Has a totally blocking physical partition ever been used in between the slits in order to keep a particle waves to join after having gone through the two slits?
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This sounds to me like a home-experiment; see this answer for photos of a quick&dirty setup, and the other answer there for advice on constructing a more traditional two-slit system from inexpensive materials. Note that, to understand what you're seeing, you'll need to know how the single-slit diffraction pattern is "convolved" with the double-slit diffraction pattern; this is completely skipped in popular-science descriptions of the double-slit experiment, and it's even elided in some introductory textbooks.
If your partition is absorbing, you would expect to see (half of) the single-slit diffraction pattern on either side of the partition.
If your partition is reflecting (and many smooth surfaces are "glossy," and become effectively reflecting when viewed at small angles), you might recover some double-slit interference. An individual photon might reach the image plane directly, or might come instead from the reflection of the single visible slit. The quality of this reflection-slit interference pattern will depend on the smoothness of your reflecting partition; there is room for confusing non-quantum weirdness here.
If I were going to spend an afternoon trying this with a laser pointer, I would paint a microscope slide black, use two taped-together razor blades to make parallel slits in the paint, and use a piece of cardstock-weight paper as the partition. The first three versions of the setup wouldn't work because that's what building an experiment is like. But it's not immediately clear to me that you would need any expensive optical equipment, or even a partition that extends all the way to your image plane. The end goal would be a setup where you dramatically remove the paper partition downstream of the slits and the much wider double-slit interference pattern suddenly appears on your wall.
(I don't expect to have an afternoon to spend on this for quite a while. But if you do, please come back with pictures!)
rob
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