Penetration theory of mass transfer applied to salt diffusion in cheese

Abstract

Modified penetration theory of mass transfer have been developed and applied to diffusion of salt in brine-salted cheese. The mass of salt taken up by a cheese is proportional to the brine concentration and the square root of the brining time, but is independent of cheese thickness. However, the rate of salt uptake is inversely proportional to the square root of the brining time due to a decrease in the salt concentration gradient between the cheese moisture and the brine. The dept of salt penetration δρ, defined as the distance from the interface at which the salt-in-moisture concentration is 1 percent of the interfacial value is proportional to the square root of the product D't, where D' is the pseudo-diffusion coefficient of salt in cheese moisture and t is the brining time. The penetration theory holds over a salting period in which the depth of salt penetration into cheese is lower than cheese half-thickness. In the D' range of 0.1-0.3 cm2/d, the maximum duration of the salting period in the region of penetration theory ranges from as law as 1-3 min for the cheese thickness of 1 mm, to as high as 6-19 days for the cheese thickness of 10 cm. .

Analitičkim rešavanjem jednačina prvog i drugog Fickovog zakona difuzije za slučaj prenosa mase soli iz salamure konstantnog sastava u sir beskonačne debljine, definisana je prostorna i vremenska raspodela koncentracije soli u vodenoj fazi sira pri soljenju u salamuri. Na osnovu toga, izvedene su jednačine za određivanje masenog fluksa soli u proizvoljnom preseku sira i mase akumulirane soli između dva proizvoljna poprečna preseka sira u funkciji od vremena, koeficijenta stešnjene difuzije soli u vodenoj fazi sira, međufazne površine, koncentracije soli u salamuri i zapreminskog udela vodene faze u siru. Primenom izvedenih jednačina izvršena je simulacija procesa difuzije soli, na osnovu koje su utvrđene osnovne karakteristike procesa. .