Spreading dynamics of three-dimensional droplets by the lattice-Boltzmann method

Abstract We have simulated spreading of small droplets on smooth and rough solid surfaces using the three-dimensional lattice-Boltzmann method. We present results for the influence of the initial distance and shape of the drop from the surface on scaling of droplet radius R as a function of time. For relatively flat initial drop shapes our observations are consistent with Tanner's law R ∼ t q , where q =1/10. For increasingly spherical initial shapes, the exponent q increases rapidly being above one half for spherical droplets initially just above the surface. As expected, surface roughness slows down spreading, decreases the final drop radius, and results in irregular droplet shape due to …

Strain hardening in liquid-particle suspensions

The behavior of a liquid-particle suspension induced to sheared motion was analyzed by numerical simulations. When the velocity (strain) of the suspension began to increase, its viscosity first stayed almost constant, but increased then rapidly to a clearly higher level. This increase in viscosity is shown to be related to formation of clusters of suspended particles. Clusters are shown to increase the viscosity by enhanced momentum transfer though clustered particles. This is the mechanism behind the strain-hardening phenomenon observed in small-strain experiments on liquid-particle suspensions.

Publisher’s Note: Strain hardening in liquid-particle suspensions [Phys. Rev. E72, 061402 (2005)]

Simulation of liquid penetration in paper

Capillary penetration of a wetting liquid in a microtomographic image of paper board, whose linear dimension was close to the average length of wood fibers, was simulated by the lattice-Boltzmann method. In spite of the size of the system not being large with respect to the size of structural inhomogeneities in the sample, for unidirectional penetration the simulated behavior was described well by that of the Lucas-Washburn equation, while for radial penetration a radial capillary equation described the behavior. In both cases the average penetration depth of the liquid front as a function of time followed a power law over many orders of magnitude. Capillary penetration of small droplets of…

Intrusion of nonwetting liquid in paper

The saturation curve of a sample of paper board was measured with mercury-intrusion porosimetry, and the three-dimensional structure of its pore space was determined by x-ray tomographic imaging. Ab initio numerical simulation of intrusion on the tomographic reconstruction, based on the lattice-Boltzmann method, was in excellent agreement with the measured saturation curve. A numerical invasion-percolation simulation in the same tomographic reconstruction showed good agreement with the lattice-Boltzmann simulation. The access function of the sample, determined from the saturation curve and the pore-throat distribution determined from the tomographic reconstruction, indicated that the ink-bo…

Fouling dynamics in suspension flows

A particle suspension flowing in a channel in which fouling layers are allowed to form on the channel walls is investigated by numerical simulation. A two-dimensional phase diagram with at least four different behaviors is constructed. The fouling is modeled by attachment during collision with the deposits and by detachment caused by large enough hydrodynamic drag. For fixed total number of particles and small Reynolds numbers, the relevant parameters governing the fouling dynamics are the solid volume fraction of the suspension and the detachment drag force threshold. Below a critical curve in this 2D phase space only transient fouling takes place when the suspension is accelerated from re…

Evaluation of a lattice-Boltzmann method for mercury intrusion porosimetry simulations

We have simulated intrusion of a non-wetting liquid into pores of varying shape and size. Simulations were based on the lattice-Boltzmann method and the Shan–Chen multiphase model. The liquid–solid contact angle for pores with circular cross-section was found to be equal to that for pores with square cross-section, and constant even for small pore sizes if the discretised shape of the circular cross-section was taken into account. For comparison, contact angle was also determined for a liquid column descending in a capillary tube, and the results were found to be consistent. Application of the method to mercury intrusion porosimetry is discussed.

Simulations of non-spherical particles suspended in a shear flow

The lattice-Boltzmann method was used to investigate the effects of the shape and concentration of the particles on the rheological properties of non-Brownian suspensions for non-zero Reynolds numbers. Several case studies were analyzed and the methods used were found to give accurate predictions for these systems. The viscosity of suspensions of both spherical and non-spherical particles was determined as functions of shear rate and concentration of particles. It was shown that, for high shear rates, shear thickening appears. This phenomenon is particularly pronounced for particles of irregular shape.

Clustering and viscosity in a shear flow of a particulate suspension

A shear flow of particulate suspension is analyzed for the qualitative effect of particle clustering on viscosity using a simple kinetic clustering model and direct numerical simulations. The clusters formed in a Couette flow can be divided into rotating chainlike clusters and layers of particles at the channel walls. The size distribution of the rotating clusters is scale invariant in the small-cluster regime and decreases rapidly above a characteristic length scale that diverges at a jamming transition. The behavior of the suspension can qualitatively be divided into three regimes. For particle Reynolds number Re(p) less than or approximately equal 0.1, viscosity is controlled by the char…