  We study in this paper the Blume-Emery-Griffiths model in a thin film of
stacked triangular lattices.The model is described by three parameters:
bilinear exchange interaction between spins $J$, quadratic exchange interaction
$K$ and single-ion anisotropy $D$. The spin $S\_i$ at the lattice site $i$
takes three values $(-1,0,+1)$.This model can describe the mixing phase of He-4
($S\_i =+1,-1$) and He-3 ($S\_i =0$) at low temperatures.Using Monte Carlo
simulations, we show that there exists a critical value of $D$ below (above)
which the transition is of second-(first-)order.In general, the temperature
dependence of the concentrations of He-3 is different from layer by layer. At a
finite temperature in the superfluid phase, the film surface shows a deficit of
He-4 with respect to interior layers. However, effects of surface interaction
parameters can reverse this situation. Effects of the film thickness on
physical properties will be also shown as functions of temperature.
