A person applies an insect repellent onto an exposed area of A = 0.5 m2 of their body. The mass of spray used is M = 10 grams, and the spray contains 25% (by mass) active ingredient. The inactive ingredient quickly evaporates from the skin surface.
(a) If the spray is applied uniformly and the density of the dried active ingredient is p = 2000 kg/m3, determine the initial thickness of the film of active ingredient on the skin surface. The temper- ature, molecular weight, and saturation pressure of the active ingredient are 32°C, 152 kg/kmol, and 1.2 X 10-5 bars, respectively.
(b) If the convection mass transfer coefficient associated with sublimation of the active ingredient to the hydrogen in the glass fiber are DAB = 2.88 X 10-15 the air is hm
= 5 X 10-3 m/s
Hydrogen diffusion into the fiber is undesirable, since it changes the spectral transmissivity and refractive index of the glass and can lead to failure of the detection system.
(a) Determine the average hydrogen concentration in an uncoated optical fiber, C, after 100 h of operation in the hydrogen environment.
(b) Determine the corresponding change in the refractive index, n, of the fiber. For vitreous silica, n = (1.6 X 10-3 m3/kmol) X C.
cient associated with the ingredient-skin interface is K = 0.05, and the mass diffusivity of the active ingredient in the skin is DAB = 1 X 10-13 m2/s, determine how long the insect repellent remains effective. The partition coefficient is the ratio of the ingredient density in the skin to the ingredient density outside the skin.
(c) If the spray is reformulated so that the partition coefficient becomes very small, how long does the insect repellent remain effective?