Similarity solution of coagulation equation with an inverse kernel

We analyse a model for the aggregation of polystyrene particles which arises in an electrorheology system in which linear clusters grow upon the application of an alternating electromagnetic field. We consider a coagulation kernel involving negative powers of cluster sizes and investigate the reduction of the governing equations to a similarity solution in the large-time limit. Comparison between the experimental results and the theory presented here shows a good collapse of the data onto a single curve, which matches the theoretical results particularly well at the larger cluster sizes.