arXiv subjects

Herbert E. Huppert

Publications and source records attributed to Herbert E. Huppert.

14 recordsLinked to original sources

arXiv2025

Achieve equilibrium outside the contact angle hysteresis

It is common belief that the equilibrium contact angle, corresponding to the minimum system energy state, lies between advancing and receding contact angles. Here, we derive advancing and receding contact angles considering the micro contacting processes on ideal rough 2D surfaces. Equilibrium contact angles obtained via energy minimization can be smaller than the receding contact angle and reach 0 degrees, at which hysteresis diminishes on the super-hydrophilic surface. Gibbs free energy analyses, numerical simulations and physical experiments all confirm these new findings.

cond-mat.soft↗

arXiv2023

Scaling of granular column collapses on inclined planes

Granular column collapse is a simple but important problem to the granular material community, due to its links to dynamics of natural hazards, such as landslides and pyroclastic flows, and many industrial situations, as well as its potential of analyzing transient and non-local rheology of granular flows. This article proposes a new dimensionless number to describe the run-out behaviour of granular columns on inclined planes based on both previous experimental data and dimensional analysis. With the assistance of the sphero-polyhedral discrete element method (DEM), we simulate inclined granular column collapses with different initial aspect ratios, inter-particle frictions, and initial solid fractions on inclined planes with different inclination angles (2.5$^{\circ}$ - 20.0$^{\circ}$) to verify the proposed dimensional analysis. Detailed analyses are further provided for better understanding of the influence of different initial conditions and boundary conditions, and to help unify the description of the relative run-out distances of systems with different inclination angles. This work determines the similarity and unity between granular column collapses on inclined planes and those on horizontal planes, and helps investigate the transient rheological behaviour of granular flows, which has direct relevance to various natural and engineering systems.

cond-mat.soft↗

arXiv2023

Shear viscosity scaling of granular suspensions across dilute to dense regimes

In this letter, following an extensive experimental validation, we perform constant-volume shearing simulations of non-Brownian granular suspensions using the discrete element method coupled with the lattice Boltzmann method. We choose a wide range of solid fractions, shear rates, fluid viscosities, particle sizes, and inter-particle frictional coefficients to obtain a scaling solution for the viscous behavior of suspensions in both dilute and dense regimes. This letter demonstrates that, with a proposed dilute-dense transitional solid fraction, $ϕ_d$, there exists a strong correlation between the inverse relative viscosity and the shear stress. This work incorporates both the $ϕ$-dependence and the $\dotγ$-dependence of suspension viscosity in a universal framework, which provides a scaling solution for granular suspensions across dilute and dense regimes and sheds light on the dilute-dense transition mechanisms.

cond-mat.soft↗

arXiv2023

Unifying Lengthscale-Based Rheology of Dense Granular-Fluid Mixtures

In this communication, we present a new lengthscale-based rheology for dense sheared particle suspensions as they transition from inertial- to viscous-dominated. We derive a lengthscale ratio using straightforward physics-based considerations for a particle subjected to pressure and drag forces. In doing so, we demonstrate that an appropriately chosen length-scale ratio intrinsically provides a consistent relationship between normal stress and system proximity to its ''jammed'' or solid-like state, even as a system transitions between inertial and viscous states, captured by a variable Stokes number.

cond-mat.soft↗

arXiv2022

Axisymmetric column collapses of bi-frictional granular mixtures

The behavior of granular column collapses is associated with the dynamics of geohazards, such as debris flows, landslides, and pyroclastic flows, yet its underlying physics is still not well understood. In this paper, we explore granular column collapses using the spheropolyhedral discrete element method (DEM), where the system contains two types of particles with different frictional properties. We impose three different mixing ratios and multiple different particle frictional coefficients, which lead to different run-out distances and deposition heights. Based on our previous work and a simple mixture theory, we propose a new effective initial aspect ratio for the bi-frictional granular mixture, which helps unify the description of the relative run-out distances. We analyze the kinematics of bi-frictional granular column collapses and find that deviations from classical power-law scaling in both the dimensionless terminal time and the dimensionless time when the system reaches the maximum kinetic energy may result from differences in the initial solid fraction and initial structures. To clarify the influence of initial states, we further decrease the initial solid fraction of granular column collapses, and propose a trial function to quantitatively describe its influence. Due to the utilization of a simple mixture theory of contact occurrence probability, this study can be associated with the friction-dependent rheology of granular systems and friction-induced granular segregations, and further generalized into applications with multiple species of particles in various natural and engineering mixtures.

cond-mat.soft↗

arXiv2022

Predicting Safe Regions within Lava Flows over Topography

We present a shallow, isothermal, Newtonian model for the transient interaction of lava flows with topography. Numerical integrations and simple mathematical approximations are deployed to quantify how topography controls lava thicknesses and flow speeds. Considering idealised topographic features, we show that modest depressions thicken and accelerate the flow - even far downstream - whilst mounds have the opposite effect. However, deep ponds of lava form in depressions of sufficient amplitude, which introduces a long timescale for lava to fill the depression and hence the accelerated downstream flow may never be attained. Relatively large mounds completely divert the lava, providing protected lava-free regions for homes and infrastructure. There can, however, be hazardous, deep, fast flow around the edges of the mound, owing to diversion. Additionally, we show that our model accurately predicts the lava-free region that has been observed in the eruption 35 kyr ago at Marcath Volcano, Nevada.

physics.flu-dyn↗

arXiv2022

Transient Rheology of Immersed Granular Materials

In this letter, we investigate the transient rheological behavior of immersed granular flows using both experiments of submerged granular column collapses and corresponding numerical simulations. The simulations are performed with the lattice-Boltzmann method (LBM) coupled with the discrete element method (DEM) and provide a significant amount of data of the stress and deformation conditions at different positions and times during the granular collapse. We derive a new dimensionless number $\mathcal{G}$ that can unify the rheology of transient granular flows in different regimes for all the simulation data points. $\mathcal{G}$ smoothly transforms from an inertial number into a viscous number, unifying both extremes of the rheology law. We also show the need to introduce the kinetic stresses to achieve a universal relation. The findings establish a transient constitutive framework for visco-inertial granular flows and are important for a better understanding of granular-fluid mixtures in both natural and engineering situations.

cond-mat.soft↗

arXiv2022

Influence of Cross-section Shape on Granular Column Collapses

We investigate granular column collapses with different column cross-sections and associate the cross-section shape influence with a finite-size analysis. Previous research, confined to initially circular configurations, reviewed the importance of granular column collapse studies and concluded that the run-out distance scales with the initial aspect ratio. In this work, granular columns with three different types of initial column cross-sections (square, equilateral triangular, and rectangular cross-sections) are simulated using the discrete element method (DEM). We explore how non-circular cross-sections lead to different run-out distances. Based on the previously obtained finite-size analysis, we further link the initial radius in different directions to the relative size of a column and perform the finite-size analysis to explain the cross-section influence. In the end, a universal relationship, which includes frictional properties, relative sizes, and the cross-section influence, is proposed. Our results are shown to have direct relevance to various natural and engineering systems.

cond-mat.soft↗

arXiv2021

Finite-Size Analysis of the Collapse of Dry Granular Columns

In this letter, we focus on the size effect of granular column collapses, which are potentially connected to the dynamics of complex geophysical flows, even if the link between microscopic structures of granular assemblies and their macroscopic behaviors is still not well understood. Using the sphero-polyhedral discrete element method (DEM), we show that the column radius/grain size ratio has a strong influence on the collapse behavior. A finite-size analysis, which is inspired by a phase transition around an inflection point, is performed to obtain a general scaling equation with critical exponents for run-out distances. We further link the size effect with the strong force network and formalize a correlation length scale that exponentially scales with the effective aspect ratio. Such a scaling solution shows similarities with the percolation problem of two-dimensional random networks and can be extended to other similar natural and engineering systems.

cond-mat.soft↗

arXiv2021

Deposition Morphology of Granular Column Collapses

Granular column collapses result in an array of flow phenomena and deposition morphologies, the understanding of which brings insights into studying granular flows in both natural and engineering systems. Guided by experiments, we carried out computational studies with the discrete element method (DEM) to identify fundamental links between the macro-scale behavior and micro-scale properties of granular columns. A physics-based non-dimensional number combining particle and bulk properties of the column, $α_{\textrm{eff}}$, was found to determinate three collapse regimes (quasi-static, inertial, and liquid-like), revealing universal trends of flow regimes and deposition morphologies under different conditions. This non-dimensional number represents physically the competing inertial and frictional effects that govern the behavior of the granular column collapse, including energy conversion and dissipation. The finding is important for understanding quantitatively the flow of granular materials and their deposits.

cond-mat.soft↗

arXiv2021

Dense Suspension Flow in a Penny-Shaped Crack, Part I : Theory

We study the dynamics of proppants carried by fluid driven into an evolving penny-shaped fracture. The behaviour of the slurry flow is investigated in two phases: pressurised injection and elastic closure. During injection the slurry is modelled using a frictional rheology that takes into account the shear-induced migration and jamming of the proppants. Making pragmatic assumptions of negligible toughness and cross-fracture fluid slip, we find self-similar solutions supporting a range of proppant concentration profiles. In particular, we define an effective viscosity, which equates the fracture evolution of a slurry flow with a given proppant volume fraction, to a Newtonian flow with a particular viscosity. Using this framework, we are able to make predictions about the geometry of the growing fracture and the significance of tip screen-out. In the closure phase, proppants are modelled as incompressible and radially immobile within the narrowing fracture. The effects of proppant concentration on the geometry of the residual propped fracture are explored in full. The results have important applications to industrial fracking and geological dike formation by hot, intruding magma.

physics.flu-dyn↗

arXiv2020

Stokes drift through corals

We investigate the all-penetrating drift velocities, due to surface wave motion in an effectively inviscid fluid that overlies a saturated porous bed of finite depth. Previous work in this area either neglects the large-scale flow between layers [Phillips (1991)] or only considers the drift above the porous layer [(Monismith (2007)]. We propose a model where flow is described by a velocity potential above the porous layer, and by Darcy's law in the porous bed, with derived matching conditions at the interface between the two layers. The damping effect of the porous bed requires a complex wavenumber k and both a vertical and horizontal Stokes drift of the fluid, unlike the solely horizontal drift first derived by Stokes Stokes (1847) in a pure fluid layer. Our work provides a physical model for coral reefs in shallow seas, where fluid drift both above and within the reef is vitally important for maintaining a healthy reef ecosystem [Koehl et al. (1997), Monismith (2007)]. We compare our model with measurements by Koehl \& Hadfield (2004) and also explain the vertical drift effects described in Koehl et al. (2007), who measured the exchange between a coral reef layer and the (relatively shallow) sea above.

physics.flu-dyn↗

arXiv2016

Maximal liquid bridges between horizontal cylinders

We investigate two-dimensional liquid bridges trapped between pairs of identical horizontal cylinders. The cylinders support forces due to surface tension and hydrostatic pressure which balance the weight of the liquid. The shape of the liquid bridge is determined by analytically solving the nonlinear Laplace-Young equation. Parameters that maximize the trapping capacity (defined as the cross-sectional area of the liquid bridge) are then determined. The results show that these parameters can be approximated with simple relationships when the radius of the cylinders is small compared to the capillary length. For such small cylinders, liquid bridges with the largest cross sectional area occur when the centre-to-centre distance between the cylinders is approximately twice the capillary length. The maximum trapping capacity for a pair of cylinders at a given separation is linearly related to the separation when it is small compared to the capillary length. The meniscus slope angle of the largest liquid bridge produced in this regime is also a linear function of the separation. We additionally derive approximate solutions for the profile of a liquid bridge making use of the linearized Laplace-Young equation. These solutions analytically verify the above relationships obtained for the maximization of the trapping capacity.

cond-mat.soft↗

arXiv2006

Gravity currents in a porous medium at an inclined plane

We consider the release from a point source of relatively heavy fluid into a porous saturated medium above an impermeable slope. We consider the case where the volume of the resulting gravity current increases with time like $t^α$ and show that for $α<3$, at short times the current spreads axisymmetrically, with radius $r\sim t^{(α+1)/4}$, while at long times it spreads predominantly downslope. In particular, for long times the downslope position of the current scales like $t$ while the current extends a distance $t^{α/3}$ across the slope. For $α>3$, this situation is reversed with spreading occurring predominantly downslope for short times. The governing equations admit similarity solutions whose scaling behaviour we determine, with the full similarity form being evaluated by numerical computations of the governing partial differential equation. We find that the results of these analyses are in good quantitative agreement with a series of laboratory experiments. Finally, we briefly discuss the implications of our work for the sequestration of carbon dioxide in aquifers with a sloping, impermeable cap.

physics.flu-dyn↗