P. Pallav, PhD

In the next page we will will configure what we call (flow) channels in the theoretical set up with the flat and later curvy molars of the previous pages.

Materials, used for plastic restorations, such as composites, glass ionomers, etc. generally wear faster or even much faster than enamel. These materials tend to occur in the parts marked with color; the fissures (grooves) between the cusps.

Flow Channel

This picture is a cross-section perpendicular to any of the fissures. In this case the cusp of the upper molar is drawn too. The dotted lines indicate the width of the channel and the points of contact.

The picture represents the narrowest cross-section for the food, which flows square to the plane of drawing. Just behind or in front of the plane of drawing, the cross-sections look similar only all the heights are greater.

Effect of the Height

The flow conditions are explained with Example 3 in Velocity in Fluids. Because the fluid follows the way of the least resistance, more food will flow at the center where the height (h) is greater and more wear (erosive activity) will occur here.

The height at the margin in the picture is about 70% of the height at the center. Because the erosive activity varies with h², it will be 50% here (0.7²=0.5).

At first glance the effect of the height on the wear rate may seem to be in contradiction with what is explained with our set up in the previous pages. There the erosive activity ('wear rate') varied with 1/h² while here it varies with h², which is completely the opposite.
This arises because in the other pages the height (h) varied in the direction of the flow. Here it varies perpendicular to the flow.

This is a top view on the channel. The upper molar and the food have to be transparent for this. 

The horizontal dash-dotted line through the contacts is the position of the cross-section above.

The arrows refer to the magnitude and the direction of the Velocity Gradient at either surface.
Note that if the arrows would represent the velocity of the food, the differences in the lengths would have to be much greater. Right now, the arrow at the center is nine times as long as the smallest arrows at the not-yet-contacts left and right. In this case, the speed of the food at the center is twenty seven times the speed at the contacts.

The pressure at the horizontal dotted line is about the same from left to right. This is because the pressure is constant square to the direction of the flow. The fluid will always flow in the direction in which the pressure drops the most rapidly, because that is the direction of the forces acting on it. The only (very small) inaccuracy is that we forget about kinetic effects (mass, inertia) after all, chewing water will not give a lot of stresses.

A structure like this works like a channel, because the contacts are in the way. The pressure does not vary from left to right, therefore the erosive activity varies only with the velocity gradient, which varies with h². With 0.3 millimeter at the contacts and 0.9 at the center (1:3) the ratio between the erosive activity in these places will be 1:9.