Mechanical and structural model of fractal networks of fat crystals at lowdeformations

Fat-crystal networks demonstrate viscoelastic behavior at very small deform ations. A structural model of these networks is described and supported by polarized light and atomic-force microscopy. A mechanical model is describe d which allows the shear elastic modulus (G') of the system to be correlate d with forces acting within the network. The fractal arrangement of the net work at certain length scales is taken into consideration. It is assumed th at the forces acting are due to van der Waals forces. The final expression for G' is related to the volume fraction of solid fat (Phi) via the mass fr actal dimension (D) of the network, which agrees with the experimental veri fication of the scaling behavior of fat-crystal networks [S. S. Narine and A. G. Marangoni, Phys. Rev. E 59, 1908 (1999)]. G' was also found to be inv ersely proportional to the diameter of the primary particles (sigma approxi mate to 6 mu m) within the network (microstructural elements) as well as to the diameter of the microstructures (xi approximate to 100 mu m) and inver sely proportional to the cube of the intermicrostructural element distance (d(0)). This formulation of the elastic modulus agrees well with experiment al observations. [S1063-651X(99)14511-2].