Validation of an approximate model for the thermal behavior in acoustically driven bubbles

Area of Science:

• Chemical Engineering
• Physical Chemistry
• Acoustics

Background:

• Radical production in acoustically driven bubbles is key to sonochemistry.
• Accurate modeling of bubble temperature and heat exchange is essential for predicting reaction rates.
• Existing models vary in complexity and assumptions regarding temperature distribution.

Purpose of the Study:

• To compare a detailed partial differential equation (PDE) model with a simplified ordinary differential equation (ODE) model for bubble temperature.
• To evaluate the accuracy of the ODE model (uniform average temperature, boundary layer approximation) against the spatially resolved PDE model.
• To determine the conditions under which the simplified model provides reliable predictions.

Main Methods:

• Developed and implemented a detailed PDE model for spatially resolved bubble temperature.
• Developed and implemented a simplified ODE model assuming uniform average bubble temperature and boundary layer heat exchange.
• Compared model predictions for temperature fields and heat exchange under varying acoustic pressure amplitudes.
• Assessed model agreement within the range of bubble spherical stability.

Main Results:

• Both PDE and ODE models show good agreement for bubble temperature and heat exchange.
• Agreement is maintained within the pressure amplitude range where bubbles remain spherically stable.
• The simplified ODE model provides a computationally efficient alternative for stable bubble conditions.

Conclusions:

• The simplified ODE model is a valid and efficient approach for modeling temperature in acoustically driven bubbles under stable conditions.
• Accurate temperature field evaluation is critical for modeling chemical reactions within bubbles.
• Model choice depends on the required accuracy and computational resources for sonochemical applications.