6 on viscosity are investigated respectively.The difference of the CMC synthesized in medium benzene ethanol and ethanol is studied.The addition of benzene is beneficial to improve the viscosity and stability of CMC solutions.The CMC with homogeneous distribution of substituent along the chain and the high substitution at position C 6 possess a good compatibility with organic acids and excellent resistance to alkali,salts and acid.