Excessive clotting can cause bleeding over a vast capillary area. We study the mesoscopic dynamics of clotting by using the fluid particle model. We assume that the plasma consists of fluid particles containing fibrin monomers, while the red blood cells and capillary walls are modeled with elastic mesh of "solid" particles. The fluid particles interact with each other with a short-ranged, repulsive dissipative force. The particles containing fibrin monomers have a dual character. The polymerization of fibrin monomers into hydrated fibrins is modeled by the change of the interactions between fluid particles from repulsive to attractive forces. This process occurs with a probability being an increasing function of the local density. We study the blood flow in microscopic capillary vessels about 100 microm long and with diameters in order of 10 microm. We show that the model of polymerization reflects clearly the role played by fibrins in clotting. Due to the density fluctuations caused the by the high acceleration, the fibrin chains are produced within a very short time (0.5 ms). Fibrin aggregation modifies the rheological properties of blood, slows down the incipient flow, and entraps the red blood cells, thus forming dangerous clots.