[en] The observed escape of ions from the ionosphere of Titan suggests a potential role of the solar wind in the interaction with the upper atmospheric layers. We investigate such a plausible scenario using a hydrodynamic fluid approach for the plasma expansion in the upper ionosphere of Titan, combining (Maxwellian) electrons and three different species of positive ions which interact with the solar wind electrons and protons. Using a self-similar transformation, a numerical analysis is performed to solve the basic equations and characterize the plasma density, velocity, and electric potential during the expansion. It is found that increasing the solar wind proton number density leads to a reduction of the ion escape, while the effect of electrons is opposite stimulating the ion escape. Moreover, the expansion domain does not change for more energetic protons. The heavier ions play the leading role in controlling the ion escape, i.e. by comparison with CH${}_5^{+}$ ions, C₂H${}_5^{+}$ ions appear to have more influence in the loss from Titan ionosphere. For a higher temperature contrast between ions and electrons, the depletion rate of the density increases and the ions move faster, leading to a higher ionic loss.