## Abstract

A mathematical method was developed to study the skin penetration of volatile organic compounds (VOCs) after exposure to a high dose of the substance. While closed-form solutions exist to describe the diffusion and evaporation from small amounts, numerical approaches are often implemented to predict dermal transport involving large doses. This work offers a Laplace transform-based method to estimate the time constant and dynamic and steady-state behaviors. First, the process was divided into two stages, separated by the time it took for excess chemicals to be depleted from the skin surface. Series solutions were written for the percutaneous VOC concentration, absorption and evaporation in the first stage. Application of Laplace transform methods yielded transient profiles after the compound dissipated from the surface of the stratum corneum. In addition, the procedure facilitated the calculation of the time constant and steady-state values. The method was validated using benchtop and fume hood experiments conducted with N,N-diethyl-3-methylbenzamide (DEET) and air velocities of 0.165 m/s and 0.72 m/s, respectively. The increase in the flow rate decreased the total amount of VOC absorbed and reduced the period required for the surface fluid to disappear.

Original language | English (US) |
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Article number | 108889 |

Journal | Mathematical Biosciences |

Volume | 351 |

DOIs | |

State | Published - Sep 2022 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Modeling and Simulation
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics

## Keywords

- Absorption
- Effective time constant
- Evaporation
- Mathematical modeling
- Volatile organic compounds