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The hydrodynamics and mixing during the nonaxisymmetry impingement of a micro-droplet and a sessile droplet of the same fluid are investigated by many-body dissipative particle dynamics (MDPD) simulation. In this work, the range of the impingement angle (θi) between the impinging droplet and the sessile droplet is 0°–60° and the contact angle is set as 45° or 124°. The droplets impingement and mixing behavior is analyzed based on the droplet internal flow field, the concentration distribution and the time scale of the decay of the kinetic energy of the impinging droplet. The dimensionless total mixing time (τm) is calculated by a modified mixing function. With the Weber number (We) ranging from 5.65 to 22.7 and the Ohnesorge number (Oh) ranging from 0.136 to 0.214, we find τm hardly changes with We and Oh. Whereas, θi and surface wettability are found to have a significant effect on τm. We find that θi has no clear effect on τm on a hydrophobic surface, while on the hydrophilic surface, τm increase with the θi. Thus, reducing the impinging angle is a valid method to shorten the τm.

Measurements of the zeta potential using streaming potential method are frequently used to characterise flows in subsurface settings owing to a broad range of applications of this petrophysical property; examples include CO2 geological storage, hydrocarbon reservoirs, geothermal sources and freshwater aquifers. Many experimental studies of the zeta potential have been carried out covering a wide range of parameters including different rock mineralogy, brine concentration and composition, and temperature to understand the impact of each parameter. The capability of the streaming potential method to be used on intact rock samples, single-/ and multi-phase flows, wide range of salinity, pressure and temperature makes the method suitable for representation of typical subsurface conditions. However, none of previous studies reported high multi-phase measurements at high pressure conditions typical for deep reservoirs. To adequately represent subsurface conditions of carbon geological storage sites, the minimum experimental pressure of 7.38 MPa and minimum temperature of 31 °C, consistent with the supercritical-CO2 (scCO2), need to be used. Obtaining stable measurements of the streaming potential under these conditions is extremely challenging. We report a detailed design of a high-pressure experimental system and experimental protocol for multi-phase streaming potential measurements that were carried out on scCO2-sandstone-brine systems at temperature of 40 °C, pressures ≤10 MPa and with a variety of aqueous solutions.The obtained results demonstrate for the first time that the multi-phase zeta potential correlates with the measured scCO2 residual saturation and rock’s wetting state interpreted from other parameters. Moreover, our results unambiguously identify for the first time the polarity and likely magnitude of the scCO2-brine interfacial zeta potential. Our findings improve the current understanding of the complex wetting behaviour of scCO2 and provide important experimental data for numerical (surface complexation, molecular dynamics), analytical (DLVO) or combined models.

Zeta potential is an important interfacial property that controls electrostatic interactions between mineral, water, and non-aqueous phase fluids. These interactions play an important role in defining the wetting state of reservoir rocks and transport of ionic species through porous media. The zeta potential is shown to be an efficient means for a broad range of applications including monitoring of single- and multi-phase flows in subsurface settings, characterization of fracture networks, efficiency of CO2 sequestration, hydrogen underground storage and enhanced oil recovery. It is widely agreed that the zeta potential in carbonate rocks is controlled by the concentration of potential determining ions (PDI), but the understanding of the underlying mechanisms is still limited as there are little experimental data on quantitative characterization of the dependence of the zeta potential on concentration of negative potential determining ions (PDI) such as SO42-, CO32-, HCO3-, especially when their concentration is high and exceeds that of the positive PDIs.In this study, the streaming potential method is used to investigate the zeta potential of natural carbonate rock samples in contact with natural aqueous solutions of low-to-high ionic strength and with varying concentration of sulphate (SO42-) and carbon (C4) related (HCO3-, CO32-) ions. In each set of experiments the total ionic strength was kept constant to eliminate the impact of concentration on the zeta potential so that the increasing/decreasing concentration of negative PDI was adjusted by decreasing/increasing concentration of indifferent Cl- ions. The study probed the concentration of negative PDIs that has never been reported before, with their respective lowest concentration consistent with previously reported equilibrium values, and the highest concentration being equal to the maximum achievable through stripping the tested solutions of Cl-.Our results demonstrate for the first time that magnitude of the negative zeta potential increases linearly with log10 of C4 concentration, however its dependence on the log10 of SO42- concentration is non-linear suggesting varying mechanisms of this PDI’s specific adsorption. Moreover, the results demonstrate that the zeta potential strongly depends on the total ionic strength, interpreted from slopes of the linear regressions for each negative PDI in different background solution. This observation suggests that equilibrium constants of negative PDI specific adsorption may be affected by the total ionic strength. Our findings improve the current understanding of the complex physicochemical processes that take place at calcite-water interface and provide important experimental data for surface complexation modelling of carbonate-brine systems.

Despite the broad range of interest and applications, controls on the electric surface charge and the zeta potential of silica in contact with aqueous solutions saturated with dissolved CO2 at conditions relevant to natural systems, remains unreported. There have been no published zeta potential measurements conducted in such systems at equilibrium, hence the effect of composition, pH, temperature and pressure remains unknown. We describe a novel methodology developed for the streaming potential measurements under these conditions, and report zeta potential values for the first time obtained with Fontainebleau sandstone core sample saturated with carbonated NaCl, Na2SO4, CaCl2 and MgCl2 solutions under equilibrium conditions at pressures up to 10 MPa and temperatures up to 40 °C. The results demonstrate that pH of solutions is the only control on the zeta potential, while temperature, CO2 pressure and salt type affect pH values. We report three empirical relationships that describe the pH dependence of the zeta potential for: i) dead (partial CO2 pressure of 10-3.44 atm) NaCl/Na2SO4, ii) dead CaCl2/MgCl2 solutions, and iii) for all live (fully saturated with dissolved CO2) solutions. The proposed new relationships provide essential insights into interfacial electrochemical properties of silica-water systems at conditions relevant to CO2 geological storage.

Particle-resolved, three-dimensional, time-dependent simulations of rigid and flexible cylinders fluidized by a liquid flow in fully periodic domains have been performed by means of the lattice-Boltzmann method supplemented with immersed boundaries. The solids volume fraction ranges from 0.10 to 0.48 and the length-over-diameter aspect ratio of the cylinders from 4 to 12. The bending stiffness of the cylinders is the third major input parameter. The resulting Reynolds numbers based on the average slip velocity of the cylinders and their equivalent diameter range from 6 to 70. It is shown that increasing the flexibility—that is, decreasing the bending stiffness—reduces the Reynolds number, an effect that is most pronounced for low solids volume fractions and long cylinders. As for rigid cylinders, the distribution of the orientation relative to the direction of gravity of the flexible cylinders is a pronounced function of the solids volume fraction and the aspect ratio. Flexibility tends to somewhat randomize the orientation distribution, which could explain the effect of flexibility on the slip velocity and thus the Reynolds number.

We investigate the three-dimensional, time-dependent behaviour of coherent flow structures inside two cyclone separator geometries, a Stairmand cyclone and a swirl tube, operating in the turbulent regime. For this, large-eddy simulations (LES) with a standard Smagorinsky subgrid-scale model are carried out on the single-phase flow employing a non-orthogonal curvilinear hexahedral mesh. Reynolds numbers (Re) are in the range 9·104–4·105. The simulations successfully capture the quasi-periodic precessing vortex core (PVC) phenomenon. The spectra derived from the temporal signals of different flow variables viz. static pressure, tangential velocity, axial velocity and radial velocity in the Stairmand cyclone exhibit two distinct frequencies at all Re, whereas the spectra for the swirl tube show a single peak. These spectra strongly resemble those reported in the experimental literature. The periodicity pertaining to the inner vortex about its rotational axis is also analyzed. Next, the effect of Re on the two distinct spectral peaks have been evaluated for the Stairmand cyclone. Lastly, we present the effect of Re on mean and fluctuating fields and their variations along the geometrical axis of the cyclone.

Three-dimensional, time-dependent simulations of dense agitated solid-liquid suspensions involving particles of cylindrical shape in a Newtonian liquid have been performed. The liquid flow is resolved by the lattice-Boltzmann method at length scales finer than the size of the particles, which implies particle-resolved simulations. The flow solution includes the hydrodynamic forces and moments on each particle that are used to integrate their linear and rotational equations of motion. No-slip at the particle surfaces is imposed by an immersed boundary method (IBM). The marker points of the IBM are also used to detect and carry out collisions between particles. This numerical procedure has been applied to systems contained in a rectangular box and agitated by a revolving disk as well as by a pitched-blade turbine with an impeller-based Reynolds number of 87, which indicates laminar flow. The overall solids volume fraction has been fixed to 15%; the number of particles is of the order of one thousand. We study the effect of impeller type and particle shape (in terms of the length over diameter ratio of the cylinders that has been varied between 1 and 4) on the extent to which the solids are suspended and on the way the cylinders orient themselves.

Zeta potential is an important petrophysical property that controls electrostatic interactions between mineral, water, and non-aqueous phase fluids. These interactions play an important role in defining the wetting state of reservoir rocks. The zeta potential can be interpreted from the streaming potential measurements, which are shown to be an efficient means for a broad range of applications including monitoring of single- and multi-phase flows in subsurface settings, characterization of fracture networks, efficiency of CO2 sequestration, hydrogen underground storage and enhanced oil recovery. It is widely agreed that the zeta potential in carbonate rocks is controlled by the concentration of potential determining ions (PDI), but the understanding of this is still poor and there are very limited experimental data on quantitative characterization of the dependence of the zeta potential on concentration of negative potential determining ions (PDI) such as SO42-, CO32-, HCO3-, especially when their concentration is high and exceeds that of the positive PDIs.In this study, the streaming potential method is used to investigate the zeta potential of natural carbonate rock samples in contact with natural aqueous solutions of low-to-high ionic strength and with varying concentration of sulphate (SO42-) and carbon (C4) related (HCO3-, CO32-) ions. In each set of experiments the total ionic strength was kept constant to eliminate the impact of concentration on the zeta potential. The study probed the concentration of negative PDIs that has never been reported before, with their respective lowest concentration consistent with previously reported values, and the highest concentration equal to the maximum achievable by stripping the tested solutions of Cl-.Our results demonstrate that zeta potentials strongly depend on concentration of the negative PDIs, thus providing explicit empiric relationship between the zeta potential and a broad range of PDI concentration. Our findings improve the current understanding of the complex physicochemical processes that take place at calcite-water interface and provide important experimental data for surface complexation modelling of carbonate-brine systems.

International audience; Electrochemical interactions at calcite-water interface are characterized by the zeta potential and play an important role in many subsurface applications. In this work we report a new physically meaningful surface complexation model that is proven to be efficient in predicting calcite-water zeta potentials for a wide range of experimental conditions.Our model uses a two-stage optimization for matching experimental observations. First, equilibrium constants are optimized, and the Stern layer capacitance is optimized in the second stage. The model is applied to a variety of experimental sets that correspond to intact natural limestones saturated with equilibrated solutions of low-to-high salinity, and crushed Iceland Spar sample saturated with NaCl at non-equilibrium conditions.The proposed linear correlation of the Stern layer capacitance with the ionic strength is the main novel contribution to our surface complexation model without which high salinity experiments cannot be modelled. Our model is fully predictive given accurately known conditions. Therefore, the reported parameters and modelling protocol are of significant importance for improving our understanding of the complex calcite-water interfacial interactions. The findings provide a robust tool to predict electrochemical properties of calcite-water interfaces, which are essential for many subsurface applications including hydrology, geothermal resources, CO2 sequestration and hydrocarbon recovery.

Despite the broad range of interest and applications, controls on the electric surface charge and the zeta potential of silica in contact with aqueous solutions saturated with dissolved CO

We study aggregation of equally-sized spherical particles under mildly turbulent flow conditions (Reynolds numbers in the range 4000–8000) in a mixing tank through numerical simulation. The dynamics of the liquid flow is solved in terms of the volume-averaged Navier-Stokes equations by an extended lattice-Boltzmann method on a fixed uniform cubic grid. The particle dynamics is updated through applying Newton’s second law to each particle. The simulations include a two-parameter model for the attractive force between the particles that causes aggregation. The dynamics of solids and liquid are two-way coupled through a mapping procedure. An overall solids volume fraction of 10% has been investigated. The level of aggregation of particles in the mixing tank mainly depends on the strength of the attractive force and on the impeller-based Reynolds number, not so much on the distance over which the aggregative force is active. A higher Reynolds number leads to less aggregation.

The coalescence of an impinging droplet colliding with a sessile droplet at an angle(θi) is investigated by numerical simulation. The range of θi is 0° - 60° and the surface wettability are set as hydrophilic or hydrophobic, and both of them can affect the droplet mergence behavior. By using a modified mixing function, the dimensionless total mixing time τm can be calculated. The results show that there is no clear effect of θi on τm on a hydrophobic surface, while τm increases as θi increases on the hydrophilic surface. With the Weber number(We) ranging from 5.65 to 22.7 and the Ohnesorge number(Oh) ranging from 0.136 to 0.214, we find τm hardly changes with We and Oh. By dividing the mergence and mixing process in a convection and a diffusion stage, we find that the diffusion is much larger than the convection time.

ACKNOWLEDGEMENT This research was sponsored by Shanghai Sailing Program (No. 20YF1416000) and SUES Distinguished Overseas Professor Program.

Solids suspension in a stirred tank with a down-pumping pitched-blade turbine impeller has been investigated by using particle image velocimetry (PIV) experiments as well as direct numerical simulations (DNS) with a lattice-Boltzmann (LB) method. The flow regime of this solid–liquid two-phase system is transitional with the impeller-based Reynolds numbers Re = 1334. The refractive index matching (RIM) method is applied in the experiments. The overall solids volume fractions are up to 8% in the experiments as well as in the simulations. The liquid flow fields around the particles are highly resolved in both experimental and simulated cases which makes it possible to investigate solid-liquid interactions in detail. The average distributions of the solids over the tank volume as predicted by the simulations are in good agreement with the experimental results. It is shown that the presence of particles reduces the average velocities as well as the turbulent fluctuation levels of the liquid in both the experiments and simulations although the reduction in the simulations is weaker as compared to in the experiments.

We study dense solid-liquid suspensions through numerical simulations. The liquid flow is solved by the lattice-Boltzmann method on a fixed (Eulerian), cubic, uniform grid. Spherical solid particles are tracked through that grid. Our main interest is in cases where the grid spacing and the particle diameter have the same order of magnitude ( d / Δ = O ( 1 ) ). Critical issues then are the mapping operations that relate properties on the grid and properties of the particles, e.g. the local solids volume fraction seen by a particle, or the distribution of solid-to-liquid hydrodynamic forces over grid points adjacent to a particle. For assessing the mapping operations we compare results for particles settling under gravity in fully periodic, three-dimensional domains of simulations with d / Δ = O ( 1 ) to much higher resolved simulations ( d / Δ = O ( 10 ) ) that do not require mapping. Comparisons are made in terms of average slip velocities as well as in terms of liquid and fluid velocity fluctuation levels. Solids volume fractions are in the range 0.3 to 0.5, Reynolds numbers are of order 0.1 to 10.

We perform Eulerian-Lagrangian simulations of solid-liquid flow in a mixing tank. The simulations are three-dimensional and time dependent and in the transitional flow regime. The lattice-Boltzmann method is used to solve the volume-averaged Navier-Stokes equations. The overall solids volume fraction is of the order of 10%. Situations with the solids only partly suspended are compared to those with fully suspended solids. The emphasis is on the effect of the particle size distribution (PSD) on the suspension behavior. Four PSD’s all having the same d 32 were investigated. It is harder to fully suspend particles with wider size distribution as compared to narrow distributions.

We study—through numerical simulations—a droplet sliding over a solid substrate as a result of a simple shear flow. We use a free-energy lattice Boltzmann (LB) scheme and compare its results with those of molecular dynamics (MD) simulations. According to the MD, at sufficiently low Reynolds and capillary numbers, the dimensionless sliding speed is a unique function of the equilibrium contact angle. Reproducing the MD results with LB simulations requires the use of a non-equilibrium boundary condition at the substrate and tuning a free parameter in the boundary condition.

Particle image velocimetry (PIV) experiments on a laminar stirred tank flow with floating particles at just drawdown conditions were performed. Careful refractive index matching of the two phases allowed to resolve the flow around the particles. The maximum solids volume fraction was 4%. The impeller was a pitched blade turbine with upward and downward pumping modes and with different off-bottom clearances, and the impeller-based Reynolds number ranged from about 50 to 120. Computational fluid dynamics (CFD) coupled to a discrete phase model (DPM) and discrete element method (DEM) was used to predict the flow field, with an emphasis on the tangential velocity component. The liquid velocity profiles predicted by the CFD simulations are in good agreement with the PIV experimental data. The drawdown process and local particle accumulation simulated by the DPM-DEM model agrees with the experimental phenomena as well. Tangential velocity and particles collisions around the shaft trigger the onset of the drawdown of the floating particles.

Acknowledgement Sincere thanks to Andrew Bayly and Yi He (University of Leeds, UK) for bringing this flow system to my attention.

Multi-particle suspension in a laminar stirred tank flow agitated by a standard Rushton turbine was investigated experimentally and numerically. In the experiments, the motion of the particles was measured by two high-speed cameras and was quantitatively analyzed. Two very stable particle patterns were observed. Strong flow is required to break these patterns because their formation hinders the particle lift-off process. The experimental trajectories and vertical velocities of the particles were measured, and highly reproducible results were found. Direct numerical simulations based on the lattice-Boltzmann method and the resolved particle model were performed to fully resolve the motion of the particles and the flow field. The influence of the friction coefficient and the subgrid lubrication force model on particle suspension was evaluated. Except for the random characteristics of particles interaction at the initial lift-off stage, the predicted trajectories and velocities of the particles are in good agreement with the experimental results. The pressure gradient around the particles is a key mechanism for the lift-off process.

Particle Image Velocimetry (PIV) experiments on turbulent solid-liquid stirred tank flow with careful refractive index matching of the two phases have been performed. The spatial resolution of the PIV data is finer than the size of the spherical, uniformly sized solid particles, thereby providing insight in the flow around individual particles. The impeller is a down-pumping pitch-blade turbine. The impeller-based Reynolds number has been fixed to Re = 104. Overall solids volume fractions up to 8% have been investigated. The PIV experiments are impeller-angle resolved, that is, conditioned on the angular position of the impeller. The two-phase systems are in partially suspended states with an inhomogeneous distribution of solids: high solids loadings near the bottom and near the outer walls of the tank, much less solids in the bulk of the tank. The liquid velocity fields show very strong phase coupling effects with the particles increasingly attenuating the overall circulation patterns as well as the liquid velocity fluctuation levels when the solids volume fraction is increased. © 2017 American Institute of Chemical Engineers AIChE J, 63: 389–402, 2018

The way in which the single phase flow of Newtonian liquids in the vicinity of the impeller in a Rushton turbine stirred tank goes through a laminar-turbulent transition has been studied in detail experimentally (with Particle Image Velocimetry) as well as computationally. For Reynolds numbers equal to or higher than 6000, the average velocities and velocity fluctuation levels scale well with the impeller tip speed, that is, show Reynolds independent behavior. Surprising flow structures were measured—and confirmed through independent experimental repetitions—at Reynolds numbers around 1300. Upon reducing the Reynolds number from values in the fully turbulent regime, the trailing vortex system behind the impeller blades weakens with the upper vortex weakening much stronger than the lower vortex. Simulations with a variety of methods (direct numerical simulations, transitional turbulence modeling) and software implementations (ANSYS-Fluent commercial software, lattice-Boltzmann in-house software) have only partial success in representing the experimentally observed laminar-turbulent transition. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3610–3623, 2017

The financial support from the National Key R&D Program of China (2016YFB0302801), National Natural Science Foundation of China (No. 21676007), and the Fundamental Research Funds for the Central Universities (XK1802-1) are gratefully acknowledged.

Deformation and breakup of a liquid drop immersed in another immiscible liquid and flowing through a single pore has been studied numerically using a conservative phase-field lattice Boltzmann method. Several benchmarks were conducted to validate the code, including the recovery of Laplace pressure, the layered flow of two immiscible liquids, and the implementation of wetting boundary conditions on a curved surface. Gravity-driven motion of a drop through the pore space was qualitatively compared to the available experimental results. Quantitative assessment of the pressure field across the interface of the moving and deforming drop was performed. Our results show that high Weber number due to low surface tension and low Reynolds number due to low velocity of the continuous liquid promote drop breakage. More viscous drops break easier than less viscous drops. We present the phase charts (Weber vs capillary number) and the critical conditions (Weber as a function of Reynolds number) of drop breakage.

CO2 has been considered as an effective fluid to replace CH4 in shale rock. Wetting behavior of water in CO2/CH4 mixtures in organic nanopores is a key parameter influencing CO2 based enhanced gas recovery processes in shale. However, there is lack of fundamental understanding of water wetting in such systems. We perform Molecular Dynamics (MD) simulations of nanoscopic liquid water drops on a graphite substrate mimicking an organic-rich shale pore in the presence of CH4/CO2 mixtures at temperatures in the range 300 K–400 K. The equilibrium contact angle of the water droplets on graphite is a pronounced function of CH4 as well as CO2 pressure with the water droplet lifting-off, that is reaching a 180° contact angle, at a threshold pressure of 12 MPa for CO2 and 78 MPa for CH4. The contact angles recovered from simulations match well with experimental literature via the modified Young's equation. The line tension in our studied systems does not show a specific dependence on temperature. As compared to methane, CO2 exhibits a stronger interaction with organic-rich surfaces, which has strong impact on wettability. For CH4/CO2 mixtures, this translates in an approximately linear increase of the contact angle with the CO2 mole fraction.

Collisions of charged droplets in the shear flow of an electrolyte were simulated to investigate the effects of surface charges and double layers on the critical conditions for coalescence. A lattice Boltzmann method phase field flow solver was coupled with an iterative finite-difference solver for the linearized Poisson–Boltzmann equation describing electric double layers. The simulations resolve both the phase field diffuse interface and electric double layer. The critical capillary numbers for coalescence were determined under varying strengths of the electric interactions. Critical capillary numbers between 0.03 and 0.2 were found for droplet radii spanning 25–50 lattice nodes (12.5–25 times the characteristic interface thickness), with lower critical values for larger droplets. The droplet interfaces had a constant potential. Once electric repulsion becomes comparable to the viscous shear force on the drops, the critical capillary numbers decrease, and the decrease is smaller for longer Debye lengths. Though the ratio of droplet size and Debye length that can be achieved in the simulations is constrained by high computational demands, the simulations provide insight into the effects of surface charge on the interactions between interfaces in multiphase flows.

Liquid drops were released in laminar and transitional jet flows to investigate their deformation and breakup characteristics. Silicone oil and deionized water were the dispersed phase and continuous phase, respectively. Calibration experiments of oil drops rising in quiescent ambient water were performed to benchmark the experimental system and the image processing method. In jet flow, drop breakup probability, breakup time, and the characteristics of daughter drops were investigated in detail. To address the underlying mechanisms of the drop breakup, visualization experiments and two-dimensional particle image velocimetry (PIV) experiments of the single-phase jet flow were performed. Visualization experiments show that the jet flow changes from laminar to transitional in the Reynolds number interval between 1283 and 1610. Critical capillary and Weber numbers for drop breakup were estimated based on the mean flow velocity and mean deformation and were found to be of the order of 0.2 and 30 respectively for this particular flow system.

International audience; During the last decade, many approaches for resolved-particle simulation (RPS) have been developed for numerical studies of finite size particle-laden turbulent flows. In this paper, three RPS approaches are compared for a particle-laden decaying turbulence case. These methods are, the Volume-of-Fluid Lagrangian method, based on the viscosity penalty method (VoF-Lag); a direct forcing Immersed Boundary Method, based on a regularized delta-function approach for the fluid/solid coupling (IBM); and the Bounce Back scheme developed for Lattice Boltzmann method (LBM-BB). The physics and the numerical performances of the methods are analyzed. Modulation of turbulence is observed for all the methods, with a faster decay of turbulent kinetic energy compared to the single-phase case. Lagrangian particle statistics, such as the velocity probability density function and the velocity autocorrelation function, show minor differences among the three methods. However, major differences between the codes are observed in the evolution of the particle kinetic energy. These differences are related to the treatment of the initial condition when the particles are inserted in an initially single-phase turbulence. The averaged particle/fluid slip velocity is also analyzed, showing similar behavior as compared to the results referred in the literature. The computational performances of the different methods differ significantly. The VoF-Lag method appears to be computationally most expensive. Indeed, this method is not adapted to turbulent cases. The IBM and LBM-BB implementations show very good scaling.