It's not silent, but it isn't as fully articulated as it is in many contexts; the closure is audible (and visible on an sound spectroscope), but there's no (or minimal - depending on register) plosion. As an example, there's a difference between the sounds of 'hot land' and 'Holland' (apart from the obvious difference in the second vowel).
In standard Oxford English, for example, the "t" is pronounced, but often not released (as BobK describes) in the words you cite. In many British dialects, such as Cockney, it is replaced with a glottal stop: the airflow is cut off at the back of the throat.
In many British dialects, the combination "tl" (as in "butler" or "bottle") is often pronounced as a click sound for which we have no separate letter, similar to (but not exactly like) the kind of lateral click which is a feature of some African languages, like Xhosa. It sounds a bit like a mixture of "k" and "l", and indeed small children learning to speak are apt to say "bockle" for "bottle".
In old-fashioned BBC English, the "t" was enunciated and released very, very carefully. BBC English was used on the radio in the days when reception was often very poor, and so a deliberately over-careful pronunciation helped listeners decipher what was being said against a background of pops, whistles and interference.
The t is pronounced both in next and in next day. (At least, where I am from it is.)
I've got a question about assimilation. Wouldn't it take place in a phrase like 'next day'? I mean assimilation of /t/ with /d/? Also in the example from Peter123's question ('next station'), shouldn't elision and assimilation take place? Not so much time ago, I was said by my teacher of phonetics that in such a case ('next station') /t/ from the word 'next' would disappear and remaining /s/ would assimilate with the initial /s/ from the word 'station.' In my way of thinking it would go like that: /'nekst 'steiʃn/ --> /'neks 'steiʃn/ --> /,nek'steiʃn/ --> /nək'steiʃn/ (in fast speech). What do you think about that? Comments from other member are welcomed as well.
Last edited by seba_870701; 10-Feb-2008 at 16:09.
Reason: I added something..