Viscosity Equation Research Articles

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.

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.

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.

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.

Low-temperature rheological properties and viscosity equation of Al/HTPB suspension system

The rheological behavior of propellant slurries is crucial for ensuring the feasibility of the 3D printing process, controlling print quality, regulating performance, and simulating predictions. However, there have been relatively few prior studies on the rheological properties of composite solid propellant slurries at low temperatures, which hinders the application of 3D printing propellant technology under extreme temperature conditions. In addition, the use of 3D printing technology to manufacture propellants at low temperatures is advantageous for improving safety. This paper investigates the rheological properties of monodisperse systems with aluminum powder as a solid filler and end-hydroxy polybutadiene (HTPB) as the dispersed phase at low temperatures (−15∼10 °C). It explores the effects of solid content, temperature, and particle size on their rheological properties. Results show that the viscosity of the system in the range of −15∼10 °C increases exponentially with the decrease in temperature, and the viscosity at −15 °C increases by 616.90 % compared with that at 10 °C when the volume fraction (φ) of Al-1 is 35.8 %; the larger size of the particles the larger the viscosity is when the temperature and φ are the same, which is interpretes in terms of interfacial properties between the systems. The low-temperature correction factor is introduced into the Einstein-Roscoe equation to obtain the modified viscosity-volume fraction equation, and the correction factor is 0.0173, as evidenced by its excellent agreement with the experimental data.

The Minima of Viscosities.

The Trachenko-Brazhkin equation of the minimal possible viscosity is analysed, emphasising its validity by the account of multibody interactions between flowing species through some effective masses replacing their true (bare) masses. Pressure affects the effective masses, decreasing them and shifting the minimal viscosity and the temperature at which it is attained to higher values. The analysis shows that effective masses in the Trachenko-Brazhkin equation are typically lighter compared bare masses; e.g., for tin (Sn) the effective mass is m = 0.21mSn, whereas for supercritical argon (Ar), it changes from m = 0.165mAr to m = 0.129mAr at the pressures of 20 and 100 MPa, respectively.

Attractive carbon black dispersions: Structural and mechanical responses to shear

The rheological behavior of colloidal dispersions is of paramount importance in a wide range of applications, including construction materials, energy storage systems, and food industry products. These dispersions consistently exhibit non-Newtonian behaviors, a consequence of intricate interplays involving colloids morphology, volume fraction, and interparticle forces. Understanding how colloids structure under flow remains a challenge, particularly in the presence of attractive forces leading to cluster formation. In this study, we adopt a synergistic approach, combining rheology with ultra small-angle x-ray scattering, to probe the flow-induced structural transformations of attractive carbon black (CB) dispersions and their effects on the viscosity. Our key findings can be summarized as follows. First, testing different CB volume fractions, in the high shear rate hydrodynamic regime, CB particles aggregate to form fractal clusters. Their size conforms to a power law of the shear rate, ξc∝γ˙−m, with m≃0.5. Second, drawing insights from the fractal structure of clusters, we compute an effective volume fraction ϕeff and find that microstructural models adeptly account for the hydrodynamic stress contributions. We identify a critical shear rate γ∗˙ and a critical volume fraction ϕeff∗, at which the clusters percolate to form a dynamical network. Third, we show that the apparent yield stress measured at low shear rates inherits its properties from the percolation point. Finally, through data scaling and the integration of Einstein’s viscosity equation, we revisit and discuss the Caggioni–Trappe–Spicer model, revealing a significant connection between its empirical parameters and the structural properties of CB dispersions under flow.

Considering cell viability in 3D printing of structured inks: A comparative and equivalent analysis of fluid forces

In conventional extrusion-based three-dimensional (3D) printing (E3DP), smaller needles reduce cell viability due to increased fluid forces like pressure and shear stress. A novel E3DP approach has emerged, involving 3D printing with structured inks. Fluid forces in both conventional and structured ink-based methods were evaluated through computational fluid dynamics (CFD) simulations. By employing 18G needles, we showcased the advantages of structured inks, including 2-symmetric, 4-symmetric, vascular-like, and hepatic lobule analogue-like inks, which demonstrated consistently lower pressures and shear stress compared with conventional inks. Specifically, vascular-like inks with a 2:1:1 extruded fiber layer distance showed significantly lower shear stress (average 6.595e+0 Pa, maximum 2.069e+2 Pa) than conventional methods. Equivalent analyses explored commonly used symmetric and core–shell inks, examining fluid forces on cells. Particularly, in core–shell inks with a 2.8 mm core layer radius, cells in the flow domain of the shell layer experienced an equivalent viscosity of 3.70 Pa·s, while in the core layer, it was 1.72 Pa·s. The analyses revealed a positive correlation between equivalent homogeneous ink viscosity and shear stress. The proposed workflow, emphasizing cell viability, offers an efficient approach for structured ink design. Also, experiments that used vascular-like ink-based printing as an example indicated significantly higher cell viability when compared with conventional printing. This research provides valuable insights for enhancing cell viability in 3D printing and advancing printing material design.

Riemann problem for a general variable coefficient Burgers equation with time-dependent damping

In this paper, we study the Riemann problem for a general variable coefficient Burgers equation with time-dependent damping. We use a nonlinear time-dependent viscosity equation with a similarity variable. Thus, when the viscosity goes to zero, we obtain Riemann solutions to the general variable coefficient Burgers equation with time-dependent damping. Moreover, we use the Lax–Friedrichs scheme to obtain numerical evidence of the Riemann solutions.