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Research Papers: Multiphase Flows

# Maximum Spread of Droplet on Solid Surface: Low Reynolds and Weber Numbers

[+] Author and Article Information
Ri Li1

Thermal Systems Laboratory, GE Global Research, One Research Circle, Niskayuna, NY 12309liri@ge.com

Nasser Ashgriz

Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, M5S 3G8, Canadaashgriz@mie.utoronto.ca

Sanjeev Chandra

Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, M5S 3G8, Canadachandra@mie.utoronto.ca

1

Corresponding author.

J. Fluids Eng 132(6), 061302 (Jun 15, 2010) (5 pages) doi:10.1115/1.4001695 History: Received September 27, 2009; Revised April 23, 2010; Published June 15, 2010; Online June 15, 2010

## Abstract

This theoretical study proposes an analytical model to predict the maximum spread of single droplets on solid surfaces with zero or low Weber and Reynolds numbers. The spreading droplet is assumed as a spherical cap considering low impact velocities. Three spreading states are considered, which include equilibrium spread, maximum spontaneous spread, and maximum spread. Energy conservation is applied to the droplet as a control volume. The model equation contains two viscous dissipation terms, each of which has a defined coefficient. One term is for viscous dissipation in spontaneous spreading and the other one is for viscous dissipation of the initial kinetic energy of the droplet. The new model satisfies the fundamental physics of drop-surface interaction and can be used for droplets impacting on solid surfaces with or without initial kinetic energy.

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## Figures

Figure 2

Schematic of spreading states of a droplet impacted on a solid surface: state 1 is upon impact, state 2 is equilibrium shape, state 3 is maximum spontaneous spread, and state 4 is maximum spread

Figure 1

Previous models of maximum spread: (a) Dm versus Weber number (θe=30 deg and Oh=1) and (b) Dm versus equilibrium contact angle (We=0.1 and Oh=1).

Figure 7

New model of maximum spread as a function of equilibrium contact angle (Oh=1)

Figure 6

New model of maximum spread as a function of Weber number (Oh=1)

Figure 5

New model of maximum spread as a function of Weber number (CS=1)

Figure 4

Maximum spread of a spontaneously spreading droplet as a function of CS

Figure 3

The amount of potential energy that is released during spontaneous spreading (Eq. 14). The dotted lines show the maxima of P at equilibrium spreads.

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