Creep Flows Research Articles

Sensitivity analysis of the Cercignani - Lampis accommodation coefficients in prototype rarefied gas flow and heat transfer problems via the Monte Carlo method

In rarefied gas dynamics, the Cercignani-Lampis (CL) scattering kernel, containing two accommodation coefficients (ACs), namely the tangential momentum and normal energy ones, is widely employed to characterize gas-surface interaction, particularly in non-isothermal setups, where both momentum and energy may simultaneously be exchanged. Here, a formal and detailed sensitivity analysis of the effect of the CL ACs on the main output quantities of several prototype problems, namely the cylindrical Poiseuille, thermal creep and thermomolecular pressure difference (TPD) flows, as well as the plane Couette flow and heat transfer (Fourier flow), is performed. In each problem, some uncertainties are randomly introduced in the ACs (input parameters) and via a Monte Carlo propagation analysis, the deduced uncertainty of the corresponding main output quantity is computed. The output uncertainties are compared to each other to determine the flow configuration and the gas rarefaction range, where a high sensitivity of the output quantities with respect to the CL ACs is observed. The flow setups and rarefaction regimes with high sensitivities are the most suitable ones for the estimations of the ACs, since larger modeling and experimental errors may be acceptable. In the Poiseuille and Couette flows, the uncertainties of the flow rate and shear stress respectively are several times larger than the input uncertainty in the tangential momentum AC and much smaller than the uncertainty in the normal energy AC in a wide range of gas rarefaction. In the thermal creep flow, the uncertainty of the flow rate depends on the input ones of both ACs, but, in general, it remains smaller than the input uncertainties. A similar behavior with the thermal creep flow is obtained in the TPD flow. On the contrary, in the Fourier flow, the uncertainty of the heat flux may be about the same or even larger than the input ones of both ACs in a wide range of gas rarefaction. It is deduced that in order to characterize the gas-surface interaction via the CL ACs by matching computations with measurements, it is more suitable to combine the Poiseuille (or Couette) and Fourier configurations, rather than, as it is commonly done, the Poiseuille and thermal creep ones. For example, in order to estimate the normal energy AC within an accuracy of 10 %, experimental uncertainties should be less than 4 % in the thermal creep or TPD flows, while may be about 10 % in the Fourier flow.

Dynamic serviceability and safety reliability analysis of aging PC girder bridges with non-prestressed reinforcement considering concrete shrinkage, creep and stochastic vehicle load flows

Prestressed concrete (PC) bridges’ service performance displays time-dependency due to several factors including concrete shrinkage, creep, resistance degradation, and stochastic vehicle load flows. These non-stationary vehicle load flows, combined with concrete shrinkage, creep, and resistance degradation, result in sequential alterations of internal forces and deformations in simply supported PC girder bridges, ultimately influencing their dynamic reliability. This study proposes a robust methodology that considers the impact of traffic loading, shrinkage, and creep to analyze the dynamic reliability of simply supported PC girder bridges through the development of a load probability model. A stochastic model for truck loads is generated using motion measurement data, which can be used to calculate bridge internal forces and subsequent quantitative analysis of structural deformation due to shrinkage and creep. Subsequently, the formula for the first exceedance probability under resistance degradation is presented and validated through Monte Carlo simulation. Reliability analysis is conducted for both serviceability and load carrying capacity limit states to assess the impact of shrinkage, creep, and increased mean vehicle load on structural reliability. The proposed method offers the theoretical foundation and practical guidance for assessing the structural health status of in-service bridges, thereby providing valuable insights into their long-term performance and maintenance requirements.

Axisymmetric finite strain consolidation model for soft soil consolidation with vertical drains under combined loading considering creep and non-Darcy flow

Vertical drain assisted by vacuum and/or surcharge preloading is an effective method for improvement of soft ground with high water content. A large settlement will occur, and the water flow may deviate from the Darcy's law. The creep is also non-negligible in estimating the long-term settlement of such soft ground. To accurately predict the consolidation process, this study develops an axisymmetric finite strain consolidation model based on Barron's free-strain theory incorporating the creep, radial and vertical flows, non-Darcian flow law, and void ratio-dependent hydraulic conductivity during the consolidation process. First, to mathematically validate the model and highlight the new model's features, the existing model not considering the creep and the non-Darcy flow is also adopted as a reference for comparison based on a benchmark simulation. Then, Rowe cell tests involving non-Darcian flow are simulated by the new model to experimentally validate the predictive performance. Furthermore, the model is applied to simulate the consolidation process of a long-term monitoring embankment to examine the applicability of the model for engineering practice. All results demonstrate that the model is capable of accurately describing the consolidation of soft soils with vertical drains under combined loading with features of creep and non-Darcy flow.

Time-Dependent Reliability Analysis of RC Bridges Considering Shrinkage, Creep, Resistance Degradation, and Vehicle Load Flows

Due to concrete shrinkage, concrete creep, resistance degradation, and vehicle load flows, the long-term performance of reinforced concrete bridges exhibits time-varying characteristics. The vehicle-borne process is a nonstationary random process, which interacts with concrete shrinkage, concrete creep, and resistance degradation to cause constant changes in bridge internal force and deformation, further, bridge dynamic reliability occurs. This study presented a reasonable method for calculating the time-varying reliability of simply supported girder bridges under the effects of traffic loads and shrinkage creep. Stochastic truck-load models were simulated based on site-specific weigh-in-motion measurements, then the internal forces of the bridge were calculated when the mean value of vehicle-mounted effects increases by 1% per year. Considering the resistance degradation and load effect increase, the reliability of the RC bridge in serviceability limit state and capacity-carrying ultimate state were analyzed using first-passage probability method and Monte Carlo method, respectively. The accuracy of the proposed method was verified by comparison. The evaluation results show that the failure probability including shrinkage and creep has increased significantly; creep is affected by the bridge span and the number of main girders, and the reliability assessment results are safer for bridges with smaller spans.

Time-variant reliability analysis of simply supported PC girder bridges considering shrinkage, creep, resistance degradation and vehicle load flows

The long-term performance of simply supported Prestressed Concrete (PC) girder bridges exhibits dynamic characteristics because of concrete shrinkage, concrete creep, resistance degradation and vehicle load flows. The vehicle loads are non-stationary and random, which interacts with concrete shrinkage, concrete creep and resistance degradation to cause dynamic changes of bridge internal force and deformation, further, bridge dynamic reliability occurs. This study presented a reasonable method for calculating the time-varying reliability of simply supported PC girder bridges under the effects of traffic loads and concrete shrinkage creep. Stochastic truck-load models were simulated based on site-specific weigh-in-motion measurements, then the internal forces of the bridge were calculated when the mean value of vehicle loads increases by 1% per year. Considering the resistance degradation and load effect increase, the PC bridge reliability for serviceability limit state and capacity-carrying ultimate state were analyzed using first-passage probability method and Monte-Carlo method, respectively. The accuracy of the proposed method was verified by comparison. The evaluation results show that the failure probability including concrete shrinkage and creep has increased significantly, creep is affected by the bridge span and the number of main girders, and the reliability assessment results are safer for bridges with smaller spans.

Gas-surface interaction in rarefied gas flows through long capillaries via the linearized Boltzmann equation with various boundary conditions

Reliable gas–surface interaction modeling is of major importance in consistent simulation of rarefied gas flows with applications in vacuum technology and micro-electromechanical systems. The effectiveness of the most prominent kinetic boundary conditions, namely the ones by Maxwell, Cercignani-Lampis and Epstein, is elaborated by numerically solving the classical plane Poiseuille and thermal creep flows via the linearized Boltzmann equation, subject to these boundary conditions. The flow rates are provided in a wide range of the gas rarefaction for many values of the accommodation coefficients of each scattering kernel, identifying in parallel, the sensitivity of the flow rates in small variations of the free parameters. A comparison with available experimental data is performed to deduce that the Cercignani-Lampis and Epstein scattering kernels, compared to the Maxwell one, are more suitable to characterize coupled momentum and energy accommodation modes. With these boundary conditions, the accommodation coefficients may be extracted by fitting computations with measurements, in the Poiseuille flow in a wide range of gas rarefaction, but in the thermal creep flow, experimental data under rarefied conditions, as high as possible, are recommended. The present work may be useful in determining the measurement conditions and uncertainties, allowing accurate extraction of the accommodation coefficients.

Fluvial interpretations of stratigraphic surfaces across Upper Triassic to Lower-Middle Jurassic continental red beds northeastern Mexico

This work broadens the understanding of previous interpretations from Late Triassic-Early-Middle Jurassic reds beds in northeastern Mexico from the Huizachal Group. Proposed bounding surfaces in El Alamar, La Boca, and La Joya formations are informal. The surfaces are here assigned allostratigraphic hierarchies for genetic interpretations. The formations are continental and provide no sea-level markers to tie the surfaces to the marine base level, but these fluvial-alluvial environments produce various scales of traceable scour surfaces.Upper Triassic-Middle Jurassic sandstones were analyzed at ten localities. Sedimentary profiles provide details for two facies associations and two main facies, which share 20 sedimentary lithofacies. The documentation of fluvial architecture considers sedimentary structures and paleocurrents in the sand bodies to features of five fluvial styles driving the depositional system, including mixed debris flow and braided river systems, gravelly or sandy meandering river, ephemeral sand-bed meandering river, and ephemeral sheet-flood distal sand-bed river.This model provides greater detail for more accurate stratigraphic correlation to sedimentary conditions under which these rocks were deposited, as it allows identifying four major bounding surfaces that can be tied to fluvial processes of amalgamation, aggradation, degradation, or flooding. The exercise estimates provisional regional tracts in continental deposits with no apparent impact by the marine base level. Amalgamation surfaces are underneath laterally extensive sheets of amalgamated channel-belt architectural elements, the contacts with underlying surfaces are disconformable, but locally are angular unconformities. The amalgamated beds also include sediment-gravity flows deposited such as channelized debris flows. Aggradation underlies and binds volcaniclastic rocks and facies with common mass wasting deposits from creep or debris flows, as well as overland flow and gullying over broad alluvial plains forming upward-coarsening sequences. It locally records the rapid burial of landscapes by mass wasting, distinguishing it from typical valleys that are cut by normal channel processes. Degradation binds incised valleys that confine channels and floodplains, and unconformably overly fining-upward sequences. Flooding marks sediment accumulation formed by overbank flows in low-energy environments.

A model of micro lubrication between two walls with unequal temperature distribution based on kinetic theory

Micro lubrication of a gas between two walls with arbitrary and independent temperature distributions is studied on the basis of the Bhatnagar–Gross–Krook–Welander (BGKW) model of the Boltzmann equation. The BGKW equation is studied analytically using the slowly varying approximation. Following the author's previous study [T. Doi, “A model of micro lubrication between two walls with an arbitrary temperature difference based on kinetic theory,” Phys. Fluids 32, 052005 (2020)], the leading-order approximation, which ought to be the solution of the nonlinear heat transfer problem, is replaced by its free molecular solution. A lubrication model of the Reynolds-type equation is derived in closed form. A direct numerical analysis of the lubrication flow subject to localized heating or cooling of the walls is conducted for an assessment of the lubrication model. The lubrication lift calculated using the model agrees with that of the direct numerical solution within an error of 5% when the Knudsen number based on the gap size lies between 0.1 and 10. The result of the lubrication model agrees also with that of the Boltzmann equation for a variable hard sphere gas. A sharp peak arises in the pressure distribution for large Knudsen numbers owing to the effect of thermal creep flows induced by localized heating.

Sidewall friction in confined surface flows of granular materials

We report numerical simulations of surface granular flows confined between two sidewalls. These systems exhibit both very slow and very energetic flows. Zhu et al. [1] have shown that in energetic confined systems, the Froude number at sidewalls and the sidewall effective friction coefficient are linked through a unique relation. We show that this relation is also valid for creep flows. It is independent of the angle of the flow but depends on the sidewall-grain friction coefficient. Our results shed light on boundary conditions that have to be used at sidewalls in continuum theories aiming to capture the behavior of granular systems from creeping to energetic flows.

On the Room-Temperature Creep Behavior and Its Correlation with Length Scale of a LiTaO3 Single Crystal by Spherical Nanoindentation.

Relying on nanoindentation technology, the room-temperature creep behavior of a LiTaO3 single crystal in the typical orientation (012), i.e., Y-42° plane was investigated. Three kinds of spherical tips with the radii of 0.76, 2.95 and 9.8 μm were respectively applied to detect nanoindentation length scale effect on creep deformation at both elastic and plastic regions. Superficially, both creep displacement and rate were nearly linearly increased with increasing holding depth and independent of tip size, which could be ascribed to the simultaneously enlarged holding strain and deformation volume beneath the indenter. At a similar holding strain, creep deformation, i.e., creep strain and strain rate were more pronounced under smaller spherical tips. Strain rate sensitivities of creep flows under different spherical tips and holding strains were also estimated. The potential room-temperature creep mechanism of LiTaO3 under high shear compression stress was discussed.

Uncertainty analysis of computed flow rates and pressure differences in rarefied pressure and temperature driven gas flows through long capillaries

Abstract The computation of the mass flow rate in the Poiseuille and thermal creep flows and of the pressure difference in the thermomolecular pressure difference (TPD) flow through long capillaries is well-known and available in the literature. Here, the uncertainty in the solution due to induced uncertainties in the input data, namely, the capillary radius and length, the pressure and/or temperature imposed at the capillary ends and the accommodation coefficient of the Maxwell diffuse-specular boundary conditions, is investigated. The uncertainty analysis is performed by the Monte Carlo Method. Conducting the required number of trials the distribution function of the output quantity and its associated uncertainty are obtained. In most cases, the uncertainty in the input quantity driving the flow has the largest effect on the output uncertainties. This is always true in the TPD flow and for small pressure and temperature differences in the Poiseuille and thermal creep flows respectively. In the case of large driving thermodynamic forces, in the latter two flows, the radius becomes the most important source of uncertainty. The accommodation coefficient uncertainty is always the less important one. Documenting the expected effect of the uncertainty in each input parameter is certainly beneficial in computational as well as experimental work.

Polyatomic thermal creep flows through long microchannels at large temperature ratios

Rarefied polyatomic gas flows through long microchannels of circular cross section due to small temperature and pressure gradients have been studied on the basis of the Rykov model in a wide range of the gas rarefaction and for various values of the reference flow temperature. Results are presented for N2, CO2, CH4, and SF6 representing linear and nonlinear polyatomic gas molecules. The present numerical results for N2 and CO2 are in good agreement with the corresponding results of previous studies. In addition, a simple method of calculation of the thermal creep under large temperature differences, which has been proposed in previous studies for monatomic gases, is extended in the present work in the case of polyatomic gases. The results based on the polyatomic modeling differ significantly from the corresponding monatomic ones and the differences depend on the gas rarefaction, the working gas, and the flow temperature. Special attention is also given to the computation of the thermomolecular pressure effect in the case of polyatomic gases under large temperature ratios. Furthermore, the dependence of both the thermal creep and the thermomolecular pressure effect on the viscosity variation with temperature along the microchannel is pointed out. Finally, the numerical data are provided as supplementary material for modeling any polyatomic gas flow in a wide range of the gas rarefaction and flow temperatures.

Flow fields around pinned self-thermophoretic microswimmers under confinement.

We measure the flow field around a pinned micrometer-sized self-thermophoretic Janus particle confined in a slit pore of different slit widths. The flow field is determined with the help of gold nanoparticles, which are thermophoretically inactive and thus do not respond to the generated temperature gradients directly. The flow fields are altered when the slit pore is narrowing and reveal clear features of thermo-osmotic flows generated by the temperature gradients along the confining glass cover slip surfaces. Based on these observations, we suggest that many observations of active and passive particle clustering around phoretic swimmers are influenced by such osmotic creep flows induced at the substrate boundary.

Room-Temperature Creep Behavior and Activation Volume of Dislocation Nucleation in a LiTaO3 Single Crystal by Nanoindentation.

The crystal orientation effect on mechanical heterogeneity of LiTaO3 single crystals is well known, whilst the time-dependent plastic behavior, i.e., creep is still short of understanding. Relying on nanoindentation technology, we systematically studied room-temperature creep flows at various holding depths (100 nm to 1100 nm) in three typical orientations namely the X-112°, Y-36° and Y-42° planes. Creep resistance was much stronger in the X-112° plane than the others. In the meanwhile, creep features were similar in the Y-36° and Y-42° planes. The orientation effect on creep deformation was consistent with that on hardness. The nanoindentation length scale played an important role in creep deformation that creep strains were gradually decreased with the holding depth in all the planes. Based on strain rate sensitivity and yield stress, the activation volumes of dislocation nucleation were computed at various nanoindentation depths. The activation volumes ranged from 5 Å3 to 23 Å3 for the Y-36° and Y-42° planes, indicating that a point-like defect could be the source of plastic initiation. In the X-112° plane, the activation volume was between 6 Å3 and 83 Å3. Cooperative migration of several atoms could also be the mechanism of dislocation activation at deep nanoindentation.

A novel technique for conducting creep experiments in equibiaxial elongation

A recently developed rheological technique known as continuous lubricated squeezing flow (CLSF) is adapted to perform constant stress, or creep, experiments in equibiaxial elongation flows of polymer melts. By modifying the CLSF technique, which was developed for constant strain rate deformations, we demonstrate that the technique can also be used to generate constant stress flows. Measured steady state viscosities are compared to constant rate elongation results for polymer melts having different molecular characteristics. Linear polymers show strain softening and compare well in constant stress and constant strain rate deformations. The branched polymer shows strain hardening and a viscosity that is slightly higher in constant stress for low rates. Limitations of the current version of the CLSF technique for creep flows are also briefly discussed.

A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

AbstractA kinetic model of the Boltzmann equation for non-vibrating polyatomic gases is proposed, based on the Rykov model for diatomic gases. We adopt two velocity distribution functions (VDFs) to describe the system state; inelastic collisions are the same as in the Rykov model, but elastic collisions are modelled by the Boltzmann collision operator (BCO) for monatomic gases, so that the overall kinetic model equation reduces to the Boltzmann equation for monatomic gases in the limit of no translational–rotational energy exchange. The free parameters in the model are determined by comparing the transport coefficients, obtained by a Chapman–Enskog expansion, to values from experiment and kinetic theory. The kinetic model equations are solved numerically using the fast spectral method for elastic collision operators and the discrete velocity method for inelastic ones. The numerical results for normal shock waves and planar Fourier/Couette flows are in good agreement with both conventional direct simulation Monte Carlo (DSMC) results and experimental data. Poiseuille and thermal creep flows of polyatomic gases between two parallel plates are also investigated. Finally, we find that the spectra of both spontaneous and coherent Rayleigh–Brillouin scattering (RBS) compare well with DSMC results, and the computational speed of our model is approximately 300 times faster. Compared to the Rykov model, our model greatly improves prediction accuracy, and reveals the significant influence of molecular models. For coherent RBS, we find that the Rykov model could overpredict the bulk viscosity by a factor of two.

A critical gel fluid with high extensibility: The rheology of chewing gum

Chewing gum provides an excellent everyday example of viscoelastic behavior, and understanding its rheological properties is important for application purposes. Here, we compare the rheological behavior of selected commercial chewing gums and bubble gums. Small amplitude oscillatory shear, shear creep, and steady shear demonstrated that both chewing and bubble gums behave like power-law critical gels in the linear regime. Nonlinear viscoelastic behavior was investigated using large amplitude oscillatory shear, shear creep, and start-up flows (in shear and uniaxial extension). Bubble gums showed more pronounced strain hardening and greater stresses to break in start-up of steady uniaxial extension than chewing gums. We argue that this combination of rheological signatures is sufficient to provide a new robust definition of chewing gum that is independent of specific molecular composition. There are potentially many different formulations and design routes that can achieve this distinctive rheological fingerprint.

Solving the Boltzmann equation deterministically by the fast spectral method: application to gas microflows

AbstractBased on the fast spectral approximation to the Boltzmann collision operator, we present an accurate and efficient deterministic numerical method for solving the Boltzmann equation. First, the linearized Boltzmann equation is solved for Poiseuille and thermal creep flows, where the influence of different molecular models on the mass and heat flow rates is assessed, and the Onsager–Casimir relation at the microscopic level for large Knudsen numbers is demonstrated. Recent experimental measurements of mass flow rates along a rectangular tube with large aspect ratio are compared with numerical results for the linearized Boltzmann equation. Then, a number of two-dimensional microflows in the transition and free-molecular flow regimes are simulated using the nonlinear Boltzmann equation. The influence of the molecular model is discussed, as well as the applicability of the linearized Boltzmann equation. For thermally driven flows in the free-molecular regime, it is found that the magnitudes of the flow velocity are inversely proportional to the Knudsen number. The streamline patterns of thermal creep flow inside a closed rectangular channel are analysed in detail: when the Knudsen number is smaller than a critical value, the flow pattern can be predicted based on a linear superposition of the velocity profiles of linearized Poiseuille and thermal creep flows between parallel plates. For large Knudsen numbers, the flow pattern can be determined using the linearized Poiseuille and thermal creep velocity profiles at the critical Knudsen number. The critical Knudsen number is found to be related to the aspect ratio of the rectangular channel.

Numerical design of a Knudsen pump with curved channels operating in the slip flow regime

A numerical procedure has been developed for modeling 2D thermal creep flows with Fluent®. Complete first order velocity slip, including thermal creep and walls curvature effects, as well as temperature jump, boundary conditions, are implemented via C routines. After validation on benchmark flows, the technique is used for designing a Knudsen pump with curved microchannels and it is demonstrated that this micropump can be efficient in the slip flow regime.

Boundary layer (shear-band) in frustrated viscoplastic flows

We show that frustrated creep flows of yield stress fluids give rise to a boundary layer, which takes the form of a liquid region of uniform significant thickness separating two solid regions. In this boundary layer the shear rate is approximately constant for a given flow rate and the layer thickness varies extremely slowly with the flow rate.