Mobility of permeable aggregates: effects of shape and porosity

Vainshtein, P.; Shapiro, M.; Gutfinger, C.

doi:10.1016/j.jaerosci.2003.09.004

Cited by 41 publications

(52 citation statements)

References 28 publications

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“…These porous sphere models assume that the aggregate is spherical and require knowledge of the radial density distribution function from which the permeability is calculated. These models predict for DLCA aggregates in the continuum limit that the mobility radius scales with the number of monomers per aggregate with a mobility-mass exponent of approximately x ≈ 0.6 (Shapiro et al 2004(Shapiro et al , 2005 and private communication; Lattuada et al 2004). The ratio β = R m /R g is somewhat larger than unity for all sizes.…”

Section: Figmentioning

confidence: 95%

“…There is a significant body of work that treats the fractal aggregate as a porous and permeable object to calculate the mobility radius (Adler 1987;Tandon and Rosner 1995;Veerapaneni and Wiesner 1996;Coelho, et al 1997;Vanni 2000;Kim and Stolzenbach 2002;Lattuada, Wu, and Morbidelli 2004;Vainshtein, Shapiro, and Gutfinger 2004;Vainshtein and Shapiro 2005). These porous sphere models assume that the aggregate is spherical and require knowledge of the radial density distribution function from which the permeability is calculated.…”

Section: Figmentioning

confidence: 99%

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The Mobility of Fractal Aggregates: A Review

Sorensen

2011

Aerosol Science and Technology

314

298

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A review of the experimental and theoretical literature describing the mobility of fractal aggregates over the previous three decades is presented. Aggregates are those formed via both diffusion and reaction limited cluster-cluster aggregation processes, DLCA and RLCA, which form aggregates with fractal dimensions and prefactors of ca. 1.78 and 1.3 and 2.1 and 0.94, respectively. Emphasis is placed on DLCA aggregates. The entire Knudsen number range from continuum to free molecular is reviewed. The review finds a simple and general consensus description of mobility for the entire range.

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Section: Figmentioning

confidence: 95%

Section: Figmentioning

confidence: 99%

The Mobility of Fractal Aggregates: A Review

Sorensen

2011

Aerosol Science and Technology

314

298

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“…(2), (4). In kinetic theory the mean force exerted on a particle by fluid molecules is the product of the molecule-particle collision rate times the mean momentum transfer per collision [18].…”

Section: Methodsmentioning

confidence: 99%

“…The main approximation of our work, and the approximation implicit in Eqs. (2), (4), is that the dominant contribution to the friction force arises from the collision rate. If the mean momentum transfer is taken to be independent of aggregate morphology the ratio of the friction coefficients f k /(kf 1 ) becomes the appropriate ratio of collision rates shown in Eq.…”

Section: Methodsmentioning

confidence: 99%

On the friction coefficient of straight-chain aggregates

Isella¹,

Drossinos²

2011

Journal of Colloid and Interface Science

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A methodology to calculate the friction coefficient of an aggregate in the continuum regime is proposed. The friction coefficient and the monomer shielding factors, aggregate-average or individual, are related to the moleculeaggregate collision rate that is obtained from the molecular diffusion equation with an absorbing boundary condition on the aggregate surface. Calculated friction coefficients of straight chains are in very good agreement with previous results, suggesting that the friction coefficients may be accurately calculated from the product of the collision rate and an average momentum transfer, the latter being independent of aggregate morphology. Langevin-dynamics simulations show that the diffusive motion of straightchain aggregates may be described either by a monomer-dependent or an aggregate-average random force, if the shielding factors are appropriately chosen.

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“…The fractal dimension allows for the evaluation of the interior of the aggregates and their physical properties, including: porosity, density, permeability, at the same time disclosing the degree of complexity of the object (Li and Logan 2001, Vainshtein et al 2004, Zhao et al 2013. In literature, much attention is also paid to the evaluation of the fractal dimension of fl ocks in activated sludge, in the aspect of control of such single processes as sedimentation, dehydration, coagulation or fl occulation (Jin et al 2003, Qi et al 2011, Wang et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Analysis of particle size and fractal dimensions of suspensions contained in raw sewage, treated sewage and activated sludge

Kuśnierz¹,

Wiercik²

2016

Archives of Environmental Protection

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The analysis of particle size in suspensions carried out with use of the laser diffraction method enables us to obtain not only information about the size of particles, but also about their properties, shape and spatial structure, determined basing on fractal dimension. The fractal dimension permits the evaluation of the interior of aggregates, at the same time showing the degree of complexity of the matter. In literature, much attention is paid to the evaluation of the fractal dimension of fl ocs in activated sludge, in the aspect of control of single processes, i.e. sedimentation, dehydration, coagulation or fl occulation. However, results of research concerning the size of particles and the structure of suspensions existing in raw and treated sewage are still lacking.The study presents optical fractal dimensions D 3 and particle size distributions measured with use of laser granulometer in raw and treated sewage and activated sludge collected from six mechanical-biological wastewater treatment plants located in the Lower Silesian region.The obtained test results demonstrate that wastewater treatment plants that use both sequencing batch reactors and continuous fl ow reactors are more effi cient at capturing suspension particles of a size up to 30 μm and are characterized by an increased removal of particles of a size ranging from 30 μm to 550 μm to the outfl ow. Additionally, in the case of samples of treated sewage and activated sludge collected at the same location, at short intervals, similar particle distributions were observed. As far as the analysis of fractal dimensions is concerned, particles contained in the raw sewage suspension were characterized by the lowest values of the fractal dimension (median equals 1.89), while the highest values occurred in particles of activated sludge (median equals 2.18). This proves that the spatial structure of suspension particles contained in raw sewage was similar to a linear structure, with a large amount of open spaces, while the structure of particles contained in the activated sludge suspension was signifi cantly more complex in the spatial aspect.Brought to you by | MIT Libraries Authenticated Download Date | 5/11/18 5:22 PM

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Mobility of permeable aggregates: effects of shape and porosity

Cited by 41 publications

References 28 publications

The Mobility of Fractal Aggregates: A Review

The Mobility of Fractal Aggregates: A Review

On the friction coefficient of straight-chain aggregates

Analysis of particle size and fractal dimensions of suspensions contained in raw sewage, treated sewage and activated sludge

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