Analytical and numerical solutions of pore formation in elastic food materials during dehydration

Pore development in viscoelastic foods during drying

“…4, for simulations with τ core = τ skin = 1 s, R in / R out = 0.01, G skin / G core = 20, and Π ext / G core = {100, 500, 1000, 1500}. We note that the upper bound of Π ext / G core is limited by numerical stability, but calculations show that under these conditions a w ≈ 0.1, 12 which is below the target of most food drying processes ( a w ≈ 0.2). Hence, the upper bound is also a practical limit.…”

“…In previous models, we have assumed isothermal and pure elastic food materials. 11,12 In this paper, we extend our earlier 1D model to viscoelastic food materials, which are also subject to heating. However, we retain the above simple spherical geometry.…”

“…The strong form of the mass balance in the material frame is:∂ t c = ∂ R N w,R The corresponding weak form is:with the molar flux equal to:where D X is the contravariant diffusion coefficient, which follows from the mapping from the current frame to the material frame. 12 It follows:In short, λ θ 2 accounts for changes in the surface area between the control volume, and λ r corrects for changes in the thickness of control volumes.…”

“…This mechanism of pore formation during drying is valid using numerical models, representing vegetables as a hydrogel covered with an elastic skin and a central pore (cavity). 11,12…”

“…This limitation was overcome in the theory developed by Suo and coworkers, which is capable of handling anisotropic and inhomogeneous deformation 16,17 – which has been applied in our earlier models. 11,12 There we solved the mass balance for moisture, coupled to the steady state momentum equation (∇· σ = 0). Importantly, Suo and coworkers consider hydrogels as a single phase, governed by a single thermodynamic potential ( i.e.…”