I would like to know scope of research in leaching pesticide due to heavy rainfall or spilling of pesticides on the surface. Is there any scope for mathematical modelling of leaching as in chemical engineering point of view?
I think there is considerable research in this area. Essentially you want degradation rates, adsorption/adsorption, hydrophilic/hydrophobic, and soil properties to movement of the pesticide. This will be an extensive literature review (possibly a good sized book if you include all pesticides). You will need a university library to gain access to the older literature.
Typing in "pesticide leaching model" as a google search yields 957,000 hits. The top two hits reference PEARL, GeoPEARL, and KTURF models for soil leaching of pesticides. The existence of such models suggests considerable knowledge about the fate and movement of pesticides over and through soils in regards to the physical and chemical properties of the pesticide and the soils.
Due EU directives that limit pesticide concentrations in groundwater, all regulatory approvals or renewals require experimental demonstration (backed by modelling) of leaching potential. As Timothy pointed out there is a mountain of data and numerous models available and the earliest models (such as PRZM and LEACHP) date back to 1980's / 90's). Because there is no single value for many of the input parameters such as degradation half life and partition coefficients, it is useful to run Monte Carlo type simulations with range of available inputs to get a good handle on risk to GW etc. USEPA website has good info on models available.
The big risks are soluble chemicals that are not strongly sorbed, on sandy soils with underlying aquifers that are used for drinking or irrigation water.
As we know that we can not always prevent chemicals that are needed for crop production from reaching the soil, the best approach is to collect the leachate before reaching the aquifer and take the chemicals out and save the water for reuse. We have a first design system to do it.