We have computationally investigated the introduction of copper elemental particles in an inductively coupled plasma torch connected to a sampling cone, including for the first time the ionization of the sample. The sample is inserted as liquid particles, which are followed inside the entire torch, i.e., from the injector inlet up to the ionization and reaching the sampler. The spatial position of the ion clouds inside the torch as well as detailed information on the copper species fluxes at the position of the sampler orifice and the exhausts of the torch are provided. The effect of on- and off-axis injection is studied. We clearly show that the ion clouds of on-axis injected material are located closer to the sampler with less radial diffusion. This guarantees a higher transport efficiency through the sampler cone. Moreover, our model reveals the optimum ranges of applied power and flow rates, which ensure the proper position of ion clouds inside the torch, i.e., close enough to the sampler to increase the fraction that can enter the mass spectrometer and with minimum loss of material toward the exhausts as well as a sufficiently high plasma temperature for efficient ionization.