Natural sediment flocs are highly porous particulate aggregates composed of biogenic and minerogenic materials. They can be an important component of suspended sediment load in rivers, estuaries and the marine environment and modelling floc dynamics and behaviour is very important for many aquatic industries, maintenance of waterways and conservation and management of aquatic water bodies. X-ray computed microtomography has recently been applied to quantify the complex three-dimensional (3D) geometry of natural sediment flocs. Here, X-ray images of 3 selected natural millimetre-sized flocs sampled from the Thames River have been digitalised and converted into geometries used in Stokesian Dynamics calculations of the hydrodynamic properties of the flocs, where each floc is represented as a rigid ensemble of spherical beads moving in the creeping flow regime. Our approach is a substantial step from previous attempts in which synthetic fractal structures were simulated. In addition to describe the complex dynamics of floc settling, we compute: (i) the hydrodynamic radius of the flocs; (ii) the floc mobility and resistance tensors; and (iii) the relation between sedimentation velocity and fractal dimension. The simulations show that the coupling of gravitational forces with lateral velocities, which we analysed by examining the cross-components of the mobility matrix, produces a helical motion of the flocs as they settle. We argue that this lateral motion may lead to an enhancement of floc–floc aggregation by differential sedimentation due to an increase in the effective collisional area. Furthermore, the simulations demonstrate significant differences in the dynamics of settling between the three flocs despite a similar gross shape. Our work exemplifies how high-resolution X-ray techniques can be coupled with accurate particle-resolved simulations to understand the settling dynamics of real (as opposed to synthetic) flocs collected from estuarine, coastal or waste-water environments.

Graphene nanosheets display relatively large hydrodynamic slip lengths in most solvents and, because of this, adopt a stable orientation in a shear flow, instead of rotating, when the effect of thermal fluctuations is not too large (Kamal et al. in Nat Commun 11(1):2425, 2020). In this paper, we combine molecular dynamics simulations and continuum boundary integral simulations to demonstrate that the time-averaged ‘S’ shape adopted by a flexible graphene nanosheet subject to moderate thermal fluctuation is almost identical to the shape predicted for negligible thermal fluctuations. The stable ‘S’ shape adopted by the particle results primarily from the normal hydrodynamic traction, which is sensitive to the orientation of the particle with respect to the flow direction. Our 2D results imply that thermally-induced shape fluctuations may have a relatively minor effect on the time-averaged rheology of dilute suspensions of graphene nanosheets for relatively large but finite Péclet numbers.

The time-dependent shape of an evaporating spherical water drop containing graphene oxide (GO) nanosheets is measured for varying solid concentration, humidity level, and pH. The drop is sitting on a superhydrophobic surface, depinned from it. Three different stages of evaporation are identified: isotropic retraction of the drop interface, buckling of the shell of particles accumulated at the fluid interface, and shrinking of the buckled shell at constant shell shape. Marked differences between acidic and basic drops are reported. It is argued that this feature is caused by the pH-dependent interfacial adsorption of the GO particles. For intermediate values of GO concentration, dried capsules with remarkably repeatable folding patterns could be obtained, whose mode numbers are compatible with those predicted by an inertialess, linear elastic shell model. When redispersed in water, the dried capsules from acidic drops retain their shape better than capsules from basic drops.

The viscosity of nanoparticle suspensions is always expected to increase with particle concentration. However, a growing body of experiments on suspensions of atomically thin nanomaterials such as graphene contradicts this expectation. Some experiments indicate effective suspension viscosities below that of pure solvent at high shear rates and low solid concentrations, i.e., the intrinsic viscosity is negative. Using molecular dynamics simulations, we investigate the shear viscosity of few-nanometer graphene sheets in water at high Péclet numbers (Pe ≥ 100), for aspect ratios from 4.5 to 12.0. These simulations robustly confirm that the intrinsic viscosity decreases with increasing aspect ratio and becomes negative beyond a threshold ≈5.5, providing a molecular-level confirmation of this behavior in a realistic graphene-water system. Comparison with continuum boundary integral modeling shows quantitative agreement in the dilute regime, confirming the effect is hydrodynamic in origin. We demonstrate that this anomalous behavior originates from hydrodynamic slip at the liquid-solid interface, which suppresses particle rotation and promotes stable alignment with the flow direction, thereby reducing viscous dissipation relative to dissipation in pure solvent. This slip mechanism holds for both fully 3D disc-like and quasi-2D particle geometries explored in the molecular simulations. As the concentration of graphene particles increases in the dilute regime, the viscosity initially decreases, falling below that of pure water. At higher concentrations, however, particle aggregation becomes significant, leading to a rise in viscosity after a minimum is reached. Our work has important implications for the design of lubricants, inks, and nanocomposites with tunable viscosity.

The density of individual particles is commonly assessed experimentally by quantifying the settling velocity of a collection of particles transferred into a settling column and allowed to settle under the action of gravity. The individual settling velocities of the particles are recorded close to the bottom of the settling column, in a region where it is assumed that the particles have reached their Stokes terminal velocity after the particle cloud has broken up. In the present study we use numerical particle-based simulations in the Stokes regime to demonstrate that this fundamental assumption might not be fulfilled in practice. Even at low volume fraction of monodisperse spheres, a large deviation from the Stokes settling velocity was found. In the case of a collection of polydisperse spheres, a distinction could be made between particles belonging to a cloud, and particles trailing the cloud. It was found that the velocity of the largest trail particles is reasonably close to their Stokes settling velocity. However, the particles close to the core of the cloud can have velocities more than ten times their Stokes velocities, making the use of the single-particle Stokes velocity based on the core particle not suitable to extract the particle density without corrections. An expression based on the local volume fraction, the cloud radius and the particle settling velocity in the cloud is proposed to estimate the single-particle Stokes settling velocity, and therefrom the particle density.

Settling velocity statistics for dilute, non-Brownian homogeneous suspensions of polydisperse spheres having a log-normal size distribution are generated from Stokesian dynamics simulations, as a function of the total volume fraction and normalised width of the particle size distribution. Several hundred instantaneous configurations are averaged to obtain reliable statistics. The paper reports data for the average and fluctuating settling velocity of each particle class in a suspension that is widely polydisperse - previous work was limited to only two or three classes, and the average settling velocity of each particle class was in most cases not reported - and provides an assessment of the accuracy of the analytical models proposed by Batchelor, Richardson & Zaki, Davis & Gecol and Masliyah-Lockett-Bassoon in predicting the simulation data. A limited comparison with dynamic simulations in which the particle microstructure is allowed to evolve in time is also included.

Particles trapped at a fluid-fluid interface by capillary forces can form a monolayer that jams and buckles when subject to uniaxial compression. Here we investigate experimentally the buckling mechanics of monolayers of millimeter-sized rigid plates trapped at a planar fluid-fluid interface subject to uniaxial compression in a Langmuir trough. We quantified the buckling wavelength and the associated force on the trough barriers as a function of the degree of compression. To explain the observed buckling wavelength and forces in the two-dimensional (2D) monolayer, we consider a simplified system composed of a linear chain of platelike particles. The chain system enables us to build a theoretical model which is then compared to the 2D monolayer data. Both the experiments and analytical model show that the wavelength of buckling of a monolayer of platelike particles is of the order of the particle size, a different scaling from the one usually reported for monolayers of spheres. A simple model of buckling surface pressure is also proposed, and an analysis of the effect of the bending rigidity resulting from a small overlap between nanosheet particles is presented. These results can be applied to the modeling of the interfacial rheology and buckling dynamics of interfacial layers of 2D nanomaterials.

Through boundary integral simulations, we investigate, in the creeping flow limit and in the absence of Brownian noise, the effects of Navier slip on the orientational dynamics and effective shear viscosity of a semidilute suspension of two-dimensional particles with either circular or elongated (platelike) shape, interacting only via hydrodynamic and contact forces. We have recently shown that it is theoretically possible for a dilute system of slip platelike particles to display an effective shear viscosity smaller than the viscosity of the suspending fluid. This large viscosity reduction is primarily due to the suppression of the tumbling motion predicted for a no-slip particle and the attainment of a stable orientation. In this paper, we show that the effect of particle-particle interaction at semidilute concentrations is to cause the particles to fluctuate about the stable orientation and, above a threshold solid fraction ccrt, to tumble. As a consequence, a sharp increase in the effective shear viscosity with solid fraction c occurs for c>ccrt. Our results suggest that, for a given particle aspect ratio, there is a value of c that maximizes the reduction in the effective shear viscosity of the suspension.

Through boundary integral simulations and asymptotic analysis, we investigate the effect of a finite Navier slip length on the rheological proprieties of a dilute two-dimensional suspension of plate-like particles in the creeping flow limit. Specifically, we study the effects of Navier slip, particle thickness and Péclet number on the effective shear viscosity and average normal stress difference of an isolated two-dimensional plate-like particle in an unbounded shear flow field. We find that Navier slip induces a significant reduction in the effective viscosity and increases the average normal stress difference. The effect of slip becomes more enhanced as the thickness of the particle decreases and as the Péclet number increases. Remarkably, the analysis suggests that it is theoretically possible for a dilute suspension of slip plate-like particles at high Péclet numbers to have a shear viscosity smaller than that of the suspending fluid.

Buckling induced by viscous flow changes the shape of sheetlike nanomaterial particles suspended in liquids. This instability at the particle scale affects collective behavior of suspension flows and has many technological and biological implications. Here, we investigated the effect of viscous hydrodynamic interactions on the morphology of flexible sheets. By analyzing a model experiment using thin sheets suspended in a shear cell, we found that a pair of sheets can bend for a shear rate ten times lower than the buckling threshold defined for a single sheet. This effect is caused by a lateral hydrodynamic force that arises from the disturbance flow field induced by the neighboring sheet. The lateral hydrodynamic force removes the buckling instability but massively enhances the bending deformation. For small separations between sheets, lubrication forces prevail and prevent deformation. Those two opposing effects result in a nonmonotonic relation between distances and shear rate for bending. Our study suggests that the morphology of sheetlike particles in suspensions is not purely a material property but also depends on particle concentration and microstructure.

Natural sediment flocs are fragile and highly heterogeneous aggregates of biogenic and minerogenic material typically with high porosity and low density. In aquatic environments dominated by fine, cohesive or mixed sediments they can dominate suspended sediment flux. Consequently, monitoring and modelling the behaviour, transport and distribution of flocs is very important for many aquatic industries, maintenance of waterways and conservation and management of aquatic waterbodies. Mathematical models that predict the behaviour of flocs rely on the accurate assessments of the size, shape, density, porosity and fractal dimension of flocs. These inherently 3-dimensional (3D) characteristics are typically derived from 2-dimensional (2D) data, largely due to the challenges associated with sampling, capturing, imaging and quantifying these fragile aggregates. We have developed new volumetric microscopy techniques which can quantify 3D internal and external structures and characteristics of sediment flocs. Here, these techniques were applied to quantify the 3D size (volume), shape and fractal dimension of natural and artificial sediment flocs and compare them to standard 2D approaches. Our study demonstrates that 2D approaches are under-estimating shape complexity and over-estimating the size and mass settling flux of flocs by up to two orders of magnitude, and the discrepancy between 2D and 3D is most marked for natural, organic rich macroflocs. Our study has significant implications for estimations of sediment flux at local to global scales within in aquatic environments. These new data and approaches offer the potential to improve the current parameterisation of sediment transport models and to improve the accuracy of current field-monitoring techniques.

In liquid-based material processing, hydrodynamic forces are known to produce severe bending deformations of two-dimensional (2D) materials such as graphene. The non-linear rotational and deformation dynamics of these atomically thin sheets is extremely sensitive to hydrodynamic particle-particle interactions. To investigate this problem, we developed a computational model of the flow dynamics of elastic sheets suspended in a linear shear flow, solving the full fluid-solid coupling problem in the two-dimensional, slender-body, Stokes flow regime. Both single and pairs of sheets in close proximity are analyzed. Despite the model being two-dimensional, the critical non-dimensional shear rate yielding single-particle buckling is comparable in order of magnitude to that reported for fully three-dimensional, disk-like sheets. For pairs of interacting sheets, hydrodynamic interactions lead either to parallel sliding or bending, depending on the value of an elasto-viscous number based on particle length. For sufficiently low bending rigidity or large shear rates, large deformations of initially stacked sheets lead to sheet reattachment after separation, unlike for the rigid case. A peeling-like dynamics where lubrication provides a viscous bonding force is observed for sheet pairs when one of the two sheets is more rigid than the other. Practical implications for graphene processing and exfoliation are discussed.

This work describes a modelling approach to SARS-CoV-2 dispersion based on experiments. The main goal is the development of an application integrated in Ansys Fluent to enable computational fluid dynamics (CFD) users to set up, in a relatively short time, complex simulations of virion-laden droplet dispersion for calculating the probability of SARS-CoV-2 infection in real life scenarios. The software application, referred to as TU Delft COVID-app, includes the modelling of human expiratory activities, unsteady and turbulent convection, droplet evaporation and thermal coupling. Data describing human expiratory activities have been obtained from selected studies involving measurements of the expelled droplets and the air flow during coughing, sneezing and breathing. Particle Image Velocimetry (PIV) measurements of the transient air flow expelled by a person while reciting a speech have been conducted with and without a surgical mask. The instantaneous velocity fields from PIV are used to determine the velocity flow rates used in the numerical simulations, while the average velocity fields are used for validation. Furthermore, the effect of surgical masks and N95 respirators on particle filtration and the probability of SARS-CoV-2 infection from a dose-response model have also been implemented in the application. Finally, the work includes a case-study of SARS-CoV-2 infection risk analysis during a conversation across a dining/meeting table that demonstrates the capability of the newly developed application.

Combining molecular dynamics (MD) and continuum simulations, we study the dynamics of propagation of a peeling front in a system composed of multilayered graphene nanosheets completely immersed in water. Peeling is induced by lifting one of the nanosheet edges with an assigned pulling velocity normal to the flat substrate. Using MD, we compute the pulling force as a function of the pulling velocity, and quantify the viscous resistance to the advancement of the peeling front. We compare the MD results to a 1D continuum model of a sheet loaded with modelled hydrodynamic loads. Our results show that the viscous dependence of the force on the velocity is negligible below a threshold velocity. Above this threshold, the hydrodynamics is mainly controlled by the viscous resistance associated to the flow near the crack opening, while lubrication forces are negligible owing to the large hydrodynamic slip at the liquid-solid boundary. Two dissipative mechanisms are identified: a drag resistance to the upward motion of the edge, and a resistance to the gap opening associated to the curvature of the flow streamlines near the entrance. Surprisingly, the shape of the sheet was found to be approximately independent of the pulling velocity even for the largest velocities considered.

In the non-dissipative regime, the potential energy is the difference between the strain energy of the deforming solid and the work done by the external forces. For configuration-dependent external forces, whose direction is perpendicular to the deformed shape, we obtain a simple formula for the strain energy release rate of peeled strips experiencing large deformations and prove rigorously that the same formula applies for external forces having fixed direction. We then apply Griffith's criterion for fracture to calculate critical loads for two cases: peeling produced by a uniform follower pressure distributed along the flexible strip and peeling produced by a localized follower shear force applied at the edge of the strip. We found that for these loads, the critical pressure for peeling follows approximately q_c∼ΓL⁻¹, where Γ is the solid–solid interface energy and L is the initial peeling length; for the shear force, the corresponding critical value instead follows Q_0c∼Γ, independently of the initial length. These formulas are, unexpectedly, independent of the bending stiffness EI of the strips and differ from the ones predicted for small deformations, i.e. q_c∝L⁻²EIΓ and Q_0c∝L⁻¹EIΓ. We apply our results to predict the critical hydrodynamic load necessary to exfoliate graphene sheets from graphite, a fluid–structure interaction problem where the load is of the follower type. We find that a follower load peeling model gives significantly improved predictions than fixed load peeling. For the same Γ, L and b, the critical hydrodynamic follower load is always lower than the one with fixed forces: approximately half for the case with uniform pressure, and one third for the case with shear force.

Using molecular dynamics simulations we investigate the shear-induced rotational dynamics of a Brownian nanographene (hexabenzocoronene) freely suspended in a liquid. We demonstrate that, owing to a finite hydrodynamic slip at the molecular surface, these flat molecules tend to align with a constant orientation angle instead of performing the classical periodic orbits predicted by Jeffery's theory. Results are extracted for different Péclet numbers and compared to the predictions by a theory developed for a rigid axisymmetric particle with orientation confined to the flow-gradient plane. The theory is based on the resolution of a one-dimensional Fokker-Planck equation for the angle φ made by one of the particle's diameters with the flow direction. Remarkably, our results show that the essential features of the three-dimensional orientational statistics of the nanographene are captured by the one-dimensional model, given that the hydrodynamic velocity is closed in terms of the slip length λ. Finally, we explore the situation in which multiple nanographenes are suspended in the liquid, and show that slip results in a reduction in specific viscosity.

The classical theory by Jeffery predicts that, in the absence of Brownian fluctuations, a thin rigid platelet rotates continuously in a shear flow, performing periodic orbits. However, a stable orientation is possible if the surface of the platelet displays a hydrodynamic slip length comparable to or larger than the thickness of the platelet. In this article, by solving the Fokker-Plank equation for the orientation distribution function and corroborating the analysis with boundary integral simulations, we quantify a threshold Péclet number, above which such alignment occurs. We found that for smaller than, but larger than a second threshold, a regime emerges where Brownian fluctuations are strong enough to break the platelet's alignment and induce rotations, but with a period of rotation that depends on the value of. For below this second threshold, slip has a negligible effect on the orientational dynamics. We use these thresholds to classify the dynamics of graphene-like nanoplatelets for realistic values of and apply our results to the quantification of the orientational contribution to the effective viscosity of a dilute suspension of nanoplatelets with slip. We find a non-monotonic variation of this term, with a minimum occurring when the slip length is comparable to the thickness of the particle.

The adsorption of graphene-oxide (GO) nanoparticles at the interface between water and vapor was analyzed using all-atom molecular simulations for single and multiple particles. For a single GO particle, our results indicate that the adsorption energy does not scale linearly with the surface coverage of oxygen groups, unlike typically assumed for Janus colloids. Our results also show that the surface activity of the particle depends on the number of surface oxygen groups as well as on their distribution: for a given number of oxygen groups, a GO particle with a patched surface was found to be more surface active than a particle with evenly distributed groups. Then, to understand what sets the thickness of GO layers at interfaces, the adsorption energy of a test GO particle was measured in the presence of multiple GO particles already adsorbed at the interface. Our results indicate that in the case of high degree of oxidation, particle-particle interactions at the water-vapor interface hinder the adsorption of the test particle. In the case of a low degree of oxidation, however, clustering and stacking of GO particles dominate the adsorption behavior, and particle-particle interactions favor the adsorption of the test particle. These results highlight the complexity of multiple particle adsorption and the limitations of single-particle adsorption models when applied to GO at a relatively high surface concentration.

Rigid platelike particles displaying interfacial slip can attain a constant orientation in a shear flow when the slip length is sufficiently large. But actual thin particles such as single-layer graphene are flexible and prone to bending deformations when exposed to shear stress. To study the effect of bending deformation on the dynamics of flexible platelike particles with large interfacial slip in a shear flow, we develop a two-dimensional (2D) fluid-structure interaction model. Our model is based on coupling the Euler-Bernoulli beam equation with a boundary integral method to solve the hydrodynamic stress at the particle surface. Emphasis is placed on resolving accurately the stress distribution at the edges of the particle. We find that (i) a stable alignment occurs even for relatively flexible particles and that (ii) edges effects on the shape of the plate are important for values of the length-to-thickness aspect ratio as large as 100. Our results are particularly relevant in view of recent research on the hydrodynamics of suspended flexible sheets made of 2D nanomaterials.