## Inkjet Lines

### Quick Start

Printing a straight line with a "dotty" technique such as inkjet has its problems. You can get a line of un-joined dots at one extreme, or a funny bulgy line at the other. It depends on the drop diameter D, the spacing p between dots and the contact angle θ of the ink.

Slide the sliders and see what sort of line you get. Then read the theory below.

### Inkjet Lines

Diameter μm
Contact angle θ
Spacing p μm
Line Width μm
p crit μm

If you want to print a line using inkjet it seems obvious that you just print a row of dots close enough together in a straight line and they will look OK.

The question is, how close together must they be to form a nice line? If the dots are of a diameter (before landing on the substrate) of D and the equilibrium contact angle is θ then the dots will expand until they reach the limit implied by θ (see the Drop Spread app). If the dots are printed at a spacing p which is smaller than the expanded diameter then the dots will at least form a wavy line. However, if they are printed at a spacing less than pcrit then a straight line will spontaneously form. As you continue to decrease the drop spacing, the width of the line will increase. If you decrease the spacing too much, however, an instability sets in and the lines contain spontaneous bulges.

The equations (too complex to show here) for the line width and pcrit are given in a paper by Stringer and Derby1 which also provides a formula for the onset of the bulging phenomenon. For simplicity, the app shows the bulge when the spacing is less than 1.5 of pcrit. The reality is much more complex, the app merely reminds you of the sort of nasty surprise that can await you if you space too closely.

1Jonathan Stringer and Brian Derby , Formation and Stability of Lines Produced by Inkjet Printing , Langmuir 2010, 26, 10365–10372