Determining Shelf Life by Two Criteria

choose a nonisothermal temperature profile

isothermal

T

1

T

2

T

3

T

25.

degradation curve 1

n

1

1.

T

ref

1

(°C)

30.

k

T

ref

1

0.25

c

1

0.35

Conc

c

1

0.65

initial guess for

t

c

1

t

01

20.

degradation curve 2

n

2

1.

T

ref

2

(°C)

20.

k

T

ref

2

0.02

c

2

0.25

Conc

c

2

0.45

initial guess for

t

c

2

t

02

20.

axes limits

t

max

60.

T

min

0.

T

max

40.

T

2

(t) =

T

0

+(

a

1

-

T

0

) (1-exp(-0.02 t))+

a

2

sin(

a

3

t)

Consider a food or pharmaceutical product whose shelf life is determined by the loss of either of two nutrients or active components; call them markers. Then the product's shelf life depends on the storage temperature history and the degradation kinetic parameters for the two markers, showing which marker reaches its threshold concentration first. This principle is shown in simulation with markers whose degradation follows fixed-order kinetics, with rate constants following a simple exponential temperature dependence. This can be used interchangeably with the traditional Arrhenius equation. The temperature can be constant, as in some shelf-life studies, or fluctuating, as encountered in many real-life situations.