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Table 2 Particle dissolution as a function of dissolution rate and particle size

From: Derivation of first-order dissolution rates to estimate particle clearance and burden in the human respiratory tract

Dissolution rate, k (g/cm2 per day)

Initial deposited mass median particle diameter (µm)a

0.1

0.5

1

5

10

Time to 23% initial particle mass remaining, days (First-order dissolution rate, d−1)

1 × 10−3

0.0058 (253)

0.0290 (50.6)

0.058 (25.3)

0.290 (5.06)

0.581 (2.53)

1 × 10−4

0.058 (25.3)

0.290 (5.06)

0.581 (2.53)

2.90 (0.506)

5.81 (0.253)

1 × 10−5

0.58 (2.53)

2.90 (0.506)

5.81 (0.253)

29.0 (0.051)

58.1 (0.0253)

1 × 10−6

5.81 (0.253)

29.0 (0.051)

58.1 (0.0253)

290 (0.0051)

581 (0.0025)

1 × 10−7

58.1 (0.0253)

290 (0.0051)

581 (0.0025)

2905 (0.0005)

5810 (0.0003)

1 × 10−8

581 (0.0025)

2905 (0.0005)

5810 (0.0003)

29,050 (0.00005)

58,100 (0.00003)

  1. aDissolution calculations are for a particle density of 3 g/cm3 in this example. If density was doubled to 6 g/cm3, the time to 50% dissolution would also be doubled and the first-order rate constant would be halved. Conversely, if density was halved to 1.5 g/cm3, the time to 50% dissolution would also be halved and the first-order rate constant would be doubled