## Pinholes etc.

### Quick Start

Here we have two useful little apps of relevance to the adhesion formulator. The first looks at how surface energy affects not the coating itself but how thin coatings are more vulnerable to pinholes. The second looks at whether your liquid adhesive has a chance to flow into small structures (fibres, pores) via capillary forces.

If a coating of thickness h has a contact angle θ with the surface and by chance (e.g. from an air bubble) a pinhole of diameter d appears, then it will spontaneously close (i.e. the defect will disappear) if:

h/d > 2(1-cosθ)

This means, unfortunately, that thin coatings (small h) are much more prone to pinholes than thicker ones. So a coating that might be defect-free at 20μm might be full of holes when coated at 10μm even though nothing else about the system had changed. For thin coatings you either need much greater cleanliness (less defects to start with) or a lower contact angle.

### Pinholes

h μm
d μm
θ°
Pinhole:

The Washburn formula for flow of a liquid driven by capillary forces is a reasonable approximation for those who want to know if their liquid adhesive will flow into a defined surface structure. The formula is somewhat optimistic because it doesn't take into account dynamic surface tension effects and assumes perfect wetting, but given the other approximations this doesn't much matter. Washburn tells us that the distance L travelled in time t by a liquid of surface tension γ and viscosity η into a capillary of diameter D with a contact angle of θ is given by:

L^2 = (γDtcosθ)/(4η) rarr t=(4ηL^2)/(γDcosθ)

As you will see (t is in μs) when you put any reasonable numbers into the app, capillary filling is generally more than fast enough for most reasonable depths so isn't a great concern.

η cP
L μm
γ dyne/cm
D μm
θ°
t μs