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Whether wiping or rinsing under the tap, the blade should be throughly dried following the shave. I personally set the blade aside, rinse and dry my face, wash out my brush and bowl, and apply A/S, before tending to the blade. Depending on the mineral content of your water this minute or two may leave a water spot or two, especially if it is a mirror finish. Satin finished blades can also be effected but not as much as the mirror finish IME. So if that is going to be a concern tend to the blade before you tend to your face, brush and bowl.
I wipe the blade with a Kleenex type tissue when I am done. I look at the scales, inside and out, wipe them with a dry tissue if there are any droplets inside or out. I then strop it 20 to 30 round trips, depending on the phase of the moon, and if I am going to apply any rust preventative I use a product available from Birchwood Casey called R.I.G. (rust inhibiting grease). I use this stuff initially with a Q-tip applying it to the blade, wipe it off with a silicone gun cloth, and put the razor in a dry place where no moisture is present. There are many lubricants/rust preventatives that can be used alternatively.
Plain old mineral oil, Ballistol, Tsubaki oil, Tuf-Glide among many others, can also be effective in protecting our blades from corrosion. A product called Renaissance Wax is also great for protecting both blades and wooden scales. This stuff was recommended to me by Robert Williams the custom razor maker. An application of Ren-Wax followed by the gun cloth impregnated with R.I.G. and I sleep soundly knowing my blades are protected. Having said all of that I, being basically lazy, stopped religiously applying the aforementioned rust preventives to my blades. I live in a tropical climate, have air conditioning on most of the year, and therefore the humidity is largely removed from my environment.
I've read threads on the topic of where to store our straight razors and some members leave them in the medicine cabinet, or elsewhere in the bathroom, and suffer no negative consequences due to corrosion. I'm from the ounce of prevention being worth a pound of cure school, so I store my blades a drawers outside of the bathroom in a dry environment. All of the above is based on 7 years of experience with straight razor shaving on pretty much a daily basis. As in everything connected with this hobby YMMV so whatever works for each individual is sorted out by trial and, unfortunately, error. I hope this months tip is useful to someone out there in Cyberspace ....... Smooth shaving .......