Function Of Viscosity Research Articles

Investigations on the finite strain behavior of standard PVB: experiment and modeling

AbstractThe numerical simulation of the residual load-bearing capacity of laminated glass is one of the most relevant topics of current research in structural glass engineering. The mechanical description of the behavior of the interlayer plays a crucial role. Several approaches and models already exist in automotive engineering and structural protection. Structural glass design assuming quasi-static loads misses a detailed model so far. The aim of this work is the mechanical description of the time-dependent behavior of Polyvinylbutyral (PVB) under large deformations considering quasi-static loading. The results of experiments on single-layer Standard PVB are presented, and a model of finite nonlinear viscoelasticity is derived. In particular, the formulation of phenomenologically motivated viscosity functions is described. Subsequently, the model parameters are calibrated on the experimental results, and the uniaxial stress state is simulated.

Analysis of the Cessation of Convection in Mercury's Mantle

AbstractThe question of whether the present‐day mantle of Mercury is undergoing convection remains unresolved. We address this issue by estimating the minimum value of the core‐mantle boundary (CMB) temperature needed to support mantle convection and considering the time required to cool the mantle below this threshold. A simple mathematical analysis of the cooling of the core, based on the assumption of a quasi‐steady‐state thermal equilibrium of Mercury's mantle, shows that the CMB temperature falls to the critical temperature for cessation of convection roughly halfway through the planet's evolutionary history. To first order, the duration of subsolidus convection does not depend on the absolute value of the viscosity. It depends primarily on parameters that control the viscosity function, such as the stress exponent and the activation energy. Our results based on conventional assumptions suggest the absence of present‐day mantle convection in Mercury, which is consistent with numerical models of Mercury's thermal history. However, because of large uncertainties in the controlling parameters, the possibility of still ongoing mantle convection on Mercury cannot be ruled out.

Multifunctional cyanoaryl porphyrazine pigments with push-pull structure of macrocycle framing: Photophysics and possible applications

We report the experimental study of fluorescence properties of three porphyrazine derivatives, distinct in the number of fused aromatic rings in aryl groups contained in the macrocycle frame and/or presence of Pd in the macrocycle, in solutions with biological molecules and in methanol-glycerol mixtures. Spectral and lifetime fluorescence analysis has revealed that all three pigments demonstrated two fluorescence transition bands from the first S1 and the second S2 electronic excited states to the ground state S0, and thus followed the anti-Kasha’s rule. Strong dependence of the quantum yield and lifetimes in the S1 → S0 fluorescence band on solution viscosity was observed. A significant increase of the fluorescence decay times and fluorescence intensity with albumin concentration and with presence of other biological molecules in solution was observed as well. A model of the low-laying energy states of porphyrazine derivatives has been developed for elucidation of the fluorescence properties observed, that took into account several radiative and non-radiative relaxation channels in molecular excited states. In particular, the model suggests that the first electronic excited state consists of planar and bent conformations separated by a potential energy barrier and shows a typical molecular-rotor behavior as a function of solution viscosity. Potential applications of the porphyrazine pigments as viscosity sensors and fluorescence probes were considered.

Dynamic viscosity prediction for MWCNT-MgO (10%–90%)-SAE40 oil hybrid nano-lubricant using artificial neural network andmulti-dimensional nonlinear least square curve fitting

In this study, the dynamic viscosity of MWCNT-MgO (10%-90%)/SAE40 Oil Hybrid Nanofluid (HNF) is investigated. To this end, two methods are used including artificial neural network (ANN) and least square curve fitting. This nonlinear method uses a multi-dimensional least square strategy to determine coefficients of various parameters in the viscosity function. The viscosity of MWCNT-MgO (10%-90%)/SAE40 Oil HNF is predicted using three input parameters including solid volume fraction (SVF), temperature, and shear rate (SR). According to the obtained data, the optimum ANN to predict the viscosity of HNF as a function of inputs has 14 neurons with a nonlinear activation function resulting in mean square error or MSE=7.74e-4 and R2=0.999226 for all data. Moreover, temperature is the most influential parameter, and the rest of the parameters, have much fewer effects on the viscosity of MWCNT-MgO (10%-90%)/SAE40 Oil HNF. Furthermore, this can be seen in the obtained nonlinear fitted function through coefficients of input parameters. To be more precise, T coefficient is -91.2407 much higher than the solid volume fraction and shear rate with coefficients of 34.0366 and -0.166 respectively. The obtained ANN structure and nonlinear fitted function can be used for optimization purposes in future research. It is worth mentioning that although the fitted function by least square curve fitting is a very handy and symbolic equation, the ANN showed higher accuracy.

Viscosity Calculation for Al‐Si‐Mg‐Fe System through CALPHAD Method

Viscosity is a crucial parameter affecting the fluidity of metal melts, which directly influences founding properties of Al alloys. However, obtaining viscosity measurement data is difficult for metal melts, and the viscosity prediction for ternary and multi‐component alloys would provide the significant data for selection of process parameters. This study compares the applicability of the Hirai model, SDS model, and R‐K function for viscosity calculations in the sub‐binary systems of Al‐Si‐Mg‐Fe alloys. R‐K function shows the best agreement with experimental data. However, the SDS model shows lower relative error than Hirai model which would play an important role in those system lacking experimental data to predict the viscosities. Ultimately, a database capable of predicting viscosity values for the entire composition and temperature range of the Al‐Si‐Mg‐Fe system was established using the CALPHAD method. Viscosity parameters for Al‐Si, Al‐Mg, Al‐Fe, Mg‐Si, and Mg‐Fe were evaluated and optimized through the R‐K derivation, corroborated with existing experimental data. Using the R‐K function, successful extrapolation and prediction of viscosity for the Al‐Si‐Mg‐Fe ternary and quaternary systems were achieved, with a mean square error between predicted and experimental values of only 0.7%, demonstrating the successful application of the Al‐Si‐Mg‐Fe database for viscosity prediction.This article is protected by copyright. All rights reserved.

Prediction of the Bubble Growth Behavior by Means of the Time-, Temperature-, Pressure- and Blowing Agent Concentration-Dependent Transient Elongational Viscosity Function of Polymers.

Bubble growth processes are highly complex processes, which are not only dependent on the foaming process parameters (temperature, pressure and blowing agent concentration) but also on the type and structure of the polymer used. Since the elongational viscosity at the bubble wall during bubble growth also depends on these influencing factors, the so-called transient elongational viscosity plays a key role in describing the gas bubble growth behavior in polymer melts. The model-based description of the transient elongational viscosity function is difficult due to its dependence on time, Hencky strain and strain rate. Therefore, representative viscosities or shear viscosity models are usually used in the literature to predict the bubble growth behavior. In this work, the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth is described holistically for the first time. This is achieved by extending the so-called molecular stress function (MSF) model by superposition principles (temperature, pressure and blowing agent concentration) and by using the elongational deformation behavior (Hencky strain and strain rate) at the bubble wall during the initial, and thus viscosity-driven, bubble growth process. Therefore, transient uniaxial elongational viscosity measurements are performed and the non-linear MSF model parameters of the two investigated polymers PS (linear polymer chains) and PLA (long-chain branched polymer chains) are determined. By applying the superposition principles and by changing the strain mode parameter to the equibiaxial case in the MSF model, the transient equibiaxial viscosity master curve is obtained and used to describe the bubble growth process. The results show that the extended MSF model can fully predict the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth processes. The bubble growth behavior over time can then be realistically described using the defined transient equibiaxial elongational viscosity function at the bubble wall. This is not possible, for example, with a representative viscosity and therefore clearly demonstrates the influence and importance of knowing the transient deformation behavior that prevails at the bubble wall during bubble growth processes.

Effects of Proline on Internal Friction in Simulated Folding Dynamics of Several Alanine-Based α-Helical Peptides.

We have studied in silico the effect of proline, a model cosolvent, on local and global friction coefficients in (un)folding of several typical alanine-based α-helical peptides. Local friction is related to dwell times of a single, ensemble-averaged hydrogen bond (HB) within each peptide. Global friction is related to energy dissipated in a series of configurational changes of each peptide experienced by increasing the number of HBs during folding. Both of these approaches are important in relation to future atomic force microscopic-based measurements of internal friction via force-clamp single-molecule force spectroscopy. Molecular dynamics (MD) simulations for six peptides, namely, ALA5, ALA8, ALA15, ALA21, (AAQAA)3, and H2N-GN(AAQAA)2G-COONH2, have been conducted at 2 and 5 M proline solutions in water. Using previously obtained MD data for these peptides in pure water as well as upgraded theoretical models, we obtained variations of local and global internal friction coefficients as a function of solution viscosity. The results showed the substantial role of proline in stabilizing the folded state and slowing the overall folding dynamics. Consequently, larger friction coefficients were obtained at larger viscosities. The local and global internal friction, i.e., respective, friction coefficients approximated to zero viscosity, was also obtained. The evolution of friction coefficients with viscosity was weakly dependent on the number of concurrent folding pathways but was rather dominated by a stabilizing effect of proline on the folded states. Obtained values of local and global internal friction showed qualitatively similar results and a clear dependency on the structure of the studied peptide.

Do Electrostatics Control the Diffusive Dynamics of Solitary Water? NMR and MD Studies of Water Translation and Rotation in Dipolar and Ionic Solvents.

NMR-based measurements of the diffusion coefficients and rotation times of solitary water and benzene at 300 K are reported in a diverse collection of 13 conventional organic solvents and 10 imidazolium ionic liquids. Proton chemical shifts of water are found to be correlated to water OH-stretching frequencies, confirming the importance of electrostatic interactions in these shifts. However, the influence of magnetic interactions in aromatic solvents renders chemical shifts a less reliable indicator of electrostatics. Diffusion coefficients (DB) and rotational correlation times (τB) of benzene in the solvents examined are accurately described as functions of viscosity (η) by DB ∝ η-0.81 and τB ∝ η0.64. Literature values of DB and τB in alkane and normal alcohols, which were not included among the solvents studied here, are systematically faster than predicted by these correlations, indicating that factors beyond solvent viscosity play a role in determining the friction on benzene. In contrast to benzene, water diffusion and rotation are poorly described in terms of viscosity alone, even in the dipolar and ionic solvents measured here. The present data and the substantial literature data already available on dilute water diffusion show a systematic dependence of DW on solvent polarity among isoviscous solvents. The aspect of solvent polarity most relevant to water dynamics is the ability of a solvent to accept hydrogen bonds from water, as conveniently quantified by the frequency of water's OH stretching band, ΔνOH. The friction on translation, ζtr = kBT/DW, and rotation, ζrot = kBTτW, are both well correlated by functions of the form ζ(η, ΔνOH) = a1ηa2 exp (a3ΔνOH), where the ai are adjustable parameters. Molecular dynamics simulations reveal a strong coupling between electrostatic and nonelectrostatic water-solvent interactions, which makes it impossible to dissect the friction on water into additive dielectric and hydrodynamic components. Simulations also provide a tentative explanation for the unusual form of the correlating function ζ(η, ΔνOH), at least in the case of ζrot.

Explicit solution for a Sea-Breeze flow model with special viscosity functions

Explicit solution for a Sea-Breeze flow model with special viscosity functions

Process Window of Mini-LED Display Panel Packaging using Laser Assisted Bonding Technology

For high-resolution display panels using mini-LEDs, high alignment accuracy and high yield of LED transfer and bonding technology are very important parameters of packaging technologies. These parameters of packaging technologies are highly dependent on the interconnection material and bonding process. The use of laser assisted bonding (LAB) technology and epoxy-based interconnection materials has been introduced in mini-LED display panel packaging to improve bonding accuracy and yield. The bonding process of the entire display panel was performed by a tiling SITRAB process because the laser irradiation area is smaller than the LED bonding area on the substrate. For the SITRAB process, an epoxy-based SITRAB material to remove oxide on the surface of solder bump has been developed as a solvent free material. For good wetting of the solder bump during the SITRAB process, the temperature of the solder bumps must be higher than the melting temperature of solder. In general, the stage temperature of the laser process is determined to be around 100C in order to minimize the laser power. However, if the stage temperature is high, the initial properties of the SITRAB material (such as low viscosity and deoxidation function) may be lost due to the high temperature. In this study, the process window of the SITRAB material was determined for a stable SITRAB process. The process window was identified according to three different pot lifes: room temperature pot life (RPL), stage pot life (SPL), and laser pot life (LPL).

Electrohydrodynamic (In)Stability of Microfluidic Channel Flows: Analytical Expressions in the Limit of Small Reynolds Number

We study electrohydrodynamic (EHD) linear (in)stability of microfluidic channel flows, i.e., the stability of interface between two shearing viscous (perfect) dielectrics exposed to an electric field in large aspect ratio microchannels. We then apply our results to particular microfluidic systems known as two-liquid electroosmotic (EO) pumps. Our novel results are detailed analytical expressions for the growth rate of two-dimensional EHD modes in Couette–Poiseuille flows in the limit of small Reynolds number (R); the expansions to both zeroth and first order in R are considered. The growth rates are complicated functions of viscosity-, height-, density-, and dielectric-constant ratio, as well as of wavenumbers and voltages. To make the results useful to experimentalists, e.g., for voltage-control EO pump operations, we also derive equations for the impending voltages of the neutral stability curves that divide stable from unstable regions in voltage–wavenumber stability diagrams. The voltage equations and the stability diagrams are given for all wavenumbers. We finally outline the flow regimes in which our first-order-R voltage corrections could potentially be experimentally measured. Our work gives insight into the coupling mechanism between electric field and shear flow in parallel-planes channel flows, correcting an analogous EHD expansion to small R from the literature. We also revisit the case of pure shear instability, when the first-order-R voltage correction equals zero, and replace the renowned instability mechanism due to viscosity stratification at small R with the mechanism due to discontinuity in the slope of the unperturbed velocity profile.

Solute dynamics of a hydrophobic molecule in a menthol-thymol based type-V deep eutectic solvent: effect of composition of the components.

Type-V deep eutectic solvents (DESs) are a newly emerging unique class of solvents obtained by physical mixing and heating of non-ionic components. These solvents show deviation from the thermodynamic ideality. Compared to type-I to IV DESs, type-V DESs are less explored and their physical chemistry is in its nascent stage. In this work, we have chosen a type-V DES based on menthol-thymol (MT) for our working media. Solvent and rotational dynamics were studied with varying temperature using a well-known solvatochromic probe, Coumarin 153 (C153). We prepared the MT-based DES using a reported procedure at three molar ratios: 1 : 1 (M1T1), 1 : 1.5 (M1T1.5), and 2 : 1 (M2T1) of menthol (M) and thymol (T). Time-resolved emission spectra (TRES) were constructed with varying temperature. Utilizing TRES, the decay of the solvent correlation function (C(t)) was plotted. We have correlated the solvent relaxation time in these DESs as a function of viscosity. The time-resolved anisotropy decays were also collected to perceive the rotational relaxation dynamics of C153 as a function of temperature. The decay of solvent relaxation was found to be bi-exponential, and the average solvation time (〈τs〉) in M2T1 was found to be longer than those of M1T1.5 and M1T1. The rotational reorientation times (〈τrot〉) also follow the same trend. We have analysed the rotational dynamics of C153 in type-V DESs employing the Stokes-Einstein-Debye (SED) hydrodynamic model. The rotational dynamics in DESs demonstrate a good correlation with the SED model with a little deviation. In MT-based DESs, the solute's rotational relaxation times approach hydrodynamic stick boundary condition at low viscosity (or at high temperatures) for all molar compositions. Using the Arrhenius-type equations, we have correlated the activation energies for the rotational motion of C153, along with the viscous flow and non-radiative pathways for all the DESs.

Phase separation dynamics in wetting ridges of polymer surfaces swollen with oils of different viscosities.

When drops are placed on a sufficiently soft surface, the drop surface tension drives an out of plane deformation around the contact line (i.e., a wetting ridge). For soft elastomeric surfaces that are swollen with a liquid, capillarity from a drop can induce a phase separation in the wetting ridge. Using confocal microscopy, we study the dynamics of phase separation at the wetting ridge of glycerol drops on silicone elastomers, which are swollen with silicone oils of varying viscosity (i.e., molecular weight). We show that the viscosity of the swelling oil plays a large role in the oil separation size and separation rate. For networks swollen to near their maximum swelling (i.e., saturated), lower viscosity oil separates more and separates faster at early times compared to larger viscosity oil. During late-stage wetting, the growth rate of the separation is a function of viscosity and swelling ratio, which can be described by a simple diffusive model and a defined wetting ridge geometry. In this late-stage wetting, the higher viscosity oil evidently grows faster, likely because it is further from reaching equilibrium. Interestingly, the separated oil phase region grows with a nearly constant, geometrically similar shape. Understanding how phase separation occurs on swollen substrates should provide information on how to control drop spreading, sliding, adhesion, or friction on such surfaces.

A single-molecule fluorescent probe for visualizing viscosity and hypoxia in lysosomes and zebrafish embryos.

Viscosity and hypoxia, as microenvironment parameters, play important roles in maintaining normal biological processes and homeostasis. Therefore, simultaneous and sensitive detection of these elements with simple and effective methods could offer precise information in biology. Here, we report a two-site lysosome-targeting fluorescent probe, NVP, for monitoring viscosity and nitroreductase with dual emission channels (emission shift is 86 nm). The NVP probe has displayed highly sensitive and selective responses towards viscosity and nitroreductase, respectively. Significantly, the fluctuations of viscosity and NTR have been detected in vitro and in vivo. We expect that the dual-responsive fluorescent NVP probe will become a potential molecular tool for the exploration of deeper functions of viscosity and hypoxia.

Inline Bondwave Monitoring for Direct Bonding, Process Optimization and Impact on Post-Bond Distortion

Direct wafer bonding, named also fusion wafer bonding, is based on the formation of molecular bonds between the two surfaces placed in contact. By the initiation of the contact between the two surfaces the bond is self-propagating: at the initiation point a bondwave is generated, which propagates free until the entire surfaces are in contact (bonded). The dynamic of the bondwave propagation is depending on various material (substrates) and process parameters. As shown by Rieutord et al. (1), and experimentally confirmed (2), for a given material and geometry, the speed is function of adhesion energy and fluid viscosity. For industrial applications, this means that investigating the bondwave speed by inline monitoring can be a way to monitor adhesion energy. Adhesion energy itself is a function of different parameters such as surface roughness, WET treatment or water presence (2,3).Inline IR monitoring can be also a practical solution for defect detection. Compared to post bond IR inspection, the live information allows for easier root cause analysis, e.g., particle defect, surface inhomogeneity or chuck effect. Inline early detection of defective bonds and process outliers enables bonded pairs to be reworked (separated and re-bonded) without any additional metrology steps such as post bonding IR inspection or Scanning Acoustic Microscopy (SAM). In case of fast bondwave, one has to monitor any unwanted effect such as edge voids or increased distortion (4).In an automated fusion bonding equipment, EVG®850LT, a bonding chamber has been equipped with an IR camera to record the bondwave propagation. The chamber has also connected different gas and vent lines and a humidifier to control the bonding atmosphere. The bond is initiated with a mobile pin equipped with a load cell, allowing to start the bondwave in a repeatable way at different locations (each bond must be initiated in a single point, but location might vary between center or edge proximity). As shown in figure 1 for a 300 mm Si-SiO2 bonded pair, spatial information can be extracted from the IR images, allowing for bondwave speed mapping (5). The equipment is also equipped with a plasma chamber for pre-processing. This allows to evaluate, using inline bondwave observation, various process conditions such as: plasma treatment, bond chamber gas type, pressure, humidity and bond pin location. Moreover, a metrology equipment was used for bonded pair shape measurement. This data is used to predict high resolution distortion maps to monitor the effect of bonding wave speed and bonding parameters.Different use cases of bondwave monitoring for process development will be presented, as well as the influence of different process parameters on bondwave propagation. A detailed analysis of the impact of the bond wave speed on bonded stack distortion will be presented. As shown in figure 1 (a) and (b), bonding wave velocity has no impact on high order distortion but will significantly increase the runout or scaling of the bonding pair.1. F. Rieutord, B. Bataillou, and H. Moriceau, Phys. Rev. Lett., 94, 236101 (2005).2. V. Larrey, G. Mauguen, F. Fournel, D. Radisson, F. Rieutord, C. Morales, C. Bridoux, and H. Moriceau, ECS Trans., 75, 145 (2016).3. D. Radisson, Phd thesis, Université Grenoble Alpes, (2014).4. M. Broekaart, A. Castex, K. Landry, R. Fontaniere, and C. Lagahe-Blanchard, ECS Trans., 50, 371 (2013).5. Fournel, F, B Rousset, V Larrey, C Morales, R Sachs, L Sudrie, and C Morvan, WaferBond’22 Proceeding, 2022. Figure 1

Implementation of a modified Graham-Walles viscosity function within a Chaboche viscoplastic constitutive model

This work provides a numerical framework for the accurate prediction of operational life of metallic components exhibiting a non-classical creep behavior under constant loadings and very high temperature. A modified Graham-Walles type analytical viscoplastic function is implemented into a Chaboche unified viscoplastic constitutive model. The numerical model is integrated into the finite element software Lagamine following a fully-implicit two-step radial return mapping algorithm. The non-linear system of equations is solved using a robust Newton-Raphson method. The computational efficiency of the model is enhanced by implementing a sub-step routine, thereby decreasing the average number of iterations of the finite element software. The validation of the model is performed using experimental data available in the literature on the non-classical creep behavior of Incoloy 800H, a Ni-superalloy exhibiting a two-step creep strain rate minima attributed to multiple complex dislocation-precipitate interactions.

Cuttings Transport With Oil- and Water-Based Drilling Fluids

Abstract Deviated well sections are common in most modern offshore well construction designs. In the North Sea region, which is a good example of mature areas, practically all producer or injector wells have highly deviated well sections. These wells must be constructed in an optimal manner with respect to functionality, drill time, risk, and all affiliated costs. Throughout the years, most hole-cleaning and hydraulic models have been developed based on experimental results from relatively small-scale laboratory tests with model fluids. Hole-cleaning properties and hydraulic behavior of practical drilling fluids intended for field application differ from those of most model fluids. Furthermore, results from small diameter tests may not always be relevant for or scalable to field applications because of the presence of a huge number of dimensional quantities like velocity, fluid properties, time, length, and other scale differences. Hence, studies using sufficient large-scale experimental facilities in controlled laboratory environments with the application of various field-designed drilling fluids are necessary to improve engineering models and operational practices. The current paper presents results from such laboratory tests where field-applied drilling fluids have been used. In comparison tests, the different drilling fluids have similar density and viscosity functions within the relevant field-applied shear rate range. This shear rate range is also assessed in the tests. One of the drilling fluids is oil-based, and the other one is an inhibitive water-based drilling fluid of the KCl/polymer type.

Oscillatory electro-magneto-kinetics of confined-Stokes-second-problem micro-flows

We semi-analytically investigate the electro-magneto-hydrodynamics of time periodic electroosmotic flow of a Newtonian electrolyte through microchannels with oscillating boundaries, resembling a confined-Stokes-second-problem type system. Herein, a constant orthogonal magnetic field and a constant transverse electric field have been used along with the driving time periodic electric field to have better control over mixing in the microchannel or to augment the pumping. The Poisson–Boltzmann equation has been solved with Debye–Hückel linearization for the thin electric double layer to obtain the electric potential distribution. We determine the flow field for low Hartmann number (Ha) cases by the regular perturbation method. Furthermore, Laplace transformation has been used to solve the flow field for each order in the obtained perturbation series. We have obtained the solution of flow field up to O(Ha) and found an excellent match with the complete numerical solution for our range of Ha. The dependence of flow field on dimensionless parameters, such as Ha, electrokinetic number (M), and Womersley number (Wo), has been discussed thoroughly, where Ha and M are functions of the strength of applied magnetic field and transverse electric field, respectively, and Wo is the function of Debye length, kinematic viscosity, and frequency of the time periodic electric field. Interestingly, for large values Wo, we find wave like motion in the flow field, which induces vorticity as well as better mixing caliber. Additionally, we find that the interplay between Ha and M controls the mixing and modifies the flow rate according to the need. Various combinations of such parameters have been discussed to promote mixing as well as pumping for such strongly coupled microfluidic phenomena.

Learning of viscosity functions in rarefied gas flows with physics-informed neural networks

The prediction of non-equilibrium transport phenomena in disordered media is a difficult problem for conventional numerical methods. An example of a challenging problem is the prediction of gas flow fields through porous media in the rarefied regime, where resolving the six-dimensional Boltzmann equation or its numerical approximations is computationally too demanding. A generalized Stokes phenomenological model using an effective viscosity function was used to recover rarefied gas flow fields: however, it is difficult to construct the effective viscosity function on first principles. Physics-informed neural networks (PINNs) show some potential for solving such an inverse problem. In this work, PINNs are employed to predict the velocity field of a rarefied gas flow in a slit at increasing Knudsen numbers according to a generalized Stokes phenomenological model using an effective viscosity function. We found that the AdamW is by far the best optimizer for this inverse problem. The design was found to be robust from Knudsen numbers ranging from 0.1 to 10. Our findings stand as a first step towards the use of PINNs to investigate the dynamics of non-equilibrium flows in complex geometries.

Refined Schemes for Computing the Dynamics of Elastoviscoplastic Media

For a stable numerical solution of the system of equations governing an elastoviscoplastic continuous medium model, a second-order explicit-implicit scheme is proposed. An explicit approximation is used for the equations of motion, and an implicit approximation, for the constitutive relations containing a small relaxation time parameter in the denominator of the nonlinear free terms. A second-order implicit approximation for isotropic and anisotropic elastoviscoplastic models is constructed to match the orders of approximation of the explicit elastic and implicit adjustment steps. Refined formulas for correcting the stress deviators after the elastic step are derived for various viscosity function representations. The resulting solutions of the second-order implicit approximation for the stress deviators of the elastoviscoplastic equations admit passage to the limit as the relaxation time tends to zero. The correcting formulas obtained via this passage to the limit can be treated as regularizers of the numerical solutions to the elastoplastic systems.