I have applied to PhD programs in engineering in the US. I have been early in applying to most programs (deadlines range from mid-December to mid-January). I have not contacted any professors prior to applying, as I have been told by many that it would largely be a waste of time. Instead I reached out to several grad students and read/skimmed through many recent published papers by faculty. In my statement of purpose, I talked about at least two professors that I thought had interesting topics for research and why they interested me. I tailored this part of the statement for each program.
My question is, is it appropriate to contact faculty post application submission? I would like to say hello, let them know that I have applied and that I would be interested in working with them if I am fortunate enough to get in, and ask them to keep me in mind if they are looking for students.
I thought it might be a good idea to just put myself out there. Who knows? Maybe they'll recognize my name once they start going through applications and give it another good look. But I also do not want to annoy them. I recognize that these professors are busy and that they get many of these emails every day. I want to be considerate of their time too. I also do not want to come across as being arrogant or silly or needy..
What is your expert advice? Would you recommend that I sit tight? With my application already out of my hands, I understand that there is nothing I can do now to improve my chances. But I am always hoping. Thanks in advance for your advice!