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## Resources

Modeling Scenario

## 1-026-Evaporation-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: evaporation cone alcohol Petri dish

## Abstract

We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of change in the respective volumes.

## Citation

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## Description

We provide data (in EXCEL and Mathematica files) on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of evaporation for the alcohol mixture and the water, i.e. how much volume per unit of time over a given patch of surface area is lost. We suggest several differential equation models along with some elementary geometry to model the rate of evaporation in simple cylindrical configuration (Petri dish) and a more complex conical funnel situation. Finally, we seek to back out the rate of evaporation of pure isopropyl alcohol from information produced on rates of evaporation for the 91% isopropyl alcohol mixture and the rate of evaporation of pure water.

We are going to help you model evaporation of 91% isopropyl alcohol solution with water and verify the model using the data from 6 scenarios in which the liquid sits in a flat Petri dish with constant circular cross sectional area. We then consider one scenario in which the liquid is in a cone and hence has a changing cross sectional area as evaporation takes place. We will then ask you to model the evaporation of plain water in a Petri dish to determine the rate of evaporation of water from which we can use all this information to determine the rate of evaporation of pure isopropyl alcohol.

Consider evaporation. It is a complicated process and many variables are involved, e.g., temperature, humidity, fluid which is evaporating, air pressure. Each of these may contribute to the specific rate, but we would like to develop a direct or simple model for evaporation and we suggest that knowing just how fast the volume changes as liquid evaporates would be a worthy consideration. Thus if V(t) is the volume of our liquid, say in a flat Petri dish of constant circular cross sectional area, then upon what (geometrically, for we could presume all the other variables are held constant) would this rate of evaporation, V'(t), of the liquid depend?

We offer several plausible models for the rate of evaporation, i.e. the change in volume per unit time, and ask you to offer one of your own that is plausible and one that is highly implausible. In each case, for our considered three models, and your own two models, discuss the pros and cons of each.

## Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations