Geometrical properties of aggregates with tunable fractal dimension

Morphology and mobility of synthetic colloidal aggregates

“…We remark that anisotropies extend over a large range of values, even for the same (d f , k f ). As expected, our results agree with Thouy and Jullien [31], who concluded that (for fixed k f )…”

Hydrodynamic properties of rigid fractal aggregates of arbitrary morphology

“…To generate low fractal dimension aggregates, a conventional cluster-cluster aggregation algorithm has been used to generate both diffusion-limited (DLCA) clusters (d f = 1.8) and reaction-limited (RLCA) clusters (d f = 2.1), by using sticking probabilities of 1 and smaller than 1, respectively [41]. A slightly modified version of the tunable fractal dimension algorithm (originally proposed by Thouy and Jullien [42]) developed by Ehrl et al [43] was utilized to produce aggregates with higher fractal dimension values, (up to d f = 2.5). The algorithm takes pairs of clusters and combines them in order to fulfill the fractal scaling for a pre-defined value of the fractal dimension.…”

Generation and Geometrical Analysis of Dense Clusters with Variable Fractal Dimension

“…Symbols a 2D ) ratio of the major over the minor axis of the best fitted ellipse for an aggregate projection, -a 3D 1 , a 3D 2 ) ratio of the maximum principal moment of inertia over the two smaller principal moments of inertia of an aggregate, - a P ) pixel size, m A ) area, m 2 , pixel 2 , or dimensionless A, B ) indices for aggregate A and B, -c ) chord length, m or pixel C j+1/j ) j-weighted average chord length, µm d f ) mass fractal dimension defined in eqs 3 and 15, -d cf ) chord fractal dimension, -d p ) primary particle diameter, m d pf ) perimeter fractal dimension defined in eq 16, -D p , D s ) perimeter or surface dimension, 35 i,j ) dimensionless masses or enumerating indices, -〈i,j〉 ) average aggregate mass defined in eq 13, -I(0) ) zero-angle intensity of scattered light, au k f ) prefactor of the fractal scaling law, -l ) dimensionless chord length, l ) c/(r opt d p ), -l b ) box length, m, pixel, or dimensionless 35 L ) characteristic length, µm n, n clu , n g , n pro ) number of unsuccessful placements, number of clusters, grade number, and number of projections, -n (L) ) density distribution function, 1/µm N ) number of particles, -N p , N s ) number of perimeter or surface pixels, 35 -P ) perimeter, m, pixel, or dimensionless r b c ) center of gravity, m r c,AB ) distance between the centers of gravity of the aggregates A and B, r c,ab ) |r b c,ab | ) |r b c,a -r b c,b |, m r b i ) position i, m r n ) normalized resolution, r n ) d p /a p , -r opt ) absolute optical resolution, pixel/m R g ) radius of gyration, -〈R g 2 〉 i,j ) mass average square radius of gyration defined in eq 10, m R p ) radius of primary particle, m s f ) fractal slope of CLD, -S BET ) specific surface area, m 2 /g ∆t ) duration of the backscattering signal, s V ) circumferential velocity of the laser beam, m/s X A ) relative mass of aggregate A, X A ≡ N A /(N A + N B ), - …”

“…For comparison, literature data from Lee and Kramer 10 and Thouy and Jullien35 are also included. There is a strong dependency of d pf on d f .…”