Sorry for the late response, it took some time to get all components for testing.I've ordered a few solar panels:53x30mm, 5V 0.15W (30 mA)68x36mm, 5V, 0.3W (60 mA)100x28mm, 5,5V, 0.22W (40 mA)plenty of zener diodes for different voltage and BAT54 schottky diode.After some testing I decided to use 5,5V, 0.22W solar panel, 1N4733A (5.1V) zenner diode to limit voltage and BAT54 schottky diode to prevent discharging.With 1N4733A I got voltage drop ~0.1V (without load), it's appropriate as for me.BAT54 has reverse leakage current 2μA at 25V, it also fits my requirements.Thank you for help.
How long does it take to recharge the supercap, once discharged?
Depends on the illumination intensity, the capacity and the solar panel current. From the capacitor equation Q = CV, it is approximately true that (delta t) = C*(delta V)/I.
If you bother to do the experiment yourself, you will discover that it works as well as it is predicted to work.These devices obey the laws of physics, so you don't actually need to depend on someone else's results.
The problem you will face is that when the cap is discharged it will never let the panel produce power.The cap will demand a HUGE amount of current from the panel which will drop it's voltage down too low to charge the cap at all.
It might work a little, but it certainly won't be efficient at all.So if the cap is down to a voltage which kills your project, say 2V, the cap will pull the panel voltage down and keep it down at 2V. The panel might be in direct sun and able to produce 0.2W, but not at 2V, it might produce 0.02W.As a minimum you will need some kind of PWM controller to allow the panel to be operating at a higher voltage than the discharged cap.