Interfacial Dynamics

Published: June 17, 2014, By Mark Miller

When describing fluid flow onto substrates to people not living in the world of converting operations is like trying to explain rocket science to a pig. Very few people ever wonder how the glue on tape is placed, or how plastic sheets focus light on a TV screen. I guess we are some of the lucky few!

If we had to boil down the fundamentals of physics and math to explain how fluid is balanced on a substrate prior to curing it into place, what functions would we present? To begin with, fluid flow is defined mathematically as a liquid between two parallel plates. The top plate moves at a constant force on the fluid, while the bottom plate is stationary. If you can wrap your head around this idea, you are moving in the right direction. When the top plate moves, the fluid between the plates deforms with a resistive force continuously.

How the fluid distorts with force is how the fluid is defined. The force applied is shear and the reaction to the force explains how equipment and processes need to be configured to react. Within these distortions, all the laws you learned in school still apply. These laws of conservation are the fundamental functions that define fluid flow. Take conservation of mass – for a fluid with a set density, the volume of the fluid will not change with time. Because the fluid is incompressible, then the velocity of the fluid must interact in a unique way for a given fluid that can be monitored by continuity equations. What this means to you and me is that the fluid can be analyzed by math long before experiments are run.

In addition to conservation of mass, there must also be conservation of linear momentum. In this case, the momentum of the fluid flow must be equal to the net force applied. What this function provides, is an understanding of how the forces applied relate to viscosity. Combining these two laws (and the subsequent equations) provides the basis of understanding of how shear rate and viscosity interact to describe fluid flow for coating operations.

Now that we get that the bulk of the fluid is a function of the shear rate and dynamic viscosity, we should consider what is happening at the boundary conditions. The boundary conditions are where the fluid interacts with the walls of the equipment, the substrate, and the air between the fluid and the substrate. At these areas, the mathematical functions point to a number of factors that play a role. High on the list is the balance between surface tension and viscosity. If one is a stronger player than the other, the pressures and forces involved will need to be altered to encourage the fluid to adhere to the substrate.

Now one of the main questions I have been asked by others outside our industry is why the fluid doesn’t simply fall off the substrate. While gravitational forces need to be considered, the mathematical functions point to surface tension, viscosity, and process speed as forces that can be manipulated to defy gravity. So while we don’t walk on water, we do make water walk on air!