Due to high surface area to volume ratio in MEMS devices, heat losses are very high so the chances of flame quenching is very high. Is there any way to estimate the area of the heater to avoid flame quenching.
It is a rather complex subject, hard to generalize without specific details.
I would say that generally the smaller the structure, the smaller the efficiency between released chemical energy/required electric initiation energy becomes. It is not so much the area of the heater, bridgewire, EBW wire etc that matters most, its mostly the amount of electrical energy and how fast it is released into a small volume over time. For very small stuff the stored chemical energy will probably be less important compared to the electrical impulse in a good design. Thermal conductivity, reaction buildup acceleration, propagation velocity of the chemical reaction, molecular weights etc all figures in for optimum output impulse, (Sum over m*v for the ejected molecules and ions). Also, available electrical energy figures in. Electric explosive impulses can be made very small, and then material choice is mainly a concern for the accelerating plasma giving max mechanical impulse. Energetic materials at such small scales need to have very quick reaction times. Initiation is not so much heating as putting in enough energy fast enough in a small volume to exceed the reaction energy barrier in the material and creating a reaction volume large enough so that it will sustain the reaction. Calculating this is mostly a matter of comparing released energy in the reaction volume to energy lost by heat transfer to the surrounding unreacted material over time. Supplying energy to slowly is terribly inefficient and causes other failure modes as well.