Conventional Continuum Research Articles

Upscaling Water Flow in Composite Nanoporous Shale Matrix Using Lattice Boltzmann Method

AbstractWater flow in nanoporous structures in shale strongly depends on water‐pore wall interactions; specifically, water‐pore wall interactions may influence flow more than water‐water interactions. Because of strong water‐pore wall interactions, the models that govern flow in nanoporous structures deviate from conventional continuum flow models such as the Darcy equation. We develop a novel lattice Boltzmann model to study water flow in nanoporous structures rendered from shale samples. First, we reconstruct three‐dimensional (3‐D) stochastic digital models based on composite shale samples that include hydrophobic organic matter (OM) and hydrophilic clay minerals. In the reconstructed digital models, we use pore size/shape distributions, porosity, and mineralogy from experiments. Then we use lattice Boltzmann models to model water flow through nanoporous structures (OM and clay) of the reconstructed shale sample, and we upscale the results to a microporous structure of composite shale containing OM, clay, and interpores associated to other minerals. The results show contraction/expansion effects of pore‐throat‐pore systems in nanoporous OM weaken the hydrophobicity‐induced slippage effect on total water flow. In nanoporous clay, the swelling effect predominates and diminishes water slippage effects on water flow. The work also highlights the importance of (1) the accuracy of reconstructed 3‐D pore networks in terms of pore connectivity, shape, and tortuosity in individual systems of OM and clay and (2) the role of OM nanopores in connecting isolated micropores to total water flow through the composite shale system.

Design and Development of a Growing Pneumatic Soft Robot

Soft continuum robots are getting more popular in areas such as minimally invasive surgery, search and rescue, and inspection due to their inherent compliance and flexibility. However, most of the conventional continuum robots still lack the ability to significantly change size and length. Growth as a means of robotic locomotion is a novel actuation method that can be used to overcome this disadvantage. In this study, we introduce a growing pneumatic soft robot made up of pressurized thin-walled tubings that can move in three-dimensional space with an extension ratio only limited by manufacturing capabilities. Besides the ability to grow from the tip, this design provides active steering by controlling the speed of each tubing separately, controllable stiffness that can be changed during motion, and capability to carry a tool channel. We present models to estimate tip force and position and experimentally verify the force model and robot kinematics. Open-loop speed controller has an overall root mean square error of 2.69% for speeds between 20 and 300 mm/s. The position controller based on the kinematic model has a mean positioning error of 13.9 mm at 100 mm and 22.6 mm at 200 mm longitudinal distance. Robot can produce a tip force of 20.1 N at 150 kPa tubing pressure and reach a maximum speed of 1490 mm/s at 100 kPa. We also demonstrate the navigation capabilities of the robot both in open field and in constrained environments.

Simulation of diffusio-phoretic motion of colloidal particle suppressed by bound solutes within adsorption shell

Colloidal particle submerged in a non-equilibrium fluid with a concentration gradient of solutes experiences diffusio-phoresis. Such directional transport originates from the driving forces that exert on the fluid in a microscopic boundary layer surrounding the colloid. Based on a simple model of spherical colloid fixed in a concentration gradient of solutes, molecular dynamics simulations are performed to determine the interaction parameters that maximise the diffusio-phoretic mobility, which cannot be properly measured by conventional continuum theory. The diffusio-phoretic mobility is found to depend non-monotonically on the strength of the interaction between the colloid and solutes, due to the presence of bound solutes within adsorption shell that cannot contribute to diffusio-phoresis. The results also show that the phoretic mobility depends sensitively on the density of solutes in bulk, due to the uneven distribution of excess particles surrounding the colloid at a microscopic level. The simulations suggest that diffusio-phoresis may in principle be applied to the selective transport, separation and purification for colloidal systems. By substituting the spherical colloid with other realistic macromolecules, the model could provide results that are quantitatively comparable with experiments.

Material properties for fracture mechanics based strength assessment of cast iron water mains

Municipal water distribution systems in Canada and other countries include a large number of cast iron pipes that were installed almost 50 years ago. For structural integrity assessment of these pipes, the fracture mechanics approach is found to be more effective than the conventional continuum mechanics-based approach. This paper presents the mechanical properties for fracture mechanics-based strength assessment of water mains determined through testing of cast iron pipes exhumed from two cities in Canada. Microstructure analysis is conducted to understand the materials’ inherent properties. Uniaxial tensile tests are conducted to determine the stress–strain relations. The influence of the rate of loading on stress–strain behaviour and loading-unloading responses are investigated. A simplified single-edge notch beam test is used to obtain the fracture toughness. Probabilistic distributions of the parameters are provided to account for the uncertainty and variabilities observed in the test results.

An Accuracy Enhancement Method for a Cable-Driven Continuum Robot With a Flexible Backbone

In this paper, an integrated accuracy enhancement method based on both the kinematic model and the data-driven Gaussian Process Regression (GPR) technique is proposed for a Cable-Driven Continuum Robot (CDCR) with a flexible backbone. Different from the conventional continuum robots driven by pneumatic actuators, a segmented CDCR is developed in this work, which is a modular manipulator composed by a number of consecutive Cable-Driven Segments (CDSs). Based on the unique design of the backbone structure which merely allows 2-DOF bending motions, a two-variable Product-of-Exponential (POE) formula is employed to formulate the kinematic model of the CDCR. However, such an analytic kinematic model is unable to accurately describe the actual deflections of the backbone structure. Therefore, GPR is proposed to compensate the tip error of a CDCR. Compared with other machine learning methods, GPR requires less learning parameters and training data, which makes the learning process computationally efficient. To validate the effectiveness of the proposed integrated accuracy enhancement method, experiments on the actual testbed are conducted. Experimental results show that the CDCR's position and orientation errors are reduced by 68.72% and 51.74%, respectively.

New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle

Any physical laws are scale-dependent, the same phenomenon might lead to debating theories if observed using different scales. The two-scale thermodynamics observes the same phenomenon using two different scales, one scale is generally used in the conventional continuum mechanics, and the other scale can reveal the hidden truth beyond the continuum assumption, and fractal calculus has to be adopted to establish governing equations. Here basic properties of fractal calculus are elucidated, and the relationship between the fractal calculus and traditional calculus is revealed using the two-scale transform, fractal variational principles are discussed for 1-D fluid mechanics. Additionally planet distribution in the fractal solar system, dark energy in the fractal space, and a fractal ageing model are also discussed.

A self-similarity mathematical model of carbon isotopic flow fractionation during shale gas desorption

The existence of nanosized pore systems differentiates isotopic gas transport inside a shale matrix from conventional continuum flow. In this study, a novel self-similarity mathematical model was developed to investigate the effects of gas flow transport (both slip flow and free molecular diffusion flow) on isotopic gas fractionation for four different shale samples (S1 and S2 from north Germany and S3 and S4 from Xiashiwan Field, Ordos Basin, China). In this model, the nonlinear permeability and diffusion coefficients were developed for the isotopologues (12CH4 and 13CH4), respectively. By selecting appropriate exponents of the pressure gradient for 12CH4 and 13CH4, respectively, the estimated isotopic methane concentration and production rate showed a good agreement with experimental data. The developed model shows that the gas concentration of the isotopologues in samples S1 and S2 increases with time following a power law. Similarly, the gas production rates of the isotopologues in samples S3 and S4 decay with time following a power law. Moreover, the exponents of the pressure gradient for the isotopologues are close to 4 for samples S1 and S2, indicating that the effect of slip flow on isotopic gas fractionation cannot be ignored. For samples S3 and S4, the exponents of the pressure gradient for the isotopologues increase with temperature rising, which shows the promotion of isotopic gas fractionation under higher heating temperatures. The slight difference between the exponents of the pressure gradient for the isotopologues for the same shale sample reveals that the isotopic gas fractionation of carbon is a slow process.

A comparison between the performance of different Mindlin's theory based strain gradient models in local singularities

AbstractThe classical continuum mechanics theories are originally supposed to determine deformations in ranges from millimeter to meter, the so‐called macroscopic scale. In fact, these theories are approximations of physical systems neglecting the underlying microstructure. For instance, a Cauchy continuum, i.e. a continuum with an elastic energy determined as a function of the gradients of its macroscopic displacement, can only approximate the behavior of a physical system sufficiently as long as the microstructure has a much smaller length‐scale than the macrostructure [1]. Although these models were exploited in studies for large and small scales, experiments have shown that the classical models are not able to properly cover the smaller scales; in particular, problems in micron‐ and nano‐dimensions are frequently observed. Size‐effects, which cannot be captured exploiting these theories, seem to be the source of this issue. On top of that, the appearance of local singularities at the crack tips (or more broadly, in the presence of point and line loads) is one of the known limitations of the classical continuum mechanics theories. Generalizing these models by introducing additional kinematic terms to consider the underlying microstructure effects at macroscopic levels is one way of overcoming the already mentioned problems. In this contribution, we will focus on the Mindlin's theory of elasticity with microstructures [2] and its different forms. Therein, it is shown that for the first strain gradient theory, five additional parameters must be introduced. However, in practice, due to the complexities of measuring the new parameters, various simplified versions of the theory are being exploited, among them we name Altan et al. [3] and Reiher et al. [4]. Our aim here is to compare the performance of these simplified theories in removing the local singularities of the conventional continuum mechanics theory.

Damage and viscoplastic behavior of sintered nano-silver joints under shear loading

Compared with most of the traditional solder materials, sintered nano-silver shows better high-temperature service performance and is expected to replace the traditional packaging materials in the next-generation of electronic devices. However, there exist substantial voids inside the sintered nano-silver layer after sintering, and the conventional continuum damage mechanics has certain limitation to describe the shear stress-strain relationship of sintered nano-silver materials. To analyze the void evolution and microstructure of sintered nano-silver, gold-plated sintered nano-silver specimens were tested under shear loading at different temperatures. A unified viscoplastic constitutive model is proposed to describe the properties of sintered nano-silver specimen under shear loading, in which the viscous overstress is replaced by the potential function of Gurson-Tvergaard-Needleman model and the effects of void on the yield surface of viscoplastic material is considered. To describe the influence of void evolution to the deterioration of mechanics properties at high temperatures, a damage variable is incorporated into the drag strength to indicate the damage mechanism with respect to the softening of sintered nano-silver material. The numerical predictions are compared with the experimental data, which shows that the developed model can describe the shear constitutive behavior of sintered nano-silver specimen with reasonable accuracy.

The aging cardiovascular continuum

The atherosclerotic cardiovascular continuum or the conventional cardiovascular continuum(CCC)was first described by Dzau in 2006, describing a series of steps cardiovascular disease undergoes, from risk factors at the beginning to end-stage heart disease(characterized by ventricular dilation, heart failure, and death). The essential features of CCC are myocardial ischemia and myocardial infarction due to coronary artery stenosis, which originates from coronary atherosclerosis.O'Rourke proposed the aging cardiovascular continuum(ACC)in 2010 to explained the role of aging, especially vascular aging, in the development of cardiovascular disease.The continuum encompasses progressive deterioration of the proximal aorta properties with increasing arterial stiffness and dilation, resulting in adverse effects on important organs such as the heart, brain, and kidneys.The two continuums are both distinct and related, complement each other and fully illustrate the occurrence and progression of the cardiovascular continuum. Key words: Blood vessels; Aging; Atherosclerosis

Impact of shale matrix mechanical interactions on gas transport during production

Shale gas has played an increasingly important role in world energy supply in recent years. The gas transport process in the shale matrix is particularly important as it affects the long-term production behavior of shale gas. The shale matrix consists of inorganic minerals and embedded organic matter with mass transfer influenced by mechanical interactions. We develop a micro-scale discrete coupled model to explicitly account for mass transfer and mechanical interactions, and how these interactions affect the gas transport characteristics of both components. Specifically, the model comprises organic matter embedded within inorganic minerals. The proposed model is implemented and solved within the framework of COMSOL Multiphysics (Version 5.4). The model is first verified against the results of a desorption-diffusion-seepage coupled experiment and then extended to field scale. It is found that the impacts of gas pressure and effective strain are different for the gas seepage in inorganic minerals and gas diffusion in organic matter. Gas pressure may enhance the permeability of the inorganic phase due to the gas slippage effect while compactive effective strain decreases permeability during the gas depletion process. For gas diffusion in the organic matter, surface diffusion decreases and effective diffusion coefficient increases with declining gas pressure. While the impacts of effective strain on the effective diffusion are dependent on the external boundary conditions, the effective diffusion coefficient is lower than the initial value under constant stress conditions and larger than the initial value under constant volume conditions. The proposed model provides a complementary method to conventional continuum dual-media approaches and provides a clear understanding of the interactions between the two components. Field-observed oscillatory gas production data is readily history-matched and key mechanisms explained with the proposed approach presented in this work.

DSMC data-improved numerical simulation of hypersonic flow past a flat plate in near-continuum regime

Numerical simulation of hypersonic flows over a flat plate in near-continuum regime is presented to assess a data-improved Navier-Stokes (DiNS) model, which has been developed for modeling flows involving local non-equilibrium effects. The simulation is directly performed in the framework of Navier-Stokes-Fourier (NSF) equations, but with the viscosity coefficient and thermal conductivity coefficient modified according to a certain parameter Zh characterizing the local shear induced non-equilibrium effect, based on data obtained by Direct Simulation Monte Carlo (DSMC) method for typical shear flows. Excellent agreement on both drag and heat transfer coefficients are obtained by the DiNS method compared with solution of the DSMC method. The present DiNS method exhibits remarkable improvement compared with the traditional NSF method in predicting the flow profiles as well as the surface shear stress and heat flux. For the new continuum model, the extra numerical cost, compared with the conventional continuum model, is less than 30%. Hence, our new method, unlike the DSMC method, can readily be applied to engineering problems in regard with the computational cost.

Evaluation of permeability applicability based on continuum mechanics law in fluid flow through graphene membrane

Graphene is expected to be used in separation applications such as desalination. However, it is difficult to predict the flow phenomena at the nanoscale using the conventional continuum law. Particularly at a Knudsen number (Kn) of >0.1, which is applied in filtration, it has been reported that not even slip boundary conditions can be applied. In this study, to identify the parameters that affect the applicability of the continuum law, we conducted a fluid permeation simulation using graphene. The deviation of the permeability from that of the continuum model was calculated by changing the channel width, fluid temperature, and fluid type. The result showed that the channel width has the largest influence among the three factors, and that the magnitude of the divergence is sorted out based on the Knudsen number. Therefore, the permeability can be predicted even at the nanoscale where the continuum law cannot be applied.

Discrete simulation of particle manipulation in micro-fluid with acoustic force

To date the standing surface acoustic wave (SSAW) could manipulate particle meeting various demands, based on particle size, density and shape. However, particle scale information is not easy to be studied by experimental method and conventional continuum method. In this paper, the particles are described by discrete element method (DEM), the fluid is simulated by computational fluid dynamics (CFD). The acoustic force acted on each particle is implanted based on Gor'kov theory. The established model is validated as the particle flow pattern together with the focusing length and width agree well between simulations and experiments. Further simulations reveal more particle scale information at length. The particle focusing process can be catalogued into three regions, which are strongly influenced by particle and acoustic properties. The particle collides' effects are not significant as drag and acoustic force, but irreplaceable on the subsequent particle rotation in ordering the particle pattern in focused layer.

Analysis of Twist Deformation in Wire-driven Continuum Surgical Robot

Wire-driven continuum surgical robots are attracting significant interest in minimally invasive surgeries owing to their high dexterity level and miniaturization. However, twist deformation due to the external force at the end effector decreases the accuracy and controllability of these robots. In this study, we analyze the two factors responsible for twist deformation and propose models incorporating these factors. In our analyses, we first consider twist deformation due to the elastic deformation of the wire; when a tensioned wire is subjected to normal force, a sag effect occurs, which results in twist deformation in the robot. We analyze this sag effect statically considering the material properties of the wire. We also analyze the twist deformation due to the clearance between the wire and hole boundary in the spacer of the robot. Clearance is required in a wire-driven continuum robot to realize bending motion; however, this is considered one of the main causes of twist deformation and is referred to as the clearance effect. Subsequently, we propose sag and clearance effect models that quantitatively predict the twist deformation. The results of the experiments conducted to verify the accuracy of the proposed models, including a payload test using a conventional continuum robot comprising spherical joints, indicate that the accuracy of the proposed models is 95%.

Cohesive zone representation of interfacial fracture in aluminum-silicon bimaterials

Interfacial fracture in three aluminum-silicon bimaterials with different crystal orientations under tensile loading was investigated by molecular dynamics simulations. Interface crack propagates in a brittle manner regardless of crystal orientation. The overall distribution of normal stress and separation along the interface is consistent with conventional continuum fracture mechanics. Normal traction-separation curves were extracted from simulation results and compared with three cohesive zone models. Crystal orientation shows negligible effect on the trend of normal traction-separation curves. From the perspective of the trend of the normal traction-separation curves, the exponential cohesive zone model exhibits the closest match with simulation results. When it comes to fracture toughness, the bilinear cohesive zone model has the best agreement with simulation results.

Viscous heating and temperature profiles of liquid water flows in copper nanochannel

Understanding nanoscale fluidic transport becomes increasingly important due to the rapid development of nanotechnology and nanofabrication. By using molecular dynamics (MD) simulations, we investigated the viscous heating of water flows in copper nanochannels. The two scenarios that were studied are Couette flows and Poiseuille flows. We observed the scale effects on the distribution of fluid density, streaming velocity, fluid viscosity, and temperature across the channel. The results revealed the significant effects of surface forces on causing a large deviation between simulation results and classical hypothesis. We found that the energy equation coupled with the thermal-slip boundary conditions still fails to predict the temperature distributions. Hereby, further scale effects are taken into account, which leads to better predictions. The model that we developed in this study shows the relative deviation to the simulation data within 5 %, which is small compared to the conventional continuum approach (i.e., up to 51 %).

A new type of plankton food web functioning in coastal waters revealed by coupling Monte Carlo Markov chain linear inverse method and ecological network analysis

Abstract Plankton food webs (PFW) typology is based on different categories of functioning, according to the dominant processes and the role played by heterotrophic bacteria, small vs large phytoplankton, and small vs large zooplankton. Investigating the structure and the function of planktonic food webs in two SW Mediterranean waters (inshore and marine sites) at four seasons, using inverse (LIM-MCMC) and ecological network (ENA) analyses, we identified a new type of food web, called the “bacterial multivorous food web”. This food web adds to the conventional trophic continuum as previously reported. The “bacterial multivorous food web” present in winter showed the lowest primary production among seasons, but highest bacterial production. Several food web ratios characterized this new typology e.g. picophytoplankton net primary production to total primary production varied from 0.20 to 0.28; bacterial to primary production ratio is higher than values reported in global scale (≅1); bacterial net production to the potential protozoan prey net production was high (>0.2). In this special food web, carbon was mostly recycled, with a moderate fraction channeled to deep waters, which lead to a higher retention of carbon inside the ecosystem. This winter PFW also seemed to be the most organized, specialized, stable and mature, as related to common interpretations of ENA. The spring was characterized by herbivorous food web, with highest activity coinciding with low stability. Although less usual, the herbivorous pathway was also observed during summer, in inshore waters. The autumn food webs, which functioned as multivorous or microbial food webs, appeared to be stable and mature. Finally, our study demonstrates the usefulness of food web models derived ratios combined with ecological network analysis indices to conduct evaluation of the structure and functioning of ecosystems and potentially to support management decisions in marine environment.

On the use of high aspect ratio finite elements to model hydraulic fracturing in deformable porous media

Hydraulic fracturing is a technique based on the injection of a viscous fluid at high pressure into an engineered well with the intention of initiating and propagating multiple fractures in a rock formation containing hydrocarbons to increase well-reservoir connectivity. This work proposes a framework to simulate the initiation and propagation of hydraulically induced fracture based on the Continuum Strong Discontinuity Approach (CSDA) and solid finite elements with high aspect ratio (HAR) in the context of conventional continuum constitutive (stress–strain) relationships (based on damage theory). The porous media considered here are deformable and the hydro-mechanical problem is solved in a fully-coupled manner. Full details about the proposed continuous approach to model hydraulic fractures are presented, including the finite element equations and their approximations. The new approach is validated against analytical and numerical solutions. Moreover, the influence of the dimensions of the HAR interface elements on the results is also investigated.

A mesh objective continuum damage model for quasi-brittle crack modelling and finite element implementation

In the framework of continuum damage mechanics, a computational model for quasi-brittle crack modelling is proposed. The proposed model has significant mesh-objectivity and accuracy advantages over existing methods for modeling quasi-brittle crack. These stem from the combination of the local crack tracking algorithm, the new calculation of crack bandwidth and the non-local treatment regarding strain field. Resorting to the implementation of local crack tracking algorithm, it is desirable that the spurious dependence of conventional continuum damage mechanics-based model on mesh bias can be effectively addressed. The new estimation of the real-time crack bandwidth can be not only depending on the element size and pattern, but also on the physical crack path within each consolidate cracked element. Thus, the energy dissipation during crack propagation can be characterized in a more accurate, physically based manner. The non-local averaging regarding the strain field in the course of failure evolution is carried out within an elliptical domain, the configuration of which is related to finite element and crack trajectory obtained by the local crack track algorithm. With this combined technique, it is expected that a more accurate crack evolution course can be achieved numerically, which allows engineers to adopt relatively coarse unstructured discretizations without sacrificing solution accuracy. By numerical examples, the proposed model, empowered by the combined techniques, demonstrates significant improvements in the prediction of crack propagating of quasi-brittle materials. This model may provide engineers a more reliable tool in practical application of computational material failure.