brainstorm some product names:
corn mesh= The Corn Cob Compostable Drain Cleaner
enzymes= Everyday Green Drain Machine
shaver= The Drain Hair Mower
pet monster/worm composter in drain= Feed ME, Green Drain Composter
flo-bee= The Drain Monster
flat screen= Custom Drain Protector
mesh drain ball= Woofle Ball Drain Guard
design cover= Build-your-own Designer of the Drain!
drain mill= The Daily Grind Drain Mill

My chosen idea, The Daily Grind Drain Mill, came about by thinking about how food always gets caught in the sink drain protector, and it's gross. I don't like cleaning other people's weird gunk out of the sink and pounding it loudly against the side of the garbage to get it emptied. Then I thought about how a food mill looks like a drain, except it has a series of interchanging blades on the bottom that grind particles into liquid. Why couldn't we use the same concept for a drain?

I went to the hardware store and tried to find parts, such as a handle to turn the blade on the drain. I asked the the guy helping me at the store if he had handles or cranks. He brought me to the kitchen section and pointed me to a life size food mill. Wow, that was not at all what I was looking for. Then I glanced to the left and saw.... a flour sifter! Yes! That is the same concept, only it is the size of a drain. So I took the stuff home, disassembled the flour sifter and repurposed it for the sketch model. (see images below)

There is already an enzyme drain cleaner (since 1966), but I would want to have people use this on a regular basis, like shower spray, after each use or daily. I'm not sure if that makes it different enough.

There is totally a drain shaver already! That is so cool!

There is thankfully not a patent on a drain monster. There is a vermiculture compost bin, however.

There are flat screens as drain protectors, but it would be easy to alter one (a la the coffee cozies), to become patentable.

I didn't find a patented mesh drain ball.

I didn't find personified drain covers.

I didn't find a drain mill.

Enzymes you use to clean your sink and drain that eat the common stuff in drains, breaks down hair, body fluids, toothpaste, etc. Drain cleaners like it exist, but it would be nice to have something you used on a daily basis or something when you wanted to keep the drain from building up gunk. It already has a market, but it would be a modification, and I think it is feasible, it just requires research and a change in intensity of the current product.

Similar to a disposal, it would be great if when you closed the drain, you could pull rotating blades (like an electronic shaver) up to the drain to shave any hair into super small pieces. I don't think this is super feasible, but it is novel, but probably too dangerous to market, except people spend lots of money to rid drains of hair, and it's not less dangerous than a disposal.

I really want a pet monster who lives under my sink and eats my compost, and anything else I put in the drain. Not sure if that is an idea, except it could be, for a geneticist. Feasible, no. Novel (except the Flintstones movie). Marketable, definitely.

Use something like a flow-bee to suck stuff out of the drain. Feasible/novel--there is a flow-bee, but it would have to be like an attachment for a wet-dry vac. That might be more feasible. I believe that's marketable, especially as an attachment. Those are two ideas: flow-bee and attachment.

A flat screen that is not inverted, kind of like a diffuser on a gas range, would be a simple way to alter the often rounded or divoted drain protector. It's not super novel (alteration), but would be feasible and easy to market.

For my sketch models, I chose to make:
-a mesh ball with weights to fit in most types of sinks. ($3.99)
Novel- Yes, it passes the trendy houseware gadget test at Target, people would buy it because it was novel.
Marketable- Yes, I believe so.
Feasible- I built a version of it, but I want to toy with it more. It isn't the right size or built with quite the right weight and screen.

-a drain screen with food-mill type attachment to process large particles and to help clean the screen. ($7.99)
Novel: This is my favorite idea because it is novel and cross-product in a useful way.
Marketable I've received feedback from lots of people that they thought it was a good idea, not in the me asking them way, but by showing them and having friends and strangers say, "hey, that's cool! I would buy that," out of a handful of ideas that I showed them.
Feasible
Well, since I built one, and it seems to work, I think it is feasible!

-personified drain screens, that you could design to look like anything. ($.99 each, or in a kit, $4.99) for example, ladybugs, monsters eating what fell into the drain, or venus fly traps (like my biomimicry).
Novel: I've never seen anything like this.
Marketable: People love customizing things, but it's kind of a gross thing to start as a ladybug, and end up covered in muck. I think it would be easier to sell at first, and harder to get people to buy them again.
Feasible: This idea is inexpensive, and I think China is meant for a project like this because it would require lots of cheap plastic components.

I tested these sketch models with my roommates, which I know doesn't quite fit the non-friend test, but two of them are professional designers, and they are never afraid to disagree with me, and did have criticism, so I felt it was a good first market test.

It would be great to be able to genetically modify a plant to consume the stuff in a drain. Kind of like the monster in the Flintstone's movie.

combine: What ideas or parts can be combined?
It could also be a food mill.

adapt: What ideas could I incorporate?
combine the strainer with a trash compactor or an incinerator or garbage disposal.

magnify: Can it be duplicated?
I think it should be duplicated and become something easy to toss, or that dissolves over a short period once exposed to water (within a thresh hold)

modify: How do I add extra value?
Make it fit in any drain.

put to other use: What else can it be made from?
It could be plastic or metal.

eliminate: What feature can I understate or omit?
The baby consuming part (babies wouldn't use it because it would be dirty).

reverse: Can I interchange components?
It could be more like a funnel, the mesh could be a smaller component.

rearrange: Backwards? Inside/Out?
Maybe they should be inverted strainers, which seem to be easier to clean.