Objective

Create a marketable proof-of-concept device that meets the customer need space of solving the foggy bathroom mirror problem after showering.

Outcome

Successfully created an inexpensive device that runs a thin layer of laminar flow over the mirror surface, collects the water at the base of the mirror, and recycles it back up to the top of the mirror.

The goal here was to come up with all ideas, not just the "good" ones; it is important to brainstorm all possible ideas out of the way in order to get to the best ones. As a joke, I suggested that if the mirror was already wet, it couldn't get foggy. Curiosity got the best of us and we ended up testing the idea out.

First Prototype

We took a trip to the local thrift store to pick up some used items for testing, and then made some quick 3D prints. We created three different small prototypes as shown in the pictures.

After testing the "deposit module" in the middle picture, we saw that running laminar flow over the mirror certainly had potential and was a much more creative solution to the problem than other solutions; most patents we had seen used either heat or some mirror coating to solve the problem. When running water down the mirror, the first half-inch or so was pure laminar flow, which was smooth enough to see oneself in the mirror. After that, the water quickly became turbulent. Here in this picture, I am holding the deposit module firmly against the mirror, and you can see the laminar region boxed in white with turbulent areas shown in red:

It can also be seen that as the water accelerated down the mirror, it became more attracted to itself rather than sticking to the mirror surface. This was not ideal, since we wanted the mirror to be completely visible to the user and have no annoying features or hinderances. 

As one who has taken a fluid mechanics course knows, Reynold's number is the dimensionless quantity that indicates whether or not a flow is laminar, turbulent, or somewhere in between. Reynold's number is defined by a characteristic length (in our case, it can be defined as the length of the mirror or the length of the deposit module's opening, depending on a few factors), the fluid density, fluid velocity, and fluid dynamic viscosity. The length and the velocity are the two most plausible elements of the equation that we could modify, so we opted to design several different deposit modules with different size openings, and also buy a new pump with a variable flow rate so that we could minimize the Reynold's number to the best of our ability.

Second Prototype

We tested several more deposit module designs and our new pump with variable flow, but noticed that when we minimized the Reynold's number, the water was flowing so slowly that it began to separate. This happened because there wasn't enough water to "wet" the mirror and it didn't have enough momentum to overcome sticking to itself. Think of a rainy window: if there is not enough rain, the water travels down the mirror in specific pathways instead of spreading out over the entire surface. Unsurprisingly, glass is quite hydrophobic. 

As it seemed, every parameter we tried to minimize for the Reynold's number began to maximize the flow thinning effect, so our device design became an optimization problem. I conducted as much research on this topic as I could, and created the following chart to help illustrate the effects on both problems:

Theta is the contact angle of the fluid to the mirror (determined by the hydrophilicity of the mirror surface), U is the fluid velocity, L is the mirror's length, D is the opening length of the deposit module, mu is the dynamic viscosity of the fluid, and gamma is the surface tension of the fluid.