Читать книгу The Rheology Handbook - Thomas Mezger - Страница 132

This analysis model was developed to evaluate chocolate melts at T = +40 °C in the range of

γ ̇ = 2 to 50 s-1 (or in an extended range of γ ̇ = 1 to 100 s-1, resp.) [3.15].

Flow curve model function with yield point τ0 [Pa]; shear stress τ1 [Pa] which leads to the “maximum shear-induced structural change” (at the intersection of τ-axis and the straight line fitted to the flow curve in the high shear rate range); shear rate γ ̇ * [s-1] at the point

τ* = τ0 + (τ1 - τ0) ⋅ (1 – 1/e), and slope value of the flow curve at high shear rates termed η∞ [Pas], (“final viscosity“, “steady-state viscosity”; this approaches usually to a constant value for most chocolate melts in the range of γ ̇ = 60 to 100 s-1); see Figure 3.31.

Figure 3.31: Flow curve fitting according to Windhab

The following applies for γ ̇ = 0:

τ = τ0 + (τ1 - τ0) ⋅ (1 – e0) + 0 = τ0 + (τ1 - τ0) ⋅ (1 – 1) = τ0 + 0 = τ0

Result: “Structural strength at rest” is represented by the “yield point” in the range of τ ≤ τ0.

The following applies for γ ̇ = ∞:

τ = τ0 + (τ1 - τ0) ⋅ (1 – e-∞) + η∞ ⋅ γ ̇ = τ0 + (τ1 - τ0) ⋅ (1 – 0) + η∞ ⋅ γ ̇ = τ1 + η∞ ⋅ γ ̇

Result: In the “high-shear” range, the slope of the flow curve is constant, which corresponds to “Bingham behavior”.

The following applies for γ ̇ = γ ̇ *:

τ = τ0 + (τ1 - τ0) ⋅ (1 – 1/e) + 0 = τ0 + 0.632 ⋅ (τ1 - τ0) = τ*

Result: Between τ0 and τ1 is the “range of shear-induced structural change” (with structural decomposition at increasing shear load, i. e. in the “upwards ramp”; or with structural regeneration at decreasing load, i. e. in the “downwards ramp”). Above the yield point τ0 the point τ* (or γ ̇ *, resp.) is reached at the shear stress value τ = 63.2 % (τ1 - τ0).