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Having installed (and removed) miles of caulk, I have developed a strong preference for Polyseamseal Tub and Tile Adhesive Caulk. It is touted as being mildew "proof. It is not quite that, but it is by far the most mildew resistant caulk I have ever used. Very few products are as good as they say they are, but this is one of the few that makes the grade.
I have three daughters who shared the same tub/shower enclosure for over ten years. Needless to say, it wasn't cleaned as often as their usage would seem to demand! Silicone and other latex caulks lasted for a year at best before discoloration would begin. Polyseamseal lasted for nearly five years without a hint of mildew. Even at six years, I could probably have done touchups and gotten away with a few more years.
Make sure that you prepare the walls properly. I have all the dirty details online at https://www.naturalhandyman.com/iip/infxtra/infcau.html .
You may or may not have problems finding this brand of caulk. None of the home stores in my area carry it, nor do any of the hardware stores! I was fortunate enough to find it at a local plumbing supply house, so keep looking! Remember to get the right one... Polyseamseal has a full line of caulks but not all are as mildew resistant as their Tub and Tile Adhesive Caulk.
Polyurethane caulk is available in many home and hardware stores. However, I don't believe that there is a polyurethane caulk available specifically for bathroom use... yet. In my experience, even manufacturers who produce polyurethane do not recommend using it in bath enclosures. Part of the reason may be that polyurethane is not as mildew resistant as the best "mildew-proof" acrylic latex caulks, manufactured by companies such as MD (Macklanburg-Duncan) and Polyseamseal.
It is a given that polyurethane is superior in both adhesive ability and flexibility (or "stretchiness") than either latex or silicone caulks. This is great in some applications, especially exterior joints where there is significant seasonal expansion and contraction. It is not generally necessary in bath enclosures. The stress on the joints in bath applications is just not that great, so the additional adhesive strength is essentially overkill! Since ALL bathroom caulks eventually become mildewed or simply loosen, the extra adhesive strength may even work against you come repair time!
As far as mildew resistance goes, I would choose acrylic latex caulk over silicone caulk any day, especially the "mildew proof" varieties mentioned earlier. This is from personal experience with miles of mildewed caulk!
To be compassionately blunt, the so-called caulking strips are pretty much useless as a caulk replacement! They may have some usefulness in low moisture situations where the decorative appearance is more important than actual function. However, the adhesive is unreliable and, in my experience, will not last very long. As more than a few of my clients discovered to their dismay, the strips may "appear" to be working... while the wall behind is being savaged by moisture!
I would strongly suggest against using them within any tub or shower enclosure.
Thanks for the useful tip. Rest assured I will give it more than a footnote when I update our caulking page!
Filling the bathtub prior to caulking was a traditional method of getting the best possible seal... especially when the tub was not securely supported beneath! Amazingly, few home repair books even mention it, even some I have dating back to the fifties and sixties. You would have thought it would have been gospel in those days, since the caulks were much less flexible and not nearly as adhesive as they are today!
As many handymen discover, tile installers rarely if ever caulk around a tub in a new installation... they use the same grout as they did on the walls. Needless to say, within a short time the grout begins to break. Caulks are designed to solve this problem, flexing and stretching to adjust to movement in the tub. However, if the movement is more than a small amount, the seal will eventually break and the caulking will need to be redone.
Hence the second value of your tip! If anyone has caulked and discovers a break in the seal, recaulk yes... but first fill the tub with water to settle it! Rub-a-dub-dub. three handymen in the tub... Oops!