A Fluid Dynamics Primer for the Contact Lens Fitter
By Gary R. Bell, OD,
A tractor trailer truck barreling down the highway may relate to the eye and contact lenses more than you think.
You might wonder what fluid dynamics has to do with contact lens practice. Remember that contact lenses float in a fluid environment on the eye. Patients often report that they feel their lenses are "rubbing" or "scratching" their eyes, like the lenses are causing unwanted friction. Friction in a fluid environment is called viscous drag. In our case, the viscous drag problem is that "rubbing" lens.
Unfortunately, things get complicated. Blinking interrupts the fluid flow and makes it turbulent. The neat mathematical formulas of fluid flow break down in turbulent environments. Still, fluid dynamics can help us understand contact lens phenomena in a generalized application.
A Roadside Scenario
Picture yourself on the shoulder of a highway. As a semi-tractor trailer passes by, an erratic blast of wind hits you. A nearby leaf is sent spinning wildly. What you have felt and the spinning leaf have demonstrated are turbulent vortices of air. The air traveled from the pathway of the truck to where you felt it, showing that turbulence can and does propagate outward from the pathway of its creation.
If you moved closer to the truck, the force of the wind would increase dramatically. If you moved back from the pathway of the truck, the force of its wake would decrease. Turbulence radiates out from its original pathway, but dissipates with distance. If you stayed in the same place, but the truck slowed down, you would feel much less turbulence. Velocity of a moving object in a fluid affects the amount of turbulent friction it creates.
An empty truck would create less turbulence than if it was loaded down. Mass or density also has a direct effect on the amount of viscous drag created by an object moving in a fluid.
If the truck, traveling at the same speed, had an efficient aerodynamic shape, we would notice a decrease in turbulent wake. Aerodynamic shape affects the amount of viscous drag that a moving object in a fluid gives off. Spoilers hold trucks closer to the road. This restricts the amount of air passing under the truck, also reducing the amount of turbulent wake that the truck throws off.
If the truck had dirt caked on it, but was followed by an identical truck that was clean and had a fresh paint job, you would notice that the dirty truck gave off more turbulent wind than the clean truck. This dirty/clean differentiation shows the fluid dynamics concept of skin drag.
Trucks to Contact Lenses
Let's look at each characteristic in our truck example to see how it applies to contact lenses.
Velocity. The fast-moving truck increased winds and produced wild vortices. Fast-moving contact lenses are less comfortable, eliciting complaints of the lenses "scratching" or "rubbing." Rapid-moving lenses are strongly associated with increased desiccation, such as 3 and 9 o'clock staining. Turbulent forces of fluid may cause these stains. Because velocity is squared in fluid dynamics formulas involving immersed objects, reducing the movement of a loose lens increases comfort exponentially.
Distance from pathway. The force of the truck's wake was inversely related to the distance we stood from the truck's pathway. This relationship is also true with contact lenses. "Dry eye" patients don't really have a dry eye, but a tear film of reduced thickness. They experience more lens awareness and have more friction-related staining than those with a thicker tear film. Rewetting eye drops give immediate, but temporary relief, perhaps by increasing the distance of the lens from the corneal epithelium.
Mass. A fully loaded truck gave off more turbulence than an empty one. Likewise, reducing RGP lens mass increases comfort. Mass is less critical to comfort in soft lenses because they move very little. Recall that even a fully-loaded truck gave off very little turbulence if it moved very slowly.
Figure 1. Aerodynamics and contact lens shape. Curve A shows the raindrop shape. Curve B shows the preferred shape for contact
Aerodynamics. The aerodynamic truck produced less turbulence than the boxy truck. Aerodynamic principles also apply to contact lenses. The ultimate aerodynamic shape is that of a falling raindrop, which air resistance stretches into a narrow ovoid with a pointed end. A contact lens can't look like a raindrop, but the lens edge can be shaped in a manner similar to the bottom portion of a raindrop. However, the raindrop's shape is perfectly symmetrical, whereas the preferred edge of a contact lens, as established by Mandell and others, is asymmetric in shape (Figure 1). This asymmetry, also found in "ideal" wing shapes, is due to lift.
Lift. We mentioned earlier that a truck with a spoiler had reduced lift and produced less turbulence than a truck without such a device. This is why many expert contact lens fitters recommend fitting RGPs with "low edge lift." The ideal RGP edge is not symmetrical like the raindrop, but has the apex of the edge decentered toward the cornea. The tear flow on the cornea and the lens movement are in a curved arc, so the attacking edge of the contact lens bumps into the fluid particles of the tear film at an angle. This angular collision, called an "angle of attack," exerts a lifting force on the lens edge. This lift force adds to the drag force to increase turbulence. Decentering the apex of the edge toward the cornea neutralizes our angle of attack. This produces the low edge lift design, which is associated with improved comfort and reduced 3 and 9 o'clock staining.
Skin drag. The truck with the new paint job created less turbulence than the dirty truck. Similarly, contact lenses need a high quality, polished surface and wettability. The wetting angles of various materials are not as big a factor as we used to think. The newer Boston materials, for instance, have high wetting angles (Boston 7, 54 degrees; Boston ES, 52 degrees; Boston EO, 49 degrees), yet they are as wearable as materials with lower wetting angles.
Surface quality, on the other hand, is an important factor in lens comfort and wearability. The smoother a lens surface is, the less staining and discomfort it produces. The dramatic difference in comfort RGP patients experience when you polish their scratched lenses illustrates the power of a smooth surface. Minimizing the surface area of the attacking edge of a contact lens with the raindrop type tapering of the edge profile should minimize skin drag. Increased thickness is part of skin drag formulas. Reducing lens thickness should reduce skin drag as well as mass.
Another aspect of skin drag that plays a role in contact lens comfort is what's called a boundary layer. Boundary layer integrity exists in a "good wetting" contact lens situation. A non-wetting area of a contact lens is a boundary layer separation (Figure 2). A boundary layer separation increases turbulence. Patients with non-wetting lens areas experience increased discomfort and staining.
Fluid Dynamics of Dry Eye
For a dry eye patient who doesn't wear contact lenses, we can substitute the upper lid for a contact lens in our truck analogy, but we have fewer options in changing the design of the eyelid. If we apply fluid dynamics principles, we can roughly predict the location of corneal desiccation. The desiccation occurs, according to this theory, at the areas of maximum viscous drag.
|Figure 2. Boundary layer separation over a curved surface.|
|Figure 3. Cavitation: vacuum forces in a vortex create low pressure gas bubbles.|
Let's look at lid/blink dynamics to find the area of maximum viscous drag. As the blink commences, the upper lid moves down and nasalward. The globe retracts into the orbit an average of 3.0mm, producing a substantial inward force vector. At the same time, the lower lid moves nasalward about 2.0mm. The nasalward movements of the upper and lower lids push the tear fluid in the nasal direction. Investigators have photographed a bulge of tear fluid propagated in front of the contracting upper lid, confirming the existence of an upper lid wake. When the two lids approach closure, the streams created by the two lids collide in the lower corneal area, producing an area of maximum viscous drag.
In a dry eye, reduced tear film thickness inhibits the dampening effect on the turbulent vortices. Each vortex in a fluid has a vacuum center that contains a low-pressure gas bubble. This phenomenon is called cavitation (Figure 3). This gas bubble can implode with surprising force when it strikes the surface of an object. A vortex of spinning fluid particles, with its power-packed gas bubble center, produces an erosive force when it strikes the corneal epithelium.
When we perform a tear break-up time test, we are looking for a boundary layer separation of the tear film. These tend to occur in the lower corneal area. Fluid dynamics theory suggests that these areas of boundary layer separation would occur near the location of upper lid deceleration. The way the break-up area changes with every blink demonstrates the chaotic nature of turbulent flow.
A fluid dynamics approach to RGP fitting suggests several lens design considerations. To reduce lens velocities, make the lens rather large (9.5mm 10.0mm), with a higher Dk (over 50). Use a junctionless design, with aspheric front and back surface. It should be thin with low edge lift. Make the base curve/corneal curvature relationship alignment or steep up to 0.50D. A little steepness adds thickness to the post-lens tear film, which helps the cornea dampen blink-related turbulence. With today's RGP materials, we don't need to depend on an oxygen pump to prevent corneal hypoxia and can instead look at designs that maximize comfort and corneal integrity. Lid attachment makes the lens an extension of the eyelid, not an independent source of turbulent shear.
Concerning soft lenses, the same aerodynamic tapering of the edge is mandatory for maximum comfort. The ballasted edge of a toric soft lens should have the shape of a "cambered foil," an ideal wing shape for slower aircraft. Several companies boast of such a design feature. Velocities are usually decreased with soft lenses, which increase comfort. The water-absorbing nature of the hydrophilic material reduces mass or density in soft lenses. Concerning distance from the pathway, Vistakon has steepened the recommended base curves of the new Acuvue 2 lens, often recommending the 8.3mm base curve, compared to the 8.8mm recommendation of the original Acuvue. The steeper base curve may increase the post-lens tear film thickness, which may help reduce dry eye symptoms. Tight lens symptoms are less of a concern with today's thin lenses.
You can request fluid dynamics formulas that apply to contact lenses from Dr. Bell at firstname.lastname@example.org.
To receive references via fax, call (800) 239-4684 and request document #73. (Have a fax number ready.)
Dr. Bell is in private practice in Corona, CA. He has served as a clinical instructor at Southern California College of Optometry and is currently serving as a vision care consultant for a regional Medicaid HMO.