SL theory drop impact calculator

Unifying theory of scaling in drop impact

A cleaner interface for reading the core idea first, then evaluating how \(We\) and \(Oh\) set the Reynolds number, impact regime, and predicted maximum spreading.

Read the paper OA
Watch the talk

Overview

What this page is for

Drop impact on a rigid surface depends on the droplet velocity, size, and material properties. This calculator focuses on the two dimensionless control parameters that organize the scaling theory: the Weber number \(We\), which compares inertia and surface tension, and the Ohnesorge number \(Oh\), which measures viscous effects.

The theory is built from direct numerical simulations spanning \(1 \leq We \leq 10^3\) and \(10^{-3} \leq Oh \leq 10^2\). It separates the dominant dissipation mechanisms across the impact process and predicts the maximum spreading diameter while clarifying why viscous dissipation remains important even at low \(Oh\).

Inputs

Dimensionless groups

Weber number

\(We = \frac{\rho V_0^2 D_0}{\gamma}\)

Higher values indicate stronger inertial forcing relative to surface tension.

Ohnesorge number

\(Oh = \frac{\mu}{\sqrt{\rho \gamma D_0}}\)

Higher values indicate stronger viscous influence during impact.

Phase diagram

Weber-Ohnesorge parameter space

Phase diagram of the four impact regimes in Weber-Ohnesorge parameter space

Talk

Video overview

Open on YouTube

Batch

CSV upload

Upload a CSV with We and Oh header columns. The model fills in beta as the third column for every row and returns the completed file.

First row must be a header containing We and Oh. Extra columns are preserved unchanged.