Fuel injector flow vs time relation assumption

I think that another assumption about the fuel injector flow realtion with time that is one to one linear realtion that is if the pulse witdh equal to the cycle time flow will be maximum, how accurate is this assumption?

Maximum flow would occur at 100% duty cycle if injectors behaved in a perfectly linear fashion, but sometimes injectors are a bit non linear near their upper limit, which can cause max flow to occur at values a little below 100% duty cycle.

All injectors (even DI injectors) have three phases of operation, Dead Time, Non Linear and Linear operation. The Dead Time is the time that it takes for the coil to energise sufficiently to generate enough force to lift the injector pintle off of the seat. The Non Linear region is when the pintle has lifted off of the seat and is starting to flow fuel, but hasn't fully opened. In this region the area available for the fuel to flow through is rapidly changing and can have some strange behaviour. There are some injectors that will lose flow at a larger injector pulse width as the pintle opens fully, hits the end stop and bounces back down towards the seat.

Once the Non Linear region has been exited, the injector flow rate will remain linear in that x% of increase of injector pulse width will result in x% increase in fuel delivered, i.e. an increase of 10% in the Injector Pulse Width will deliver 10% more fuel. You can run into a condition at high Duty Cycles for the injector where the Flow vs.Pressure through the injector get to a point that either the injection spray orifices reach peak flow, or the seat opening reaches peak flow and this causes the flow to stall (similar to the behaviour of a turbo restrictor) and no or less fuel is delivered.