Cernák Jozef, Helgesen Geir
Institute of Physics, P. J. Safárik University in Kosice, Jesenná 5, SK-04000 Kosice, Slovak Republic.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 1):061401. doi: 10.1103/PhysRevE.78.061401. Epub 2008 Dec 8.
We experimentally investigated field-induced aggregation of nonmagnetic particles confined in a magnetic fluid layer when rotating magnetic fields were applied. After application of a magnetic field rotating in the plane of the fluid layer, the single particles start to form two-dimensional clusters, like dimers, trimers, and more complex structures. These clusters aggregated again and again to form bigger clusters. During this nonequilibrium process, a broad range of cluster sizes was formed, and the scaling exponents z and z;{'} of the number of clusters N(t) approximately t;{-z;{'}} and average cluster size S(t) approximately t;{z} were calculated. The process could be characterized as diffusion-limited cluster-cluster aggregation. We found that all sizes of clusters that occurred during an experiment fall on a single curve, as the dynamic scaling theory predicts. However, the characteristic scaling exponents z;{'},z and crossover exponents Delta were not universal. A particle tracking method was used to find the dependence of the diffusion coefficients D_{s} on cluster size s . The cluster motions show features of Brownian motion. The average diffusion coefficients D_{s} depend on the cluster size s as a power law D_{s} proportional, variants;{gamma} where values of gamma as different as gamma=-0.62+/-0.19 and gamma=-2.08+/-0.51 were found in two of the experiments.
我们通过实验研究了施加旋转磁场时，限制在磁流体层中的非磁性颗粒的场诱导聚集现象。在施加在流体层平面内旋转的磁场后，单个颗粒开始形成二维簇，如二聚体、三聚体以及更复杂的结构。这些簇不断聚集形成更大的簇。在这个非平衡过程中，形成了广泛的簇尺寸范围，并计算了簇数量(N(t))约为(t^{-z'})和平均簇尺寸(S(t))约为(t^{z})的标度指数(z)和(z')。该过程可表征为扩散限制的簇 - 簇聚集。我们发现，正如动态标度理论所预测的那样，实验过程中出现的所有尺寸的簇都落在一条单一曲线上。然而，特征标度指数(z')、(z)和交叉指数(\Delta)并非通用。使用粒子跟踪方法来找出扩散系数(D_s)对簇尺寸(s)的依赖性。簇的运动表现出布朗运动的特征。平均扩散系数(D_s)与簇尺寸(s)的关系为幂律(D_s\propto s^{\gamma})，在两个实验中发现(\gamma)的值差异很大，分别为(\gamma = -0.62\pm0.19)和(\gamma = -2.08\pm0.51)。
