Viscosity Equation Research Articles

Flow field computation and sealing performance analysis of high-speed micro-grooved pumping seal for new energy vehicles

A micro-grooved pumping seal for electric vehicles was investigated. In this regard, the real gas effect and viscosity were described using the virial and Lucas equations, respectively, and the oil–air ratio was used to determine the equivalent density and viscosity of the two-phase fluid formed in the mixture of the lubricant and air in the seal. The compressible steady-state Reynolds equation was solved using the finite difference method. The pumping mechanisms of the seal and the effects of operating parameters (rotational velocity, oil–air ratio, inlet pressure, and temperature) on the steady-state sealing performance were analysed. The seal produces a significant hydrodynamic effect on the sealing face. The opening force of the seal increases with rotational velocity, oil–air ratio, and inlet pressure. However, the force decreases as temperature increases. The oil–air ratio has the most significant effect on the opening force. The pumping rate first increases and then decreases as the rotational velocity increases. It increases with the oil–air ratio and temperature but decreases as the inlet pressure increases. In particular, the pumping rate reaches a maximum when the rotational velocity or temperature increases to a certain value. This phenomenon requires special attention during seal design. Our results provide input for the design of micro-grooved pumping seals for new energy vehicles.

Temperature Extended‐Two‐Fluid Tracking (txTFT) Method for Grouting Simulation in High‐Temperature Flowing Water

ABSTRACTAiming at the treatment problem for water inflow in a high geothermal environment, we proposed a grouting simulation method in high‐temperature flowing water: temperature extended‐two‐fluid tracking (txTFT) method. First, a transport model for solving the residence time of slurry was derived. Furthermore, a temperature transport model was established to describe the heat transfer between slurry and water. Finally, according to the fitted equation of slurry viscosity with residence time and temperature, the fine characterization of slurry viscosity was realized, and then the whole process simulation of grouting was realized. This method was used to reveal the blocking mechanism for grouting in high‐temperature flowing water of rock fractures. The results show that high‐temperature water limited the parallel‐flow diffusion of slurry and increased the counterflow diffusion and transverse diffusion of slurry. The higher the water temperature, the larger the grouting rate, and the lower the inlet pressure, the better the blocking effect of flowing water. The research results can provide theoretical guidance and application value for the grouting treatment of water inflow in a high geothermal environment.

Five-stage dynamics of discontinuous oil phase migration in the constricted microchannel: A quantitative analysis of the Jamin effect

The transport of discontinuous oil phases in constricted microchannels is a significant issue within the domains of the petroleum industry, bioengineering, and other industrial processes. During the transport, there is a pressure obstructing the drop flow through the narrow throat, which is named the Jamin effect. In this study, computational fluid dynamics technique is employed to observe and analyze the pressure drop of the discontinuous oil phase during its passage through a constricted microchannel and provides a quantitative analysis for the Jamin effect. The results show that the discontinuous oil phase undergoes five stages during its migration in the constricted microchannel, namely, the preparatory stage, the development stage of the forward meniscus, the quasi-stable stage, the regression stage of the rear meniscus, and the stable stage. Moreover, the composition of resistance in the Jamin effect is not solely due to capillary pressure, as traditional scholars believe. The analysis indicates that the equivalent viscosity of the discontinuous oil phase remains consistent during both the preparatory stage and the stable stage, demonstrating that the magnitude of the equivalent viscosity is unaffected by the profile of the oil phase. Additionally, the effects of oil phase saturation, viscosity, and capillary number on the Jamin effect also have been discussed.

Temperature control and energy-saving efficiency evaluation of low-energy warm-mix asphalt mixtures with composite additives

Traditional warm-mix asphalt (WMA) faces challenges in reducing mixing temperatures to achieve lower energy consumption. To address this challenge and meet global environmental goals, this study designs various composite warm-mix additives using commonly used additives and their optimal dosages. The viscosity reduction mechanisms of asphalt and asphalt mixtures are examined using viscosity–temperature and air voids-temperature curves. Regression equations for viscosity and voids as a function of temperature are developed to determine the optimal mixing temperature of WMA. The study integrates thermodynamic equilibrium equations with field data to quantify the energy consumption in producing composite WMA mixtures. The results reveal that WMA significantly reduces mixing temperatures, making it suitable for low-energy asphalt mixtures. The use of various composite additives enhances the mechanical properties of asphalt pavements. Optimal mixing temperatures are set as 60–100 °C for WMA in warm-paving applications, and 20–60 °C for WMA in cold-paving applications. Viscosity ranges from 0.17 to 0.28 Pa⋅s, with air voids varying from 6%–7% for WMA in warm-paving applications and 8%–9% for WMA in cold-paving applications. Controlling the mixing temperature improves energy-saving efficiency, achieving reductions from 47.1% to 97.6%. The study recommends the use of WMA (Sasobit/Evotherm/DAT) for warm-paving applications and WMA (Sasobit/Diesel oil) for cold-paving applications. This study provides valuable insights for developing energy-efficient and high-performance asphalt pavements.

An improved equivalent viscosity model for the bubbly oil under high shear rate

An improved equivalent viscosity model for the bubbly oil under high shear rate

Performance analysis of shear horizontal one port surface acoustic wave (SAW) resonator for optimal liquid sensing based on finite element method

This paper presents the numerical study using finite element method for optimal liquid sensing performance of one port surface acoustic wave (SAW) resonator. Simulation shows that the extend of IDT-reflector gap can be optimized to contain most of the piezoelectric displacement. Various settings of liquid placement on the mentioned region yield distinct resonant frequency responses of the SAW sensor. For concentrated liquid with higher order of viscosity, magnitude of S-Parameter and phase of the propagating SAW can be applied to sense the liquid solutions. Based on the results, optimal liquid sensing performance of the device can be achieved when liquid droplet sized about 10 % of the aperture is placed in the middle position of the IDT-reflector gap conditioned at 1.5 λ. Using the formulated strategy, the one port SAW device distinguishes well 0 % to 100 % glycerine concentrations compared to limited detection range reported in the previous study. The finding includes equation of liquid turnover viscosity before shift in direction of the changes in S-Parameter measurement. The derived parameters can be set as reference to design the microfludic cell or lab-on-chip based on the one port SAW configuration for optimized liquid sensing performance.

Equation of State, Structure, and Transport Properties of Iron Hydride Melts at Planetary Interior Conditions

AbstractIron hydrides are a potentially dominant component of the metallic cores of planets, primarily because of hydrogen's ubiquity in the universe and affinity for iron. Using ab initio molecular dynamics, we examine iron hydrides with 0.1, 0.33, 0.5, and 0.6 mol fraction hydrogen up to 100 GPa between 3,000 and 5,000 K to describe how hydrogen content affects the melt structure, hydrogen speciation, equation of state (EOS), atomic diffusivity, and melt viscosity. We find that the addition of hydrogen decreases the average Fe–Fe coordination number and lengthens Fe–Fe bonds, while Fe–H coordination number increases. The pair distribution function of hydrogen at low pressure indicates the presence of molecular hydrogen. By tracking chemical speciation, we show that the amount of molecular hydrogen increases and the number of iron in Hx≥1Fey≥0 clusters decreases as the hydrogen concentration increases. We parameterize a pressure, volume, temperature, and composition EOS and show that the molar volume and Grüneisen parameter of the melts decrease while the compressibility and thermal expansivity increase as a function of hydrogen concentration. We find that hydrogen acts as a lubricant in the melts as the iron and hydrogen become more diffusive and the melts become more inviscid as the hydrogen concentration increases. We estimate 2.7 wt% hydrogen in the Martian core and 0.49–1.1 wt% hydrogen in Earth's outer core based on comparisons to seismic models, with the assumption that the cores are pure liquid iron‐hydrogen alloy, and we compare the small exoplanet population with mass‐radius curves of iron hydride planets.

Nonlinear twofold saddle point-based mixed finite element methods for a regularized μ(I)-rheology model of granular materials

We propose and analyze new mixed finite element methods for a regularized μ(I)-rheology model of granular flows with an equivalent viscosity depending nonlinearly on the pressure and the Euclidean norm of the symmetric part of the velocity gradient. To this end, and besides the velocity, the pressure and the aforementioned strain rate, we introduce a modified stress tensor that includes the convective term, and the skew-symmetric vorticity, as auxiliary tensor unknowns, thus yielding a mixed variational formulation within a Banach spaces framework. Then, the pressure is obtained through an iterative postprocess suggested by the incompressibility condition of the fluid, which allows us to express this unknown in terms of the aforementioned stress and the velocity. A fixed-point strategy combined with a solvability result for a class of nonlinear twofold saddle point operator equations in Banach spaces, is employed to show, along with the classical Banach fixed-point theorem, the well-posedness of the continuous and discrete formulations. In particular, PEERS and AFW elements of order ℓ⩾0 for the stress, the velocity, and the skew-symmetric vorticity, and piecewise polynomials of degree ⩽ℓ+n (resp. ⩽ℓ+1) for the strain rate with PEERS (resp. with AFW), yield stable Galerkin schemes. Optimal a priori error estimates are derived and associated rates of convergence are established. Finally, numerical results confirming the latter and illustrating the good performance of the methods, are reported.

The thermophysical properties of Ga-Na liquid alloys

In this study, the thermophysical properties of Ga-Na liquid alloys were investigated. Based on the literature, the reference equations for surface tension and viscosity for liquid Ga were given. The density, surface tension, and viscosity were measured using the discharge crucible method in a temperature range of 573–873 K. The chemical composition of Ga-Na alloys was selected to show the effect of Na dissolution in Ga as potential liquid batteries. It was noticed that the addition of Na to Ga reduced all investigated properties, with the effect being greatest for surface tension. The experimental value shows good agreement with the proposed models (Butler for surface tension and Gasior, Kaptay, and Moelwyn-Hughes for viscosity).

Study on the Diffusion Mechanism of Infiltration Grouting in Fault Fracture Zone Considering the Time-Varying Characteristics of Slurry Viscosity Under Seawater Environment

Fault fracture zones are rock formations commonly encountered in submarine tunnels, and the diffusion mechanism of slurry in fault fracture zones has a crucial impact on submarine tunnel reinforcement. Based on the seepage equation of Bingham fluid, the tortuosity parameter, fractal theory, and variable viscosity equation are introduced to establish a spherical permeation grouting model of Bingham fluid considering the slurry diffusion path and viscosity time variability. The viscosity variation law with time of sulfur aluminate cement slurry under different seawater admixture conditions was tested, and the time-varying equation of viscosity of sulfur aluminate cement slurry was obtained by fitting. A set of fault fracture zone permeation grouting test system was developed, and a fault fracture zone grouting simulation test was carried out. The study shows that the diffusion distance calculated without considering the influence of slurry diffusion path and seawater is 1.63–1.91 times of the test value, which obviously overestimates the diffusion distance; the diffusion distance calculated with considering the influence of diffusion path and seawater is 1.06–1.35 times of the test value, which is in good agreement with the test value. The research results can provide some theoretical support for the design of grouting in seawater environment.

Stability of fully developed pipe flow of a shear-thinning fluid that approximates the response of viscoplastic fluids

The stability of steady, fully developed flow in a long cylindrical pipe for a shear-thinning fluid (which approximates a class of viscoplastic materials) is studied using linear stability analysis. The eigenvalues of the frequency of the perturbation of the steady-state solution are obtained using the shooting method. The eigenvalues are negative in the Reynolds number range studied and asymptotically tend to zero as the Reynolds number increases. This shows the pipe flow is stable in the Reynolds number range studied. A qualitatively similar trend is shown by the eigenvalues of a Navier–Stokes fluid of equivalent viscosity. However, the eigenvalues are much lesser than those of the shear-thinning fluid, and this shows that the flow of the Navier–Stokes fluid can be expected to be stable over a much larger Reynolds number range than the shear-thinning fluid.

Incompressible boundary layer flow past a hump with temperature-dependent viscosity

The problem of boundary layer flow past a hump placed on a flat surface, where viscosity is coupled with temperature, is investigated using triple-deck theory. The incompressible Navier–Stokes equations supplemented by the heat and viscosity equations are considered in the limit that the Reynolds number is large. The triple-deck scalings are adopted, and asymptotic expansions are used to obtain some novel triple-deck equations coupled with the thermal boundary layer. We have used the same viscosity–temperature dependence as in Jasmine and Gajjar [Int. J. Heat Mass Transfer 48, 1022–1037 (2005)], in which viscosity varies inversely proportional to the temperature. The linear analysis is performed, and the nonlinear equations are solved numerically. Our results show that increasing the characteristic constant of the viscosity leads to enhanced peaks and troughs in the pressure and in the skin friction over the hump, as compared to the constant viscosity case. This suggests that temperature-dependent viscosity is more likely to provoke separation.

Proof of concept for a nonadditive stochastic model of supercooled liquids.

The recently proposed nonadditive stochastic model (NSM) offers a coherent physical interpretation for diffusive phenomena in glass-forming systems. This model presents nonexponential relationships between viscosity, activation energy, and temperature, characterizing the non-Arrhenius behavior observed in supercooled liquids. In this work, we fit the NSM viscosity equation to experimental temperature-dependent viscosity data corresponding to 25 glass-forming liquids and compare the fit parameters with those obtained using the Vogel-Fulcher-Tammann (VFT), Avramov-Milchev (AM), and Mauro-Yue-Ellison-Gupta-Allan (MYEGA) models. The results demonstrate that the NSM provides an effective fitting equation for modeling viscosity experimental data in comparison with other established models (VFT, AM, and MYEGA), characterizing the activation energy in fragile liquids, presenting a reliable indicator of the degree of fragility of the glass-forming liquids.

Physical mechanism-driven extraction model for post-seismic deformation recorded by continuous GNSS observations

Post-seismic deformation caused by large earthquakes is one of the most effective parameters for investigating the frictional behavior of faults and the rheological characteristics of the lithosphere. This study introduces a modified functional model that accounts for both afterslip and viscoelastic relaxation effects, incorporates a physical mechanism, and effectively disentangles distinct mechanisms of post-seismic deformation captured by continuous GNSS observations.A parameter optimization solution method based on the Bayesian framework was adopted to obtain optimal estimates and corresponding confidence intervals. The effectiveness of proposed model was validated through simulation experiments. The proposed method was applied to study post-seismic deformations from the 2015 Nepal MW 7.8 earthquake, and the different characteristics of post-seismic deformations caused by different mechanisms were discovered at different stations. The afterslip effect has the duration of 2.67 years, whereas the viscoelastic relaxation effect will continue for 150.8 years. Moreover, the calculated equivalent viscosity coefficient in the southern Tibet region was 1.1 ± 0.3 × 1018 Pa·s. Our proposed model can more accurately and objectively separate different mechanisms from the post-seismic displacements observed by GNSS than previous one, and thus improve the accuracy of fault kinematics and regional lithosphere rheology investigations.

Viscosity in simple fluids: A different perspective based on the thermodynamic dimension

This work presents a different perspective on viscosity and a new interpretation of it by treating the fluid as a fractal lattice incorporating temporary molecular clusters (t-clusters) and using the thermodynamic dimension (DT) idea. The DT connects fluid viscosity to its EoS by computing the effective intermolecular potential, U(r, T), which may be found via thermodynamic relations from the fluid equation of state (EoS). Finally, a general viscosity equation is developed utilizing standard and well-established statistical thermodynamic relations. The approach is applied to nitrogen fluid as a case study because of the fluid's extensiveness data in the literature. Less than 2 % is the absolute average deviation percent (AAD%) for viscosity prediction in the range of 65 K to 1000 K for pressures less than 2000 MPa. It is simple to code the viscosity equation that is obtained.

A self-consistent unified solid-multiphase flow shock model under complex thermodynamic states: For the application of mass-loaded single-turn coils

Single-turn coil (STC) is a destructive pulsed magnet aiming at 100–300 T magnetic field. Mass-loading is the method to increase STC magnetic field. In this study, a unified solid-multiphase flow model is proposed to solve the shock contact problem between the conductor and mass-loading material. This model gives the approach to equate the solid to viscid fluid and equate the melted material to solid and derives the constitutive model for the conductor under non-adiabatic state. Especially, the method to calculate non-adiabatic modulus is investigated. The results show that the equivalent viscosity of solid decreases as the strain rate rises. Moreover, the equivalent shear modulus of the melted solid increases as the strain rate rises, and considering this equivalent shear modulus rather than setting it to zero improves the simulation convergence significantly. This model can provide not only theoretical support for the optimal design of destructive pulse magnets but also methods for theoretical modeling of other types of electromagnetic explosion and shock contact experiments under non-adiabatic condition.

Micro-Groove Optimisation of High-Speed Inner Ring Micro-Grooved Pumping Seal for New Energy Electric Vehicles

Traditional oil seals are insufficient for the high-speed and bi-directional rotation of new energy electric vehicles. Therefore, we developed a Python program focusing on micro-groove pump seals and examined the unexplored non-contact oil–air biphasic internal end-face seals. Real gas effects were described using the virial and Lucas equations. We introduced an oil–air ratio to determine the equivalent density and viscosity of the two-phase fluid in the seal. Furthermore, we solved the compressible steady-state Reynolds equation using the finite difference method. Analysing the seal’s pumping mechanisms and the effects of operating parameters on sealing performance, we assessed 17 types of hydrodynamic grooves. The results demonstrate that inverse fir tree-like grooves perform well under typical sealing conditions. Under the conditions given in this study, the pumping rate of the optimal groove type compared to other groove types even reached 633.54%. In the oil–air biphasic state, the micro-groove pump seal exerts significant dynamic pressure on the sealing surface. Seal opening force increases with rotational velocity, oil–air ratio, and inlet pressure but decreases with temperature. The pumping rate first increases and then decreases with rotational velocity, increases with oil–air ratio and temperature, and then decreases with inlet pressure. Some special working points require consideration in sealing design. Our results provide insights into designing micro-grooved pumping seals for new energy electric vehicles.

Optical Kerr effect for underlying the orientational and translational fluctuations of molecular interactions in non-polar CS2 vapor and liquid states

A femtosecond optical Kerr gate is used for first time to experimentally study the temporal behavior of the molecular interactions of carbon disulfide (CS2) vapor in comparison to its liquid state. This Kerr effect is observed due to the optical birefringence induced in a CS2 sample. Results show that the Kerr relaxation time in the vapor state is faster than in the liquid state, with an overall exponential fit of 0.8 ps molecular relaxation time versus 1.7 ps, respectively. A faster relaxation decay time is observed for the first time in free CS2 molecules, this is attributed to fewer neighboring intermolecular interactions, which results in a lower local viscosity in the vapor compared to the liquid state. Fitting the temporal response of the Kerr vapor signal to individual components of n2 arising from the ultrafast and fast components yields two main decay times: τultrfast = 126 fs and τfast = 530 fs molecular relaxation times, one which agrees with the Debye equation for the air viscosity (associated to the free rotation in air) giving 126 fs and the other is approximately close to the translational diffusion equation producing 530 fs, respectively. In the liquid state, fitting yields three main components: τultrfast = 50 as, τfast = 500 fs, and τslow = 1.5 ps, overall, the tail fits the 1.7 ps molecular relaxation time.

Physicochemical properties of extraction solvents for the advanced recycling of spent nuclear fuel

A comprehensive understanding of solvent physicochemical properties is essential to developing advanced solvent extraction processes, such as Advanced PUREX (Plutonium Uranium Reduction Extraction) and GANEX (Group Actinide Extraction), that can safely and efficiently recycle spent nuclear fuel. The densities, viscosities and surface tensions of binary mixtures of tributyl phosphate (TBP) (0.92–3.66 M) in n-dodecane and N,N-di (2-ethyl hexyl)isobutyramide (DEHiBA) (0.69–2.78 M) in n-dodecane were measured at atmospheric pressure from 278.15 to 333.15 K. Through these measurements, empirical expressions to predict the density and viscosity at any molar composition of these solvents within the studied temperature range were constructed and shown to be in good correlation with all experimental data across the studied variables. The relationship between temperature and viscosity of pure TBP and DEHiBA can be described by the Arrhenius equation for viscosity in the temperature range studied. Surface tension measurements (air-liquid interface) were obtained for varying extractant concentrations between 278.15 and 333.15 K, which showed that DEHiBA acts as a surfactant when mixed with n-dodecane whilst TBP exhibits a higher surface tension than n-dodecane.

On the use of the Astarita flow field for viscoelastic fluids to develop a generalised Newtonian fluid model incorporating flow type (GNFFTy)

The two-dimensional, steady, homogeneous flow field proposed by Astarita (J. Rheol., vol. 35, 1991, pp. 687–689) is studied for a range of viscoelastic constitutive equations of differential form including the models due to Oldroyd (the upper and lower convected Maxwell; UCM/LCM), Phan-Thien and Tanner (simplified, linear form; sPTT) and Giesekus. As the flow is steady and homogeneous, the sPTT model results also give the FENE-P model solutions via a simple transformation of parameters. The flow field has the interesting feature that a scalar parameter may be used to vary the flow ‘type’ continuously from solid-body rotation to simple shearing to planar extension whilst the rate of deformation tensor $\boldsymbol{\mathsf{D}}$ remains constant (i.e. independent of flow type). The response of the models is probed in order to determine how a scalar ‘viscosity’ function may be rigorously constructed which includes flow-type dependence. We show that for most of these models – the Giesekus being the exception – the first and second invariants of the resulting extra stress tensor are linearly related, and for models based on the upper convected derivative, this link is simply via a material property, i.e. half the modulus. By defining a frame-invariant coordinate system with respect to the eigenvectors of $\boldsymbol{\mathsf{D}}$ , we associate a ‘viscosity’ for each of the flows to a deviatoric stress component and show how this quantity varies with the flow-type parameter. For elliptical motions, rate thinning is always observed and all models give essentially the UCM response. For strong flows, i.e. flow types containing at least some extension, thickening occurs and only a small element of extension is required to remove any shear thinning inherent in the model (e.g. as occurs in steady simple shearing for the sPTT/Giesekus models). Finally, a functional form of a viscosity equation which could incorporate flow type, but be otherwise inelastic, the so-called GNFFTy (generalised Newtonian fluid model incorporating flow type, pronounced ‘nifty’), is proposed. In the frame-invariant coordinate system proposed, this model is also capable of capturing normal-stress differences.