Quitting a PhD program from one university to different university due to change in research interest with the current advisor I started working with the current advisor 2 years ago in my master's program and after a year he asked if I would like to convert to the PhD programme. I am a chemical engineer while my advisor is a mechanical engineer (he is an adjunct faculty in my department) so I believed he would provide me with enough guidance to pursue interdisciplinary research. I said yes and started working with him on a research project. The current research project was a challenging one to develop a novel detection technology and I decided to take up to project to expand my expertise. But one year into the program I realized that the technique I am working to improve is absolutely not reproducible. Moreover, the researcher whose fundamental work the idea is based on has encountered 4 paper retractions. In addition to all this, I never get any acknowledgement or guidance for any new idea I am trying to work on. I also have realised that this has lowered my motivation and my relations with him are heading south. For eg: during our individual meetings I have noticed when I bringing an idea or results pertaining to that idea he mostly sleeps or dozes off. I really do not think that the project I am working has any scope and all the ideas or talks I have with my advisor are extremely superficial and derivative from different papers. Like, let us see who our industrial competition are instead of working on the basic science level or suggesting ideas such as I recently read a paper on something why don't you make that as a part of your research. All these issues aside, my professor also sometimes insults me and regards me as lethargic despite spending nights in the lab. I am extremely interested in the nanobiotechnology area of research and I wish to apply to a different university for a PhD program.

My question is: Should I quit or continue under those circumstances? In case, I decided to quit, shall I be accepted by another program and in that case, how I can reformulate my decision to quit to the prospective program. Is this kind of behavior is what should be expected in academia? Should I also consider quitting PhD altogether if this is the way advisor push or motivate students?
Definitely move on.  I would talk with both chemE and mechE department heads at your current university (they may have an option for you without having to move on to another place).  In parallel or series, you can apply elsewhere.  I wouldn't even dwell on the flareup with the other professor but maybe try to make it a positive that you have some previous research.

Finally, be careful what problem you pick.  Make it tractable and likely to succeed. Not building a supercollider, not waiting for a Shuttle experiment, and not relying on questionable previous work.  Oh...and pick an older, established advisor who does not have an aggressive personality.  

At this point, you really should just find something and get the union card done.  Don't worry about discovering gravity.  Some research problems can really be done in a very short amount of time (I know Ph.D.s who wasted years on a flawed problem and then did something else for a year and wrote it up and got the sheepskin.)  Time is ticking for you personally so you need to look out for yourself and do something that works and quickly.