The exact D-optimal design problems for regression models has been in-vestigated in many literatures. Huang (1987) and Gaffke (1987) provided a sufficient condition for the minimum sample size for an certain set of candidate designs to be exact D-optimal for polynomial regression models on a compact interval. In this work we consider a mixture experiment with q nonnegative components, where the proportions of components are sub- ject to the simplex restriction $sum_{i=1}^q x_i =1$, $x_i ¡Ù 0$. The exact D-optimal designs for mixture experiments for Scheffe¡¦s quadratic models are investigated. Based on results in Kiefer (1961) results about the exact D-optimal designs for mixture models with two or three ingredients are provided and numerical verifications for models with ingredients between four and nine are presented.