Adipose tissue and adipocytes play a central role in the pathogenesis of metabolic diseases related to obesity. Size of fat cells depends on the balance of synthesis and mobilization of lipids and can undergo important variations throughout the life of the organism. These variations usually occur when storing and releasing lipids according to energy demand. This energy is stored as lipid droplets in their cytoplasm therefore adipocytes can adapt their size according to the lipid amount to be stored. Adipocyte size variation can reach one order of magnitude inside the same organism which is unique among cells. A striking feature in adipocytes size distribution is the lack of characteristic size since typical size distribution are bimodal. Since energy can be stored and retrieved and adipocytes are responsible for these lipid fluxes, we proposed a model of size-dependent lipid fluxes that exhibits bimodal equilibria with generic conditions. This model is a non-linear transport equation structured by the size of adipocytes and we provide a dedicated a stable numerical scheme solver able to capture the singular behaviour of solutions as concentration to Dirac masses. Using this solver, we are able to infer parameters related to lipid fluxes from size distribution. Performing recurrent surgical biopsies on rats, we measured the evolution of adipose cell size distribution for the same individual throughout the duration of feeding/refeeding experiments and use this data to assess fluxes parameters variations throughout the experiment.