Motion and deposition of solid particles in fibrous filter with circular, diamond, and square fibers are numerically investigated. A coupled Lattice Boltzmann (LB) and discrete element (DE) method is presented and applied to simulate the filtration process in particulate flow, taking into account the mutual interaction between fluid and particle. The influence of pertinent parameters such as the Reynolds number, the particle-to-fiber diameter ratio, and the particle-to-fluid density ratio on filtration performance (pressure drop and capture efficiency) is analyzed for fibrous filter with different fiber cross-sectional shapes. The simulation results indicate that both the pressure drop and the capture efficiency of filter are considerably affected by the fiber’s shape. Dimensionless drag force increases with the Reynolds number when Re > 1. The filter with diamond fiber has a lower pressure drop than that of the circular and square cases. Meanwhile, the deposition of particles on the surface of square fiber is more favorable. From the filter quality factor standpoint, filter with diamond fiber exhibits a better filtration performance.

Hydraulic fracturing is an industrial process often applied to enhance oil and gas recovery. Under this process, fractures are generated by the injection of highly pressurized fluids, which often exhibit shear-thinning rheology and yield stress. The global fracture propagation is influenced by various processes occurring near the fracture tip. To gain an insight into fracture propagation, the problem of a semi-infinite hydraulic fracture propagating in a permeable linear elastic rock is solved. To investigate the effect of fluid yield stress, we focus on a fracture driven by Herschel–Bulkley fluid. The mathematical model consists of the elasticity equation, the lubrication equation, and the propagation criterion for the semi-infinite plane strain fracture to obtain the fracture opening. The non-linear system of governing equations is represented in the non-singular form and solved numerically using Newton’s method. The solution is influenced by the competing processes related to rock toughness, fluid properties, and leak-off. The effects of these phenomena prevail at different length scales, and the corresponding limits can be described via analytical solutions. For a Herschel-Bulkley fluid, an additional limiting solution related to the fluid yield stress is obtained, and the regions of the dominance of limiting solutions affected by the yield stress are investigated. Finally, a faster approximate solution for the problem is proposed and its accuracy against a numerical solution is evaluated. The obtained result can be applied in hydraulic fracturing simulators to account for the effect of Herschel–Bulkley fluid rheology on the near-tip region.

Shaft vibration caused by rotor dynamic (RD) fluid force generated by the seal clearance flow has caused several problems. Because such vibration is a coupled phenomenon of clearance flow and shaft vibration, a coupling analysis is essential to solve these problems. In this study, a two-way coupling fluid–structure interaction (FSI) analysis of the seal clearance flow and shaft vibration of a rotor system was conducted and verified through experiments. The rotor system used was a vertical, flexible rotor system with a plain annular seal. In the numerical analysis of the seal clearance flow, the continuity equation and momentum equations, which were averaged across the film thickness, were numerically solved. To suppress the numerical instability, which is unique to the coupling analysis, and improve its numerical stability, a method of successively correcting pressure and shaft acceleration values was adopted so that the continuity equation and rotor equations of motion could be satisfied at every time step. By performing the coupling simulation, the frequency response characteristics of whirling amplitude and leakage flow were investigated. In regard to the stability of the system, the rotational speeds at which self-excited vibration occurs (onset speed of instability: OSI) in its increasing condition and ceases (onset speed of dropdown: OSD) in its decreasing condition were investigated. The coupling analysis results reasonably agree with the experimental results, which demonstrate the validity of the analysis method. In addition, the influence of static eccentricity and whirling amplitude on stability (OSI and OSD) was clarified, which are useful in the design stage of turbomachinery.

A method to passively align bonded components without direct mechanical contact has been developed. This method uses the pressure field generated by the squeeze flow between the parts during the bonding process to increase the parallelism of planar components. A computational fluid dynamic (CFD) model has been developed to study the squeeze flow phenomenon and to determine generated efforts. Based on these calculations, an assembly stage standing on a flexure pinned linkage has been developed. This assembly stage had two purposes. The first was to show the possibility of passive mechanical alignment using a squeeze flow. The second was to measure efforts to confirm the CFD model. These measurements have led to a refined CFD model taking into account the non-Newtonian behavior of the fluid at high shear rates. This technique was initially developed for the assembly of a fiber-optic-to-silicon-chip-interface. Other potential applications could be wafer bonding, bonding of multiple wafer stacks, or 3D integrated circuits.

The size and distribution of particles suspended within a fluid influence the rheology of the suspension, as well as strength and other mechanical properties if the fluid eventually solidifies. An important motivating example of current interest is foamed cements used for carbon storage and oil and gas wellbore completion. In these applications, it is desired that the suspended particles maintain dispersion during flow and do not coalesce or cluster. This paper compares the role of mono- against polydispersity in the particle clustering process. The propensity of hard spherical particles in a suspension to transition from a random configuration to an ordered configuration, or to form localized structures of particles, due to flow is investigated by comparing simulations of monodisperse and polydisperse suspensions using Stokesian dynamics. The calculations examine the role of the polydispersity on particles rearrangements and structuring of particles due to flow and the effects of the particle size distribution on the suspension viscosity. A key finding of this work is that a small level of polydispersity in the particle sizes helps to reduce localized structuring of the particles in the suspension. A suspension of monodisperse hard spheres forms structures at a particle volume fraction of approximately 47 % under shear, but a 47 % volume fraction of polydisperse particles in suspension does not form these structures.

The existing regular hexagonal cellular substrate for stretchable electronics minimizes the disruptions to the natural diffusive or convective flow of bio-fluids. Its anisotropy is insignificant, which is not ideal for mounting on skins that involve directional stretching. This paper proposes an irregular hexagonal cellular substrate with large anisotropy to minimize the constraints on the natural motion of the skin, and establishes an analytic model to study its stress–strain relation under finite stretching.

This paper details a numerical study of the dynamic stability of a cylindrical shell structure under combined hydrostatic and dynamic pressure loading within a tubular environment as compared to the traditional loading of hydrostatic pressure alone. Simulations are executed using a coupled Eulerian–Lagrangian scheme, within the dynamic system mechanics advanced simulation (DYSMAS) code, to explicitly model the (1) structural response of a single unstiffened cylindrical shell to dynamic pressure loading and (2) the fluid flow field within the surrounding environment due to the shock and the shell structural response. Simulations involve a non-pressure-compensated aluminum 6061-T6 cylindrical structure with a length-to-diameter ratio, L/D, equal to 9.6. This structure is 31.8 mm (1.25-in) in outer diameter and is concentrically and longitudinally centered within the outer tube, which has an inner diameter of 177.8 mm (7.00-in) and total internal length of 2.13 m (84-in). Simulations are run at four hydrostatic tank pressures, which are categorized by percentage of measured critical collapse pressure, P c , of the shell structure: 66% P c , 80% P c , 85% P c , and 90%P c . For each case, the shell structure is subjected to shock loading created by the detonation of a commercial blasting cap at a given standoff to the structure within the confining tube. Simulated pressure histories are compared to experimental pressure data at gage locations. The simulations and corresponding experiments produce the same overall result for three of four cases (i.e., survive: 66%P c or implode: 85%P c and 90%P c ). For the 80%P c case, the overall result differs between simulation and experiment in that the specimen in the experiment survives but the simulated cylinder implodes. However, the discrepancy between the overall experimental result and corresponding simulation is not deemed a failure for the 80%P c case; instead, this signifies a transitional case for the dynamic stability of the shell structure (i.e., collapse is sensitive to small deviations from assumed conditions in this regime).

A new type of all-solid metamaterial model with anisotropic density and fluid-like elasticity is proposed for controlling acoustic propagation in an underwater environment. The model consists of a regular hexagonal lattice as the host that defines the overall isotropic stiffness, in which all lattice beams have been sharpened at both ends to significantly diminish the shear resistance. The inclusion structure, which involves epoxy, rubber, and lead material constituents, is designed to attain a large density–anisotropy ratio in the broad frequency range. The wave-control capability of metamaterials is evaluated in terms of underwater acoustic stretching, shifting, and ground cloaking, which are generated by the transformation acoustic method. The decoupling design method was developed for the metamaterial microstructure using band-structure, effective-medium, and modal-field analyses. The acoustic performance of these metamaterial devices was finally verified with full-wave numerical simulations. Our study provides new insight into broadband underwater acoustic manipulation by all-solid anisotropic-density metamaterials.

The linear theory of dual-porosity and dual-permeability poro-chemo-electro-elasticity is presented. The theory outlines the dual-continuum formulation of multiple coupled processes involving solid deformation, pore fluid flow, and electrically charged species transport, within and in between two coexisting porosity systems of a fluid-saturated, poro-elastic medium. The described formulation is used to derive the analytical solutions to the inclined wellbore problem and axisymmetric Mandel-Type problem of dual-porosity, dual-permeability poro-chemo-electro-elasticity. The effects of chemical and electrical potentials on the distributions of stress and pore pressure are demonstrated by numerical examples pertaining to the considered problems. It is shown that the fully coupled nature of the solutions rigorously captures the seemingly anomalous time variations of the effective stress as driven by the pore fluid pressure disturbances, as well as the distribution and movement of anions/cations within the dual-porosity porous medium. The existing subset of published solutions on the subject is successfully reproduced as special cases of the solutions presented in this paper.

Stepwise crack propagation is evidently observed in experiments both in geomaterials and in hydrogels. Pizzocolo et al. (2012, “Mode I Crack Propagation in Hydrogels is Step Wise,” Eng. Fract. Mech., 97 (1), pp. 72–79) show experimental evidence that mode I crack propagation in hydrogel is stepwise. The pattern of the intermittent crack growth is influenced by many factors, such as porosity of the material, the permeability of the fluid, the stiffness of the material, etc. The pause duration time is negatively correlated with the stiffness of the material, while the average propagation length per step is positively correlated. In this paper, we integrate extended finite element method (XFEM) and enhanced local pressure (ELP) method, and incorporate cohesive relation to reproduce the experiments of Pizzocolo et al. in the finite deformation regime. We investigate the stepwise phenomenon in air and in water, respectively, under mode I fracture. Our simulations show that despite the homogeneous material properties, the crack growth under mode I fracture is stepwise, and this pattern is influenced by the hydraulic permeability and the porosity of the material. Simulated pause duration is negatively correlated with stiffness, and the average propagating length is positively correlated with stiffness. In order to eliminate the numerical artifacts, we also take different time increments into consideration. The staccato propagation does not disappear with smaller time increments, and the pattern is approximately insensitive to the time increment. However, we do not observe stepwise crack growth scheme when we simulate fracture in homogeneous rocks.

Microseismic imaging of the hydraulic fracturing operation in the naturally fractured rocks confirms the existence of a stimulated volume (SV) of enhanced permeability. The simulation and characterization of the SV evolution is uniquely challenging given the uncertainty in the nature of the rock mass fabrics as well as the complex fracturing behavior of shear and tensile nature, irreversible plastic deformation and damage. In this paper, the simulation of the SV evolution is achieved using a nonlocal poromechanical plasticity model. Effects of the natural fracture network are incorporated via a nonlocal plasticity characteristic length, ℓ . A nonlocal Drucker–Prager failure model is implemented in the framework of Biot's theory using a new implicit C 0 finite element method. First, the behavior of the SV for a two-dimensional (2D) geomechanical injection problem is simulated and the resulting SV is assessed. It is shown that breakdown pressure and stable fracturing pressure are the natural outcomes of the model and both depend upon ℓ . Next, the post-shut-in behavior of the SV is analyzed using the pressure and pressure derivative plots. A bilinear flow regime is observed and it is used to estimate the flow capacity of the SV. The results show that the flow capacity of the SV increases as ℓ decreases (i.e., as the SV behaves more like a single hydraulic fracture); however, for 0.1 m ≤ ℓ ≤ 1 m , the calculated flow capacity indicates that the conductivity of the SV is finite. Finally, it is observed that as ℓ tends to zero, the flow capacity of the SV tends to infinity and the SV behaves like a single infinitely conducting fracture.

Harnessing reversible snap-through of a dielectric elastomer (DE), which is a mechanism for large deformation provided by an electromechanical instability, for large-volume pumping has proven to be feasible. However, the output volume of snap-through pumping is drastically reduced by adverse pressure gradient, and large-volume pumping under high adverse pressure gradient by a DE pump has not been realized. In this paper, we propose a new mechanism of DE fluid pumping that can address this shortcoming by connecting DE pumps of different membrane stiffnesses serially in a pumping circuit and by harnessing synergistic interactions between neighboring pump units. We build a simple serial DE pump to verify the concept, which consists of two DE membranes. By adjusting the membrane stiffness appropriately, a synergistic effect is observed, where the snap-through of membrane 1 triggers the snap-through of membrane 2, ensuring that a large volume (over 70 ml/cycle) can be achieved over a wide range of large adverse pressure gradients. In comparison, the conventional single DE pump's pumping volume rapidly decreased beyond a low adverse pressure gradient of 0.196 kPa. At the pressure difference of 0.98 kPa, the serial DE pump's pumping volume is 4185.1% larger than that of the conventional DE pump. This pumping mechanism is customizable for various pressure ranges and enables a new approach to design DE-based soft pumping devices such as a DE total artificial heart, which requires large-volume pumping over a wide range of pressure difference.

Based on the KGD scheme, this paper investigates, with both analytical and numerical approaches, the propagation of a hydraulic fracture with a fluid lag in permeable rock. On the analytical aspect, the general form of normalized governing equations is first formulated to take into account both fluid lag and leak-off during the process of hydraulic fracturing. Then a new self-similar solution corresponding to the limiting case of zero dimensionless confining stress ( T = 0 ) and infinite dimensionless leak-off coefficient ( L = ∞ ) is obtained. A dimensionless parameter R is proposed to indicate the propagation regimes of hydraulic fracture in more general cases, where R is defined as the ratio of the two time-scales related to the dimensionless confining stress T and the dimensionless leak-off coefficient L . In addition, a robust finite element-based KGD model has been developed to simulate the transient process from L = 0 to L = ∞ under T = 0 , and the numerical solutions converge and agree well with the self-similar solution at T = 0 and L = ∞ . More general processes from T = 0 and L = 0 to T = ∞ and L = ∞ for three different values of R are also simulated, which proves the effectiveness of the proposed dimensionless parameter R for indicating fracture regimes.

Geomaterials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores with different hydromechanical properties. Moreover, these pore-networks are connected through fissures and conduits. Although some models are available in the literature to describe flows in such media, they lack a strong theoretical basis. This paper aims to fill this gap in knowledge by providing the theoretical foundation for the flow of incompressible single-phase fluids in rigid porous media that exhibit double porosity/permeability. We first obtain a mathematical model by combining the theory of interacting continua and the maximization of rate of dissipation (MRD) hypothesis, and thereby provide a firm thermodynamic underpinning. The governing equations of the model are a system of elliptic partial differential equations (PDEs) under a steady-state response and a system of parabolic PDEs under a transient response. We then present, along with mathematical proofs, several important mathematical properties that the solutions to the model satisfy. We also present several canonical problems with analytical solutions which are used to gain insights into the velocity and pressure profiles, and the mass transfer across the two pore-networks. In particular, we highlight how the solutions under the double porosity/permeability differ from the corresponding ones under Darcy equations.

This work presents a theoretical method for surface love waves in poroelastic media loaded with a viscous fluid. A complex analytic form of the dispersion equation of surface love waves has been developed using an original resolution based on pressure–displacement formulation. The obtained complex dispersion equation was separated in real and imaginary parts. mathematica software was used to solve the resulting nonlinear system of equations. The effects of surface layer porosity and fluid viscosity on the phase velocity and the wave attenuation dispersion curves are inspected. The numerical solutions show that the wave attenuation and phase velocity variation strongly depend on the fluid viscosity, surface layer porosity, and wave frequency. To validate the original theoretical resolution, the results in literature in the case of an homogeneous isotropic surface layer are used. The results of various investigations on love wave propagation can serve as benchmark solutions in design of fluid viscosity sensors, in nondestructive testing (NDT) and geophysics.

This paper investigates the tip region of a hydraulic fracture propagating near a free-surface via the related problem of the steady fluid-driven peeling of a thin elastic layer from a rigid substrate. The solution of this problem requires accounting for the existence of a fluid lag, as the pressure singularity that would otherwise exist at the crack tip is incompatible with the underlying linear beam theory governing the deflection of the thin layer. These considerations lead to the formulation of a nonlinear traveling wave problem with a free boundary, which is solved numerically. The scaled solution depends only on one number K , which has the meaning of a dimensionless toughness. The asymptotic viscosity- and toughness-dominated regimes, respectively, corresponding to small and large K , represent the end members of a family of solutions. It is shown that the far-field curvature can be interpreted as an apparent toughness, which is a universal function of K . In the viscosity regime, the apparent toughness does not depend on K , while in the toughness regime, it is equal to K . By noting that the apparent toughness represents an intermediate asymptote for the layer curvature under certain conditions, the obtention of time-dependent solutions for propagating near-surface hydraulic fractures can be greatly simplified. Indeed, any such solutions can be constructed by a matched asymptotics approach, with the outer solution corresponding to a uniformly pressurized fracture and the inner solution to the tip solution derived in this paper.

The models of normal and tangential oil film damping are established by modeling the viscous-elastic fluid as massless damping elements. The central pressure and film thickness distributions, friction coefficient, and maximum temperature rise with or without considering thermal effect indicate the proposed damping models and the solutions to the damping are valid. Thereafter, the thermal effect on oil film damping is discussed and the effects of contact force, rotation speed, and tooth number of spur gears in line contact non-Newtonian transient thermal elastohydrodynamic lubrication (EHL) on the oil film damping are investigated. The results imply that the larger damping in the normal direction is beneficial to meshing impact resistance and vibration reduction, whereas the smaller damping in the tangential direction is very helpful for fluidity enhancement and friction heat inhibition.

Penny-shaped fluid-driven cracks are often detected in many fluid–solid interaction problems. We study the combined effect of pressure and shear stress on the crack propagation in an impermeable elastic full space. Boundary integral equations are presented, by using the integral transform method, for a penny-shaped crack under normal and shear stresses. The crack propagation criterion of stress intensity factor is examined with the strain energy release rate. Dominant regimes are obtained by using a scaling analysis. Asymptotic solution of the toughness-dominant regime is derived to show the effect of shear stress on the crack opening, crack length, and pressure distribution. The results indicate that a singular shear stress can dominate the asymptotic property of the stress field near the crack tip, and the stress intensity factor cannot be calculated even though the energy release rate is finite. Shear stress leads to a smaller crack opening, a longer crack, and a slightly larger wellbore pressure. A novel dominant-regime transition between shear stress and pressure is found. Unstable crack propagation occurs in the shear stress-dominant regime. This study may help in understanding crack problems under symmetrical loads and modeling fluid–solid interactions at the crack surfaces.

Swelling and crack propagation in ionized hydrogels plays an important role in industry application of personal care and biotechnology. Unlike nonionized hydrogel, ionized hydrogel swells up to strain of many 1000's %. In this paper, we present a swelling driven fracture model for ionized hydrogel in large deformation. Flow of fluid within the crack, within the medium, and between the crack and the medium are accounted for. The partition of unity method is used to describe the discontinuous displacement field and chemical potential field, respectively. In order to capture the chemical potential gradient between the gel and the crack, an enhanced local pressure (ELP) model is adopted. The capacity of this numerical model to study the fracture and swelling behaviors of ionized gels with low Young's modulus (< 1 MPa) and low permeability (< 10 −16 m 4 /Ns) is demonstrated. Two numerical examples show the performance of the implemented model (1) swelling with crack opening and (2) swelling with crack propagation. Simulations demonstrate that shrinking of a gel results in decreasing macroscopic stress and simultaneously increasing stress at crack tips. Different scales yield opposite responses, underscoring the need for multiscale modelling. While cracking as a result of external loading can be prevented by reducing the overall stress level in the structure, reducing overall stress levels will not result in reducing the crack initiation and propagation due to swelling.

A solution to the problem of a hydraulic fracture driven by an incompressible Newtonian fluid at a constant injection rate in a permeable rock is presented in this paper. A set of governing equations are formed to obtain the fracture half-length, crack opening, and net fluid pressure. The solution is derived under the assumptions of plane strain, zero lag between fluid front and crack tip, followed by negligible fluid viscosity. The last assumption is related to a toughness-dominated fracture propagation regime therefore leading to a uniform fluid pressure along the crack surface. Early-time and late-time asymptotic solutions are obtained, which correspond to both regimes when the fluid contains within the crack and most of the injected fluid infiltrates into the rock, respectively. It is shown that these asymptotic solutions are in a simple form when the fracture propagation is dominated by the material toughness. The transient solution for the evolution from the early time to the late time is also obtained by a numerical method.