Data-driven splashing threshold model for drop impact on dry smooth surfaces

This repository provides the Python implementation for the uncertainty quantification method and the data-driven splashing threshold (DST) model presented by Pierzyna et al. (2021).

• The uncertainty quantifier (see example_uq.py) propagates user-definable measurement uncertainties through the equations of the Riboux & Gordillo (2014; 2015) splashing model. It yields the combined uncertainty of the RG splashing parameter beta (relative or absolute) for a given set of measured drop impacts.
• The DST model (see example_dst.py) can be used to calculate the splashing threshold for drop impacts on a dry smooth surface and to predict the respective splashing outcome (deposition or splashing). The threshold was derived using sophisticated machine learning techniques for a wide range of impact conditions as detailed in Pierzyna et al. (2021) and is based on the RG splashing model (Riboux & Gordillo 2014; 2015).

Please refer to our article for more details (Pierzyna et al. 2021).

Requirements / Dependencies

• Python 3
• numpy
• scipy
• sympy

The dependencies can be installed quickly with pip:

pip install -r requirements.txt

Usage

Please refer to example_dst.py and example_uq.py for detailed instructions on how to use the DST model and the uncertainty quantification method.

In general, all functions expect a vector (numpy.ndarray of shape (9, )) or a list of vectors (numpy.ndarray of shape (n, 9)) which describe the full state of the drop impact on a dry smooth surface. The expected variables are

• impact velocity V0 in m/s,
• drop radius R0 in m,
• liquid density rho_l in kg/m^3,
• liquid viscosity mu_l in Pa s,
• liquid surface tension sigma_l in N/m,
• gas density rho_g in kg/m^3,
• gas viscosity mu_g in Pa s,
• gas mean free path lambda_g in m,
• and wedge angle alpha measured between lifted liquid lamella and solid substrate.

Note, that the wedge angle is typically assumed constant at 60 degrees. For a more detailed discussion, please refer to Pierzyna et al. (2021).

Testing

Tests are provided in the tests folder to ensure that all mathematical models are implemented correctly. Reference values were caluculated with great care in Mathematica based on equations provided by Pierzyna et al. (2021) and Riboux & Gordillo (2014; 2015).

Following command runs the tests in your terminal and should exit without erros:

python -m unittests

References

• Pierzyna, Maximilian, David A. Burzynski, Stephan E. Bansmer, and Richard Semaan. "Data-driven splashing threshold model for drop impact on dry smooth surfaces." Physics of Fluids 33:12 (2021).
• Riboux, Guillaume, and José Manuel Gordillo. "Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing." Physical review letters 113.2 (2014): 024507.
• Riboux, Guillaume, and José Manuel Gordillo. "The diameters and velocities of the droplets ejected after splashing." Journal of Fluid Mechanics 772 (2015): 630-648.