Modeling of surface tension and contact angles with smoothed particle hydrodynamics

Smoothed particle hydrodynamics for free-surface and multiphase flows: a review

The smoothed particle hydrodynamics (SPH) method is expanding and is being applied to more and more fields, particularly in engineering. The majority of current SPH developments deal with free-surface and multiphase flows, especially for situations where geometrically complex interface configurations are involved. The present review article covers the last 25 years of development of the method to simulate such flows, discussing the related specific features of the method. A path is drawn to link the milestone articles on the topic, and the main related theoretical and numerical issues are investigated. In particular, several SPH schemes have been derived over the years, based on different assumptions. The main ones are presented and discussed in this review underlining the different contexts and the ways in which they were derived, resulting in similarities and differences. In addition, a summary is provided of the recent corrections proposed to increase the accuracy, stability and robustness of SPH schemes in the context of free-surface and multiphase flows. Future perspectives of development are identified, placing the method within the panorama of Computational Fluid Dynamics.

Computational mesoscale framework for biological clustering and fractal aggregation

Hierarchical clustering due to diffusion and reaction is a widespread occurrence in natural phenomena, displaying fractal behavior with non-integer size scaling. The study of this phenomenon has garnered interest in both biological systems such as morphogenesis and blood clotting, and synthetic systems such as colloids and polymers. The modeling of biological clustering can be difficult, as it can occur on a variety of scales and involve multiple mechanisms, necessitating the use of various methods to capture its behavior. Here, we propose a novel framework, the generalized-mesoscale-clustering (GMC), for the study of complex hierarchical clustering phenomena in biological systems. The GMC framework incorporates the effects of hydrodynamic interactions, bonding, and surface tension, and allows for the analysis of both static and dynamic states of cluster development. The framework is applied to a range of biological clustering mechanisms, with a focus on blood-related clustering from fibrin network formation to platelet aggregation. Our study highlights the importance of a comprehensive characterization of the structural properties of the cluster, including fractal dimension, pore-scale diffusion, initiation time, and consolidation time, in fully understanding the behavior of biological clustering systems. The GMC framework also provides the potential to investigate the temporal evolution and mechanical properties of the clusters by tracking bond density and including hydrodynamic interactions.

Consistent Thermo-Capillarity and Thermal Boundary Conditions for Single-Phase Smoothed Particle Hydrodynamics

A model for capillary phenomena including temperature-dependency and thermal boundary conditions is presented in the numerical framework of smoothed particle hydrodynamics (SPH). The model requires only a single fluid phase and is therefore computationally more efficient than surface tension schemes which need an explicit fluid-fluid or fluid-gas interface. The model makes use of a surface identification mechanism based on the SPH renormalization tensor. All relevant properties of the continuum surface force (CSF) based approach, i.e., the delta function, normal vector and curvature, are calculated in a consistent manner. The model is parametrized by physical material properties and is successfully validated by means of a large set of analytical test cases. The applicability of the proposed model to more complex scenarios is demonstrated.

Particle-Based Dynamic Water Drops with High Surface Tension in Real Time

Surface tension has a great influence on the shape of the fluid interface, and is an important physical characteristic in expressing not only liquids but also liquid metals such as mercury and gallium. In the field of physics-based particle fluid simulations, it is a challenging problem to express the high surface tension generated by fluid-air or fluid-solid interaction in real time. The main reasons for this are (1) The magnitude of the force that can be stably expressed in real-time fluid simulation is limited, so when the magnitude of the surface tension increases at a large time-step, the simulation stability decreases, and (2) If we use a small time-step, a stronger force can be expressed. However, it becomes difficult to operate in real time because the computational cost increases. Techniques were proposed to solve this problem for a few specific scenes, but there has not yet been a general approach that can reliably express high surface tension in various scenarios. In this paper, we propose a real-time particle-based fluid simulation framework that can efficiently and stably express high surface tension. Unlike the previous methods, we newly model the surface tension so that the strong surface tension force generated in the droplet area with a large curvature is applied evenly in the normal and tangent directions regardless of the size of the droplet. We also propose new pressure constraints that converge quickly and accurately using this force. Our method can be effectively used in various physics-based simulation scenarios because it can easily express and control surface tension effects that appear in materials such as liquid metal as well as water.

Computationally Efficient Multiscale Neural Networks Applied to Fluid Flow in Complex 3D Porous Media

The permeability of complex porous materials is of interest to many engineering disciplines. This quantity can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as the simulation domains become less porous or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e., porosity and tortuosity) have been proposed, but these features only partly summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains’ solid boundaries. However, prior approaches building on the convolutional neural network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a representative elementary volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be modeled properly. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large ($$>512^3$$ > 512 3 ) images in approximately one second on a single graphics processing unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer. We validate our method with a laminar fluid flow case using vuggy samples and fractures. As a result of viewing the entire domain at once, our model is able to perform accurate prediction on domains exhibiting a large degree of heterogeneity. We expect the methodology to be applicable to many other transport problems where complex geometries play a central role.

Accelerating Surface Tension Calculation in SPH via Particle Classification and Monte Carlo Integration

Surface tension has a strong influence on the shape of fluid interfaces. We propose a method to calculate the corresponding forces efficiently. In contrast to several previous approaches, we discriminate to this end between surface and non-surface SPH particles. Our method effectively smooths the fluid interface, minimizing its curvature. We make use of an approach inspired by Monte Carlo integration to estimate local normals as well as curvatures, based on which the force can be calculated. We compare different sampling schemes for the Monte Carlo approach, for which a Halton sequence performed best. Our overall technique is applicable, but not limited to 2D and 3D simulations, and can be coupled with any common SPH formulation. It outperforms prior approaches with regard to total computation time per time step in dynamic scenes. Additionally, it is adjustable for higher quality in small scale scenes with dominant surface tension effects.

Smoothed Particle Hydrodynamics multiphase modelling of an experimental microfluidic device for conformal coating of pancreatic islets

The paper discusses a Smoothed Particle Hydrodynamics (SPH) model for the analysis of the multiphase flow occurring in an experimental microfluidic device for conformal coating of pancreatic islets with a biocompatible and permeable polymer. The proposed numerical model, based on a weakly-compressible SPH approach, accurately mimics the encapsulation process while assuring phase conservation, thus overcoming potential limitations of grid-based models. The proposed SPH model is a triphasic multi-phase model that allows one: (i) to reproduce the physics of islet conformal coating, including the effects of surface tension at the interface of the involved fluids and of the islet diameter; and (ii) to evaluate how modulation of process parameters influences the fluid dynamics within the microfluidic device and the resulting coating characteristics. This model can represent a valuable, time- and cost-effective tool for the definition of optimized encapsulation conditions through in silico screening of novel combinations of conformal coating parameters, including polymeric coating blends, size range of insulin-secreting cell clusters, utilized chemical reagents, device geometry and scale.

Modelling of immiscible liquid-liquid systems by Smoothed Particle Hydrodynamics

Immiscible fluid systems are ubiquitous in industry, medicine and nature. Understanding the phase morphologies and intraphase fluid motion is often desirable in many of these situations; for example, this will aid improved design of microfluidic platforms for the production of medicinal formulations. In this paper, we detail a Smoothed Particle Hydrodynamics (SPH) approach that facilitates this understanding. The approach includes surface tension and enforces incompressibility. The approach also allows the consideration of an arbitrary number of immiscible phases of differing viscosities and densities. The nature of the phase morphologies can be arbitrary and change in time, including break-up (which is illustrated) and coalescence. The use of different fluid constitutive models, including non-Newtonian models, is also possible. The validity of the model is demonstrated by applying it to a range of model problems with known solutions, including the Young-Laplace problem, confined droplet deformation under a linear shear field, and a droplet falling under gravity through another quiescent liquid. Results are also presented to illustrate how the SPH model can be used to elucidate the behaviour of immiscible liquid systems.

Pairwise Force SPH Model for Real-Time Multi-Interaction Applications

In this paper, we present a novel pairwise-force smoothed particle hydrodynamics (PF-SPH) model to enable simulation of various interactions at interfaces in real time. Realistic capture of interactions at interfaces is a challenging problem for SPH-based simulations, especially for scenarios involving multiple interactions at different interfaces. Our PF-SPH model can readily handle multiple types of interactions simultaneously in a single simulation; its basis is to use a larger support radius than that used in standard SPH. We adopt a novel anisotropic filtering term to further improve the performance of interaction forces. The proposed model is stable; furthermore, it avoids the particle clustering problem which commonly occurs at the free surface. We show how our model can be used to capture various interactions. We also consider the close connection between droplets and bubbles, and show how to animate bubbles rising in liquid as well as bubbles in air. Our method is versatile, physically plausible and easy-to-implement. Examples are provided to demonstrate the capabilities and effectiveness of our approach.

Smoothed particle hydrodynamics study of the roughness effect on contact angle and droplet flow

We employ a pairwise force smoothed particle hydrodynamics (PF-SPH) model to simulate sessile and transient droplets on rough hydrophobic and hydrophilic surfaces. PF-SPH allows modeling of free-surface flows without discretizing the air phase, which is achieved by imposing the surface tension and dynamic contact angles with pairwise interaction forces. We use the PF-SPH model to study the effect of surface roughness and microscopic contact angle on the effective contact angle and droplet dynamics. In the first part of this work, we investigate static contact angles of sessile droplets on different types of rough surfaces. We find that the effective static contact angles of Cassie and Wenzel droplets on a rough surface are greater than the corresponding microscale static contact angles. As a result, microscale hydrophobic rough surfaces also show effective hydrophobic behavior. On the other hand, microscale hydrophilic surfaces may be macroscopically hydrophilic or hydrophobic, depending on the type of roughness. We study the dependence of the transition between Cassie and Wenzel states on roughness and droplet size, which can be linked to the critical pressure for the given fluid-substrate combination. We observe good agreement between simulations and theoretical predictions. Finally, we study the impact of the roughness orientation (i.e., an anisotropic roughness) and surface inclination on droplet flow velocities. Simulations show that droplet flow velocities are lower if the surface roughness is oriented perpendicular to the flow direction. If the predominant elements of surface roughness are in alignment with the flow direction, the flow velocities increase compared to smooth surfaces, which can be attributed to the decrease in fluid-solid contact area similar to the lotus effect. We demonstrate that classical linear scaling relationships between Bond and capillary numbers for droplet flow on flat surfaces also hold for flow on rough surfaces.

Smoothed dissipative particle dynamics model for mesoscopic multiphase flows in the presence of thermal fluctuations

Thermal fluctuations cause perturbations of fluid-fluid interfaces and highly nonlinear hydrodynamics in multiphase flows. In this work, we develop a multiphase smoothed dissipative particle dynamics (SDPD) model. This model accounts for both bulk hydrodynamics and interfacial fluctuations. Interfacial surface tension is modeled by imposing a pairwise force between SDPD particles. We show that the relationship between the model parameters and surface tension, previously derived under the assumption of zero thermal fluctuation, is accurate for fluid systems at low temperature but overestimates the surface tension for intermediate and large thermal fluctuations. To analyze the effect of thermal fluctuations on surface tension, we construct a coarse-grained Euler lattice model based on the mean field theory and derive a semianalytical formula to directly relate the surface tension to model parameters for a wide range of temperatures and model resolutions. We demonstrate that the present method correctly models dynamic processes, such as bubble coalescence and capillary spectra across the interface.

Effects of temperature on spinodal decomposition and domain growth of liquid-vapor systems with smoothed particle hydrodynamics

We present a numerical method for simulations of spinodal decomposition of liquid-vapor systems. The results are in excellent agreement with theoretical predictions for all expected time regimes from the initial growth of "homophase fluctuations" up to the inertial hydrodynamics regime. The numerical approach follows a modern formulation of the smoothed particle hydrodynamics method with a van der Waals equation of state and thermal conduction. The dynamics and thermal evolution of instantaneously temperature-quenched systems are investigated. Therefore, we introduce a simple scaling thermostat that allows thermal fluctuations at a constant predicted mean temperature. We find that the initial stage spinodal decomposition is strongly affected by the temperature field. The separated phases react on density changes with a change in temperature. Although, the thermal conduction acts very slowly, thermal deviations are eventually compensated. The domain growth in the late stage of demixing is found to be rather unaffected by thermal fluctuations. We observe a transition from the Lifshitz-Slyozov growth rate with 1/3 exponent to the inertial hydrodynamics regime with a rate of 2/3, only excepted from simulations near the critical point where the liquid droplets are observed to nucleate directly in a spherical shape. The transition between the growth regimes is found to occur earlier for higher initial temperatures. We explain this time dependency with the phase interfaces that become more diffuse and overlap with approaching the critical point. A prolonging behavior of the demixing process is observed and also expected to depend on temperature. It is further found that the observations can excellently explain the growth behavior for pure nonisothermal simulations that are performed without thermostat.

Smoothed particle hydrodynamics and element bending group modeling of flexible fibers interacting with viscous fluids

This paper presents a smoothed particle hydrodynamics (SPH) and element bending group (EBG) coupling method for modeling the interaction of flexible fibers with moving viscous fluids. SPH is a well-developed mesh-free particle method for simulating viscous fluid flows. EBG is also a particle method for modeling flexible bodies. The interaction of flexible fibers with moving viscous fluids is rendered through the interaction of EBG particles for flexible fiber and SPH particles for fluid. In numerical simulation, flexible fibers of different lengths are immersed in a moving viscous fluid driven by a body force. The drag force on the fiber obtained from SPH-EBG simulation agrees well with experimental observations. It is shown that the flexible fiber demonstrates three typical bending modes, including the U-shaped mode, the flapping mode, and the closed mode, and that the flexible fiber experiences a drag reduction due to its reconfiguration by bending. It is also found that the U4/3 drag scaling law for a flexible fiber is only valid for the U-shaped mode, but not valid for the flapping and closed modes. The results indicate that the reconfiguration of a flexible fiber is caused by the fluid force acting on it, while vortex shedding is of importance in the translations of bending modes.

Computational Coupled Method for Multiscale and Phase Analysis

On micro scale the constitutions of porous media are effected by other constitutions, so their behaviors are very complex and it is hard to derive theoretical formulations as well as to simulate on macro scale. For decades, in order to escape this complication, the phenomenological approaches in a field of multiscale methods have been extensively researched by many material scientists and engineers. Their theoretical approaches are based on the hierarchical multiscale methods using a priori knowledge on a smaller scale; however it has a drawback that an information loss can be occurred. Recently, according to a development of the core technologies of computer, the ways of multiscale are extended to a direct multiscale approach called the concurrent multiscale method. This approach is not necessary to deal with complex mathematical formulations, but it is noted as an important factor: development of computational coupling algorithms between constitutions in a porous medium. In this work, we attempt to develop coupling algorithms in different numerical methods finite element method (FEM), smoothed particle hydrodynamics (SPH) and discrete element method (DEM). Using this coupling algorithm, fluid flow, movement of solid particle, and contact forces between solid domains are computed via proposed discrete element which is based on SPH, FEM, and DEM. In addition, a mixed FEM on continuum level and discrete element model with SPH particles on discontinuum level is introduced, and proposed coupling algorithm is verified through numerical simulation.

Heterogeneities of flow in stochastically generated porous media

Heterogeneous flows are observed to result from variations in the geometry and topology of pore structures within stochastically generated three dimensional porous media. A stochastic procedure generates media comprising complex networks of connected pores. Inside each pore space, the Navier-Stokes equations are numerically integrated until steady state velocity and pressure fields are attained. The intricate pore structures exert spatially variable resistance on the fluid, and resulting velocity fields have a wide range of magnitudes and directions. Spatially nonuniform fluid fluxes are observed, resulting in principal pathways of flow through the media. In some realizations, up to 25% of the flux occurs in 5% of the pore space depending on porosity. The degree of heterogeneity in the flow is quantified over a range of porosities by tracking particle trajectories and calculating their attributes including tortuosity, length, and first passage time. A representative elementary volume is first computed so the dependence of particle based attributes on the size of the domain through which they are followed is minimal. High correlations between the dimensionless quantities of porosity and tortuosity are calculated and a logarithmic relationship is proposed. As the porosity of a medium increases the flow field becomes more uniform.

Development of a Secondary SCRAM System for Fast Reactors and ADS Systems

One important safety aspect of any reactor is the ability to shutdown the reactor. A shutdown in an ADS can be done by stopping the accelerator or by lowering the multiplication factor of the reactor and thus by inserting negative reactivity. In current designs of liquid-metal-cooled GEN IV and ADS reactors reactivity insertion is based on absorber rods. Although these rod-based systems are duplicated to provide redundancy, they all have a common failure mode as a consequence of their identical operating mechanism, possible causes being a largely deformed core or blockage of the rod guidance channel. In this paper an overview of existing solutions for a complementary shut down system is given and a new concept is proposed. A tube is divided into two sections by means of aluminum seal. In the upper region, above the active core, spherical neutron-absorbing boron carbide particles are placed. In case of overpower and loss of coolant transients, the seal will melt. The absorber balls are then no longer supported and fall down into the active core region inserting a large negative reactivity. This system, which is not rod based, is under investigation, and its feasibility is verified both by experiments and simulations.

Pore-scale modeling of competitive adsorption in porous media

In this paper we present a smoothed particle hydrodynamics (SPH) pore-scale multicomponent reactive transport model with competitive adsorption. SPH is a Lagrangian, particle based modeling method which uses the particles as interpolation points to discretize and solve flow and transport equations. The theory and details of the SPH pore-scale model are presented along with a novel method for handling surface reactions, the continuum surface reaction (CSR) model. The numerical accuracy of the CSR model is validated with analytical and finite difference solutions, and the effects of spatial and temporal resolution on the accuracy of the model are also discussed. The pore-scale model is used to study competitive adsorption for different Damköhler and Peclet numbers in a binary system where a plume of species B is introduced into a system which initially contains species A. The pore-scale model results are compared with a Darcy-scale model to investigate the accuracy of a Darcy-scale reactive transport model for a wide range of Damköhler and Peclet numbers. The comparison shows that the Darcy model over estimates the mass fraction of aqueous and adsorbed species B and underestimates the mass fractions of species A. The Darcy-scale model also predicts faster transport of species A and B through the system than the pore-scale model. The overestimation of the advective velocity and the extent of reactions by the Darcy-scale model are due to incomplete pore-scale mixing. As the degree of the solute mixing decreases with increasing Peclet and Damköhler numbers, so does the accuracy of the Darcy-scale model.

Simulation of drop movement over an inclined surface using smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) is used to numerically simulate the movement of drops down an inclined plane. Diffuse interfaces have been assumed for tracking the motion of the contact line. The asymmetric shape of the three-dimensional drop and the variation of contact angle along its periphery can be calculated using the simulation. During the motion of a liquid drop down an inclined plane, an internal circulation of liquid particles is observed due to gravitational pull which causes periodic change in the drop shape. The critical angle of inclination required for the inception of drop motion is also evaluated for different fluids as a function of drop volume. The numerical predictions exhibit a good agreement with the published experimental results.

Diffuse-interface model for smoothed particle hydrodynamics

Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking and capturing of dynamic interfaces between different materials on larger scales. Smoothed particle hydrodynamics (SPH) is also widely used to simulate fluids and solids that are subjected to large deformations and have complex dynamic boundaries and/or interfaces, but no explicit interface tracking or capturing is required, even when topological changes such as fragmentation and coalescence occur, because of its Lagrangian particle nature. Here we developed a SPH model for single-component two-phase fluids that is based on diffuse-interface theory. In the model, the interface has a finite thickness and a surface tension that depend on the coefficient k of the gradient contribution to the Helmholtz free energy functional and the density-dependent homogeneous free energy. In this model, there is no need to locate the surface (or interface) or to compute the curvature at and near the interface. One- and two-dimensional SPH simulations were used to validate the model.

Dissipative-particle-dynamics model for two-phase flows

Dissipative particle dynamics (DPD) is a mesoscopic method in which coarse graining is done at the molecular level to capture the physics at the meso level. In this paper, we present a DPD model for two-phase flows involving liquid and vapor phases. The model is based on mean-field theory. Phase segregation between the two phases is simulated by the choice of an equation of state with a van der Waals loop. Surface tension is modeled by a term that depends on higher-order density gradients and accounts for long-range attractive forces. To test the model, we present results from simulations of a liquid layer, several liquid cylinders of varying size to verify the Laplace's law, small- and large-amplitude liquid cylinder oscillations and capillary waves. In all these cases we compare DPD results with results available from analytical solutions.

Oscillation of viscous drops with smoothed particle hydrodynamics

We investigate the nonlinear oscillations of heat-conductive, viscous, liquid drops in vacuum with zero gravity, using smoothed particle hydrodynamics (SPH). The liquid drops are modeled as a van der Waals fluid in two dimensions so that the models apply to flat, disklike drops. Attention is focused on small- to large-amplitude oscillations of drops that are released from a static elliptic shape. We find that for small-amplitude motions the combined dissipative effects of finite viscosity and heat conduction induce rapid decay of the oscillations after a few periods, while for large-amplitude motions wave damping is governed by the action of both viscous dissipation and surface tension forces. The transition from periodic to aperiodic decay at Re approximately 1 as well as the quadratic decrease of the frequency with the initial aspect ratio at large Re are reproduced in good agreement with previous theoretical predictions and experimental results.

Smooth-particle phase stability with generalized density-dependent potentials

Stable fluid and solid particle phases are essential to the simulation of continuum fluids and solids using smooth particle applied mechanics. We show that density-dependent potentials, such as Phi rho=1/2 Sigma(rho-rho 0)2, along with their corresponding constitutive relations, provide a simple means for characterizing fluids and that special stabilization potentials, with density gradients or curvatures, such as Phi inverted Delta rho=1/2 Sigma(inverted Delta rho)2, not only stabilize crystalline solid phases (or meshes) but also provide a surface tension which is missing in the usual density-dependent-potential approach. We illustrate these ideas for two-dimensional square, triangular, and hexagonal lattices.