Handbook of Solvents - George Wypych - ChemTech - Ventech!

7.2 Bubbles dynamics and boiling 357
based upon thermodynamics of materials with memory. 2 The central idea of the theory is the
postulate that instantaneous stresses in a medium depend on the deformation history. This
suggestion leads to integral relationship between the stress and rate-of-strain tensors
t
τij = 2∫G1( t − t′ ) sij( t′ ) dt′ , σkk
=− 3p0 + 3 G2( t − t′ ) ekk( t′ ) dt′−
3 G ( t t )
t dt
t
t
∂θ
∫
∫ 3 − ′ ′ [7.2.4]
∂ ′
−∞
−∞
where:
θ =T-T0deviation of the temperature from its equilibrium value
p0 equilibrium pressure
G1,G2,G3 relaxation functions
The relaxation functions G1(t) and G2(t) satisfy restrictions, following from the entropy
production inequality
∂G
∂t
∂G
≤0, ≤0
[7.2.5]
∂t
1 2
Additional restriction on G1,2(t) is imposed by the decaying memory principle 3 that has
clear physical meaning: the state of a medium at the present moment of time is more dependent
on the stresses arising att=t2than on that stresses arising at t = t1 if t1