I’m wondering what would happen if the filter paper in a vacuum filtration process is bigger than the buchner funnel diameter? I mean would some differences occurs? Or would the whole experiment damage? If yes, may I know how and why?
I in fact made this mistake once while attempting to dry casein isolate from milk. If the filter paper is larger than the diameter of the büchner funnel, you will risk there being gaps on the side (or "waves" as Vinz called it in his comment), due by crumples in the paper caused by fitting the large paper into the small diameter of the funnel. The air will flow through these gaps/waves. Hence, the vacuum filtration will not work effectively, if at all, because the air is not being pulled through the paper but rather through the gaps on the side. We learn from our mistakes. As to how to fix this issue, the comment by MaxW should help you solve this.
The above photo shows two of my results when attempting to dry the casein isolate from milk. The contents of the left petri dish are predominantly a result of using a too large filter paper during vacuum filtration (among a few other errors incurred by attempting to fix this mistake), while the contents of the petri dish on the right are a result of using a well-cut filter paper that suited the diameter of the büchner funnel.
There will be leaks around the edge of the paper. If the size difference is not too large (a few mm at most) you can remedy the situation as follows: (1) turn on the vacuum with only the filter paper in the funnel, (2) take a spatula and run the tip of the spoon around the edge of the filter paper, creasing it into the corner between the flat bottom and the sides. This usually works for me.