A numerical study of the sedimentation of fibre suspensions

1998 ◽  
Vol 376 ◽  
pp. 149-182 ◽  
Author(s):  
MICHAEL B. MACKAPLOW ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Monte Carlo ◽  
Steady State ◽  
Monte Carlo Simulations ◽  
Numerical Study ◽  
Point Particle ◽  
Hydrodynamic Interactions ◽  
Dynamic Simulations ◽  
Slender Body Theory ◽  
Fibre Suspensions ◽  
The Mean

The sedimentation of fibre suspensions at low Reynolds number is studied using two different, but complementary, numerical simulation methods: (1) Monte Carlo simulations, which consider interparticle hydrodynamic interactions at all orders within the slender-body theory approximation (Mackaplow & Shaqfeh 1996), and (ii) dynamic simulations, which consider point–particle interactions and are accurate for suspension concentrations of nl3=1, where n and l are the number density and characteristic half-length of the fibres, respectively. For homogeneous, isotropic suspensions, the Monte Carlo simulations show that the hindrance of the mean sedimentation speed is linear in particle concentration up to at least nl3=7. The speed is well predicted by a new dilute theory that includes the effect of two-body interactions. Our dynamic simulations of dilute suspensions, however, show that interfibre hydrodynamic interactions cause the spatial and orientational distributions to become inhomogeneous and anisotropic. Most of the fibres migrate into narrow streamers aligned in the direction of gravity. This drives a downward convective flow within the streamers which serves to increase the mean fibre sedimentation speed. A steady-state orientation distribution develops which strongly favours fibre alignment with gravity. Although the distribution reaches a steady state, individual fibres continue to rotate in a manner that can be qualitatively described as a flipping between the two orientations aligned with gravity. The simulation results are in good agreement with published experimental data.

scholarly journals Universal dependence of the total number albedo of photons on the mean number of photon scatterings

2011 ◽  
Vol 26 (3) ◽  
pp. 249-253 ◽  
Author(s):  
Vladan Ljubenov ◽  
Rodoljub Simovic
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Analytic Functions ◽  
Least Squares Method ◽  
Mcnp Code ◽  
Initial Photon ◽  
Aluminum Iron ◽  
Universal Dependence ◽  
The Mean ◽  
Good Agreement

This paper presents the results of research on photon reflection from plane targets based on Monte Carlo simulations performed by the MCNP code. Five materials (water, concrete, aluminum, iron, and copper) are examined in the area of initial photon energies of up to 200 keV. The values of the total number albedo for photons dependent on the initial photon energy or the mean number of photon scatterings are calculated and graphically presented. We have shown that the values of the total number albedo for different target materials, expressed as a function of the mean number of photon scatterings, are in good agreement with each other and can be approximated by simple, universal analytic functions obtained by the least squares method. The accuracy of these analytic appoximations is confirmed by their comparison with the results of PENELOPE and FOTELP Monte Carlo codes.

Dynamic simulations of the inhomogeneous sedimentation of rigid fibres

2002 ◽  
Vol 468 ◽  
pp. 205-237 ◽  
Author(s):  
JASON E. BUTLER ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Sedimentation Rate ◽  
Particle Orientation ◽  
Hydrodynamic Interactions ◽  
Spherical Particles ◽  
Heterogeneous Structure ◽  
Mass Force ◽  
Dynamic Simulations ◽  
Slender Body Theory ◽  
A Value ◽  
Particle Force

We have simulated the dynamics of suspensions of fibres sedimenting in the limit of zero Reynolds number. In these simulations, the dominant inter-particle force arises from hydrodynamic interactions between the rigid, non-Brownian fibres. The simulation algorithm uses slender-body theory to model the linear and rotational velocities of each fibre. To include far-field interactions between the fibres, the line distribution of force on each fibre is approximated by making a Legendre polynomial expansion of the disturbance velocity on the fibre, where only the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution can be specified completely by a centre-of-mass force, a couple, and a stresslet. Short-range interactions between particles are included using a lubrication approximation, and an infinite suspension is simulated by using periodic boundary conditions. Our numerical results confirm that the sedimentation of these non-spherical, orientable particles differs qualitatively from the sedimentation of spherical particles. The simulations demonstrate that an initially homogeneous, settling suspension develops clusters, or streamers, which are particle rich surrounded by clarified fluid. The instability which causes the heterogeneous structure arises solely from hydrodynamic interactions which couple the particle orientation and the sedimentation rate in particle clusters. Depending upon the concentration and aspect ratio, the formation of clusters of particles can enhance the sedimentation rate of the suspension to a value in excess of the maximum settling speed of an isolated particle. The suspension of fibres tends to orient with gravity during the sedimentation process. The average velocities and orientations, as well as their distributions, compare favourably with previous experimental measurements.

scholarly journals Prospective Evaluation of a Model-Based Dosing Regimen for Amikacin in Preterm and Term Neonates in Clinical Practice

2015 ◽  
Vol 59 (10) ◽  
pp. 6344-6351 ◽  
Author(s):  
A. Smits ◽  
R. F. W. De Cock ◽  
K. Allegaert ◽  
S. Vanhaesebrouck ◽  
M. Danhof ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Steady State ◽  
Monte Carlo Simulations ◽  
Therapeutic Drug ◽  
Population Pharmacokinetic ◽  
Prospective Evaluation ◽  
Dosing Regimen ◽  
Model Based ◽  
Almost All ◽  
Trough Levels

ABSTRACTBased on a previously derived population pharmacokinetic model, a novel neonatal amikacin dosing regimen was developed. The aim of the current study was to prospectively evaluate this dosing regimen. First, early (before and after second dose) therapeutic drug monitoring (TDM) observations were evaluated for achieving target trough (<3 mg/liter) and peak (>24 mg/liter) levels. Second, all observed TDM concentrations were compared with model-predicted concentrations, whereby the results of a normalized prediction distribution error (NPDE) were considered. Subsequently, Monte Carlo simulations were performed. Finally, remaining causes limiting amikacin predictability (i.e., prescription errors and disease characteristics of outliers) were explored. In 579 neonates (median birth body weight, 2,285 [range, 420 to 4,850] g; postnatal age 2 days [range, 1 to 30 days]; gestational age, 34 weeks [range, 24 to 41 weeks]), 90.5% of the observed early peak levels reached 24 mg/liter, and 60.2% of the trough levels were <3 mg/liter (93.4% ≤5 mg/liter). Observations were accurately predicted by the model without bias, which was confirmed by the NPDE. Monte Carlo simulations showed that peak concentrations of >24 mg/liter were reached at steady state in almost all patients. Trough values of <3 mg/liter at steady state were documented in 78% to 100% and 45% to 96% of simulated cases with and without ibuprofen coadministration, respectively; suboptimal trough levels were found in patients with postnatal age <14 days and current weight of >2,000 g. Prospective evaluation of a model-based neonatal amikacin dosing regimen resulted in optimized peak and trough concentrations in almost all patients. Slightly adapted dosing for patient subgroups with suboptimal trough levels was proposed. This model-based approach improves neonatal dosing individualization.

scholarly journals RELAXATION UNDER OUTFLOW DYNAMICS WITH RANDOM SEQUENTIAL UPDATING

2005 ◽  
Vol 16 (11) ◽  
pp. 1771-1783 ◽  
Author(s):  
SYLWIA KRUPA ◽  
KATARZYNA SZNAJD-WERON
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Square Lattice ◽  
One Dimensional ◽  
Sequential Updating ◽  
The Mean

In this paper we compare the relaxation in several versions of the Sznajd model (SM) with random sequential updating on the chain and square lattice. We start by reviewing briefly all proposed one-dimensional versions of SM. Next, we compare the results obtained from Monte Carlo simulations with the mean field results obtained by Slanina and Lavicka. Finally, we investigate the relaxation on the square lattice and compare two generalizations of SM, one suggested by Stauffer et al. and another by Galam. We show that there are no qualitative differences between these two approaches, although the relaxation within the Galam rule is faster than within the well known Stauffer et al. rule.

SELF-ATTRACTING WALK ON NON-UNIFORM SUBSTRATES

2002 ◽  
Vol 16 (12) ◽  
pp. 449-457
Author(s):  
ZHI-JIE TAN ◽  
XIAN-WU ZOU ◽  
WEI ZHANG ◽  
SHENG-YOU HUANG ◽  
ZHUN-ZHI JIN
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Monte Carlo Simulations ◽  
Fractal Dimensions ◽  
Attractive Interaction ◽  
Percolation Clusters ◽  
Small Scales ◽  
End Distance ◽  
The Mean ◽  
End To End

Self-attracting walk (SATW) on non-uniform substrates has been investigated by Monte Carlo simulations. The non-uniform substrates are described by Leath percolation clusters with occupied probability p. p stands for the degree of non-uniformity, and takes on values in the range pc≲p ≤1 where pc is the threshold of percolation. For the case of strong attractive interaction u, p has little influence on the walk which is dominated by attractive interactions. Furthermore, in the case of small scales, the exponent ν of the mean end-to-end distance <R2(t)> versus time t is given by ν≃1/(ds+1), while the exponent k of visited sites versus t is given by k≃ds/(ds+1), where ds are the fractal dimensions of the substrates. For u ≃ 0, the walk reduces to the random walk on percolations with p in pc≲p≤1. Also, ν and k decrease sensitively with the reduction of p. It is found, the blocked sites in the substrates (i.e. defects) have much greater influence on the walk driven by thermal flunctuation than that dominated by the attractive interaction.

scholarly journals The atmospheric chemistry box model CAABA/MECCA-3.0

2011 ◽  
Vol 4 (2) ◽  
pp. 373-380 ◽  
Author(s):  
R. Sander ◽  
A. Baumgaertner ◽  
S. Gromov ◽  
H. Harder ◽  
P. Jöckel ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Steady State ◽  
Monte Carlo Simulations ◽  
Atmospheric Chemistry ◽  
General Public ◽  
Box Model ◽  
Rate Coefficients ◽  
Community Model ◽  
User Friendly ◽  
General Public License

Abstract. We present version 3.0 of the atmospheric chemistry box model CAABA/MECCA. In addition to a complete update of the rate coefficients to the most recent recommendations, a number of new features have been added: chemistry in multiple aerosol size bins; automatic multiple simulations reaching steady-state conditions; Monte-Carlo simulations with randomly varied rate coefficients within their experimental uncertainties; calculations along Lagrangian trajectories; mercury chemistry; more detailed isoprene chemistry; tagging of isotopically labeled species. Further changes have been implemented to make the code more user-friendly and to facilitate the analysis of the model results. Like earlier versions, CAABA/MECCA-3.0 is a community model published under the GNU General Public License.

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