By means of a computational model, we study the relation between two complementary views of gelation, rheological tests against the characterization of a network of consecutive particles. The model we propose consists of slender, plane, colloidal sized particles, which we name laths, which self-assemble into long ordered aggregates of several particles; called whiskers in the literature. Within a whisker, the interaction potential is a minimum when: the planes of two consecutive laths are aligned, thus favoring their alignment; when the center of three consecutive laths lie in a straight line, thus favoring stacking; and when the center of two consecutive laths are located at a certain distance, which mimics excluded volume. A threshold value of the potential gives a condition for sticking free laths into whiskers, and for the breaking of whiskers. The simplicity of the model allows the simulation to reach large enough times, of the order of minutes, needed to simulate numerical rheology tests. We are able to characterize the whisker formation, as well as to simulate the gel transition, by means of an oscillatory shear numerical experiment. We conclude that according to the usual rheological definition a gel transition occurs at about 250K, even though there is no branching and less than 10% of whiskers are long enough as to percolate the system.
