An inkjet printhead ejects droplets of a water-based ink of density kg m and surface…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Fluid statics and the continuum picture · Fluid statics and the continuum picture

Fluids and Continuum Physics, Ch Surface tension, capillarity and wetting

Problem

An inkjet printhead ejects droplets of a water-based ink of density

\rho = 1050

kg m

^{-3}

and surface tension

\gamma = 0.055

N m

^{-1}

. Take

g = 9.8

m s

^{-2}

and atmospheric pressure

p_{0} = 1.013\times10^{5}

Pa. The ink is a Newtonian liquid of uniform density and the air around it is at atmospheric pressure. ((a)) A droplet in flight has radius

R = 25

\mu

m. Using

R

as the length scale, evaluate the Bond number

Bo = \rho g R^{2}/\gamma

and say whether gravity or surface tension fixes the shape of the droplet. ((b)) On the paper the droplet has spread into a round dot of width

w = 0.20

mm. Solvent evaporates faster at the rim, so the surface tension there is

0.061

N m

^{-1}

while at the centre it is still

0.055

N m

^{-1}

. State which way the surface of the liquid is dragged and why, and find the tangential (Marangoni) force

\Delta\gamma\,w

that this difference exerts across the dot. ((c)) In the reservoir the free ink surface stands

45

mm above the nozzle, and the ink there is at rest with its surface open to the atmosphere. Find the absolute pressure of the ink at the nozzle, and write down the stress tensor of the ink there in terms of that pressure.

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