You could try this:
\documentclass[12pt]{article}
\begin{document}
This is a sentence.
This is a sentence.
\fontsize{8}{9.6}\selectfont
This is a sentence.
This is a sentence.
\fontsize{12}{14.4}\selectfont
This is a sentence.
This is a sentence.
\end{document}
The second argument of \fontsize is the interline spacing. If I'm not wrong, it's generally 1.2 times the fontsize (see Why is the linespread factor as it is?).

Note: the footnote size is based on the documentclass size. So, if you have an entire page with tiny font size, the footnote can be bigger than the main text, which can be strange. It's probably a bad typographic idea to change the font size in the middle of a document by this way.
Edit after a comment:
Seems also compatible with math mode:
\documentclass[12pt]{article}
\begin{document}
This is a sentence.
\[E=mc^2\]
This is a sentence. $E=mc^2$.
\fontsize{8}{9.6}\selectfont
This is a sentence.
\[E=mc^2\]
This is a sentence. $E=mc^2$.
\fontsize{12}{14.4}\selectfont
This is a sentence.
\[E=mc^2\]
This is a sentence. $E=mc^2$.
\end{document}
