Abstract
Patterns are often formed when particles cluster: Since patterns reflect the connectivity of different types of material, the emergence of patterns affects the physical and chemical properties of systems and shares a close relationship to their macroscopic functions. A radial dendritic pattern (RDP) is observed in many systems such as snow crystals, polymer crystals and biological systems. Although most of these systems are considered as dense particle suspensions, the mechanism of RDP formation in dense particle systems is not yet understood. It should be noted that the diffusion limited aggregation model is not applicable to RDP formation in dense systems, but in dilute particle systems. Here, we propose a simple model that exhibits RDP formation in a dense particle system. The model potential for the inter-particle interaction is composed of two parts, a repulsive and an attractive force. The repulsive force is applied to all the particles all the time and the attractive force is exerted only among particles inside a circular domain, which expands at a certain speed as a wave front propagating from a preselected centre. It is found that an RDP is formed if the velocity of the wave front that triggers the attractive interaction is of the same order of magnitude as the time scale defined by the aggregation speed.
Highlights
The particles move as a result of attractive and repulsive interactions with other particles
The origin of the triggering wave source, from which the triggering wave front propagates, is preselected, and the core of the Radial dendritic patterns (RDPs) that eventually forms is located at the same point
The attractive interaction occurs if ri ≤rtri(t), where ri is the distance from the source to a particle i and rtri(t) is the distance from the source to the trigger wave front
Summary
We perform numerical simulations for the model while changing the area fraction φ occupied by the particles and the propagation speed vtri of the triggering wave front. With a further decrease of vtri to [10−3] (Fig. 1(d,h)), the clusters form RDPs in which elongated clusters are spread from the centre of the triggering wave source Under this condition for φ = 0.78, the value of vagg is 1.75 × 10−3 at the propagation front and is comparable to the value of vtri. In the lower r domain, it is recognised that 〈U〉takes a small value except for in the vtri =∞case This indicates that a cluster is created in the centre where the triggering wave source is located, for vtri = 10−1, 10−2 and [10−3]. Since the present model takes into account only a minimal number of factors, the speed vtri of the triggering wave front and the area fraction φ occupied by the particles, it is expected that the mechanism for RDP formation can be applied to other systems, including real systems. The present model may provide a general mechanism for the formation of radial dendritic patterns in dense particle systems
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