If you have water vapour (as in 100% H2O) at 55°C under normal pressure, you should expect condensation even before the vapour comes into contact with the cooler air.
So, you either have humid air at 55°C or water vapour at >100°C, or pressure conditions much below ambient pressure.
Actually I have a drop which is heated at 55 degree. So the vapor will be at 55 degree. And the air near to it is at lower temperature (35 degree). I am confused whether condensation is purely dependent on tempertaure difference or anything else?
As a first assumption, I'd say condensation depends on humidity and local temperature. It also requires a condensation nucleus, but that's usually not a problem.
With the 55°C droplet, your question becomes rather interesting. You'll have several effects occurring at the same time: evaporation, diffusion and heat transfer. I expect the droplet size to be a significant factor.
Condensation? In this case it depends on the relative humidity of your 35 °C air. If that is at, or "near", saturation (RH = 100 %) then you will have condensation in the air bulk, since the air at the interface of the 55 °C droplet is saturated. If the 35 °C air is not "near" saturation then condensation will not occur. You can quantify what "near" means by looking in an air--water Mollier chart (mixing of the two moist air masses).
Time for condensation? Probably "fast" by most (human) measures. However, even if, a moist air mixture is supersaturated, condensation may not occur if nucleation is prevented (but such a mixture is of course unstable).
In my case, RH is 73%, dry bulb temp is 25 degree, wet bulb is 21 degree. So the calculated dew point is 20 degree and absolute humidity is 17g/m3. Is there any chance of condensation in air?
Use a model for evaporation as a molecular diffusion -- taking into account the heat of evaporation -- The time of full evaporation of 10 micron droplets - is not long (msec) &&& if condensation is possible - it may occur only near droplets surface -- and tiny tiny droplets that formed under these conditions .. near surface of "motherdropet" -- will evaporate much faster than ms -- and here have to take into account the enthalpy of condensation and evaporation (the Hysteresis and additional energy loss in this case). I think it very and very fleeting)// if you can solve this problem - this can be a great discovery - since such a mechanism is supposed to be a mechanism for effective heat exchange - but so far no one has done so