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Related Experiment Video

Updated: May 8, 2026

Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films

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Published on: August 18, 2018

Nonlinear least-squares method for the inverse droplet coagulation problem.

Peter P Jones¹, Robin C Ball, Colm Connaughton

¹Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kindgom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 16, 2013

Summary

This summary is machine-generated.

This study presents a method to determine particle coalescence rates from size distribution data. The approach simplifies the inverse problem, enabling analysis of various physical systems.

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Last Updated: May 8, 2026

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Area of Science:

Physics
Physical Chemistry
Materials Science

Background:

The Smoluchowski equation models particle size distribution evolution during irreversible coalescence.
Determining coalescence rates K(x,y) from observed distributions is a challenging inverse problem.

Purpose of the Study:

To develop an effective method for determining pairwise coalescence rates K(x,y) from particle size distribution measurements.
To simplify the inverse problem by assuming K(x,y) is a homogeneous function.

Main Methods:

The study models the inverse problem by assuming coalescence rates K(x,y) are homogeneous functions.
This assumption reduces the problem to determining a single-variable function and two scaling exponents (μ, ν).
A nonlinear least-squares approach is employed to solve for the exponents.

Main Results:

The method successfully determines coalescence rates for various systems, including polymer physics, cloud science, and astrophysics.
It is effective for both stationary and time-dependent particle size distributions.
Demonstrated applicability to systems with particle sources and sinks, and self-similar relaxation dynamics.

Conclusions:

The developed inverse problem method provides a robust way to infer coalescence kernel properties.
The simplification based on homogeneity significantly aids in analyzing complex coalescence phenomena.
This approach has broad applicability across diverse scientific fields involving particle aggregation.