Determination of the diffusion coefficients of small solutes in cheese: A review

Free Access

Review

Table II.

Literature review of effective diffusion coefficients found for small solutes in different cheese types.

Cheese	Composition dry matter (DM) (g·kg⁻¹), fat/DM (g·100 g⁻¹) and pH	Brining and/or ripening conditions			Geometry	Model	Effective diffusion coefficient (D _eff) (× 10⁻¹⁰ m²·s⁻¹)	Refs.
Cheese		Process considered	Temperature (°C)	Brine composition	Geometry	Model	Effective diffusion coefficient (D _eff) (× 10⁻¹⁰ m²·s⁻¹)	Refs.
Solute: NaCl
Camembert (soft-type cheese)	DM 410 fat/DM 45	Brining and ripening	14	300 g·kg⁻¹ NaCl pH 4.6	Slab	Fick (1D)	~ 2.54	[41]
Cuartirolo Argentino (soft-type cheese)	DM 480 fat/DM 51.7	Brining and ripening	7.5	205 g·kg⁻¹ NaCl agitated or brine at rest	Finite rigid slab	Fick (1D)	3.6	[51, 52]
Feta	DM 440 fat/DM 43	Dry-salted	13	–	Semi-finite geometry	Fick (1D)	2.3	[87]
White cheese (semi-hard, Turkey)	DM 450 fat/DM 42 pH 5.3	Brining	4, 12.5 and 20	150–200 g·kg⁻¹ NaCl	Finite slab	Fick (1D)	2.1, 3 and 4 (no effect of brine concentration)	[74]
White cheese (semi-hard, Turkey)	DM 450 fat/DM 42 pH 5.3	Brining	4–20	150–200 g·kg⁻¹ NaCl	Finite slab	Fick (1D)	2.2–4.2	[75]
Prato cheese (semi-hard, Brazil)	DM 517 fat/DM 53 pH 5.2	Brining	10	150–200 and 250 g·kg⁻¹ NaCl	Parallelepiped	Fick (3D) and neural network	1.64, 4.25 and 3	[7]
Romano (hard-type cheese)	DM 535 fat/DM 38	Brining	20	160 g·kg⁻¹ NaCl	Slab	Fick (1D)	2.54–3.35	[35]
Sbrinz (hard-type cheese)	DM 650 fat/DM 48	Brining and ripening	Brining at 12 °C (4 days) and diffusion at 7, 11, 15 and 20 °C	200 g·kg⁻¹ NaCl	Touching semi-infinite cylinders (after the brining step)	Fick (1D)	1.06 (± 0.15) to 1.88 (± 0.27) (temp. coef.: 0.063 × 10⁻¹⁰ m²·s⁻¹·°C⁻¹)	[29]
Cheddar (hard-type cheese)	DM 650	Ripening	10	–	Slab	Fick (1D)	1.16	[86]
Emmental (hard-type cheese)	DM 600 fat/DM 48	Brining	4–18	250 g·kg⁻¹ NaCl; 0.3 g·kg⁻¹ CaCl₂ pH 5.4	Infinite cylinder	Fick (1D)	0.62–2.22	[60]
Model cheese (Gouda style)	DM 580–630 fat/DM ~ 50	Ripening RH 87%	13	–	Slab	Fick (1D)	2.3	[28]
Model cheese (Gouda style)	DM 533, 566 and 638 fat/DM 62, 50, 22 and 12 pH 4.9–5.6	Brining	12.6	130–310 g·kg⁻¹ NaCl; 15 g·kg⁻¹ CaCl₂	Flat cylindrical shape	Fick (1D)	~ 2.3 1.16–3.24 (temp. coef.: 0.12 × 10⁻¹⁰ m²·s⁻¹·°C⁻¹)	[26]
Model cheese	DM 370 and 440 fat/DM 20 and 40 pH 6.2 and 6.5 0.5 and 1.5 g·100 g⁻¹ NaCl	Release of NaCl from the cheese into water	13	Water	Infinite cylinder	Fick (1D)	2.74–5.1 (± 0.01)	[46]
Model cheese		Release of NaCl from the cheese into water	15	Artificial saliva	Infinite cylinder	Fick (1D)	2.81–3.43	[23]
Solute: water
White cheese (semi-hard, Turkey)	DM 450 fat/DM 42 pH 5.3	Brining	4, 12.5 and 20	150–200 g·kg⁻¹ NaCl	Finite slab	Fick (1D)	15% brine: 1.96–3.64; 20% brine: 1.69–3.09	[76]
Solutes: NaCl and water
Fresh cheese Pasteurized cow and goat milk	No data	Brining	5, 15 and 20	280 g·L⁻¹ NaCl; 15 g·L⁻¹ CaCl₂	Cylinder and parallelepiped	Fick (1D)	Water: 5.71, 8.83 and 9.99; NaCl: 3.56, 8.26 and 9.17	[70]
Mahon cheese (soft-type cheese, Spain)	DM 244	Ripening RH 85%	12	280 g·L⁻¹ NaCl; 15 g·L⁻¹ CaCl₂	Parallelepiped	Fick (3D)	Water: 0.078; NaCl: 5.3	[71]
Gouda (semi-hard cheese)	DM 565 fat/DM 53	Brining	20	170 g·kg⁻¹ NaCl	Slab	Maxwell-Stefan (1D)	from the core to the edge of the cheese	[61]
Solutes: NaCl and KCl
Fynbo cheese (semi-hard, Turkey)	DM 470 fat/DM 29.6–36.2	Brining	12	100 g·L⁻¹ NaCl; 100 g·L⁻¹ KCl; 15 g·L⁻¹ CaCl₂	Diffusion cell	Fick (1D)	NaCl: 4.14; KCl: 3.91	[89]
Prato cheese (semi-hard, Brazil)	DM 540 fat/DM 52.8	Brining	10	146 g·L⁻¹ NaCl; 50.6 g·L⁻¹ KCl; 5 g·L⁻¹ CaCl₂	Parallelepiped	Fick (1D)	NaCl: 2.6; KCl: 2.77	[8]
Prato cheese (semi-hard, Brazil)	DM 540 fat/DM 52.8	Brining	10	146 g·L⁻¹ NaCl; 50.6 g·L⁻¹ KCl; 5 g·L⁻¹ CaCl₂	Parallelepiped	Fick (3D)	NaCl: 2.8; KCl: 2.94	[10]
Other solutes
Lactose in small curd cottage cheese	No available information	Washing	25	Demineralized water pH 4.5 (H₃PO₄)	Sphere	Fick (1D)	3.8	[11]
Lactose in Skimmed Quark cheese (Soft-type cheese, Germany)	No available information	–	4	–	Touching semi-infinite cylinders	Fick (1D)	1.37 (± 0.13)	[85]
Sucrose in milk	Fat 15 g·kg⁻¹	Contact with 15 g·100 g⁻¹ agar gel	20–24 (room temperature)	–	Touching semi-infinite cylinders	Fick (1D)	Initial gel sucrose concentration C _s0 787 g·L⁻¹: 1.9, C _s0 515 g·L⁻¹: 2.6, C _s0 279 g·L⁻¹: 3.9	[81]
Lactic acid and NaCl in Pategras	DM 544 fat/DM 43 Lactic acid 13 g·kg⁻¹	Ripening RH 90%	13	200 g·kg⁻¹ NaCl; 5 g·kg⁻¹ CaCl₂	Finite slab	Fick (1D) multicomponent diffusion	NaCl: 3.2 lactic acid: ~ 1	[25]
Potassium sorbate in American processed cheese	DM 600 fat/DM 45	Brining	Room temperature	250 g·L⁻¹ potassium sorbate solutions	Cubes (finite slab)	Fick (1D)	1.31	[40]
Potassium sorbate in Mozzarella	DM ~ 500 fat/DM 45	Brining	Room temperature	250 g·L⁻¹ potassium sorbate solutions	Cubes (finite slab)	Fick (1D)	0.674	[40]
Aroma compounds in model cheese: diacetyl, heptan-2-one, and ethyl hexanoate	DM 370 fat/DM 20 and 40 pH 6.2 1.5 g·100 g⁻¹ NaCl	Release of aroma compounds in the air	13	–	VASK	Fick (1D)	Diacetyl: 0.04; heptan-2-one: 0.2–0.12; ethyl hexanoate: 0.18–0.07	[47]