Do people prefer one big story or separate chapters?

I am wondering.

I am part way through writing a story inspired by the April "Take your daughter to work day" challenge. It's turning out to be a bit longer than I had expected, so I would like to get some or all of it posted before the end of the month. But I have a question.

I am writing the story in scenes, each of which is between 600 and 1,000 words in length and ends with a revelation or minor cliff-hanger - what Blake Snyder in Save The Cat calls an 'act out'. The whole thing will likely be somewhere around 10,000 words.

Do readers on this site generally prefer one big file to scroll through containing the whole story, or is it OK to post the scenes one by one, maybe every day or two?

All suggestions welcome!