Mathematical model and dependence of fish salting process duration to a given salt concentration

Abstract

Abstract The purpose of this scientific work is to build a diffusion model based on Fick's second law. The model is designed to determine the salting process duration and salt concentration in the fish muscle tissue (Atlantic herring). The method of photon correlation spectroscopy (PCS) by a certified Photocor FC correlator device was used. The device operating principle is based on Rayleigh radiation scattering, which allows us to directly determine the effective diffusion coefficients, taking into account all factors, without singling out a specific one. This research presents the spatiotemporal distributions of effective diffusion coefficients in a herring sample during brine salting. Formulas for calculating the salting duration and the average salt concentration in the thickness of fish muscle tissue are presented, and the time of reaching the sample center by salt and the average salt concentration in it were estimated. These parameters could be widely used for the finished product quality and the technical and economic indicators of production improvement. The average effective diffusion coefficient De through the sample thickness was used for calculation. The salting duration for a 30 mm thick herring sample with a saturated salt solution was 8.74 hours until the average salinity of the sample was 4.7%.