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We present a convex-splitting scheme for the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson equation of state for pure substance. The semi-implicit scheme is proven to be uniquely solvable, mass conservative, unconditionally energy stable andL∞convergent with the order of. The numerical results verify the effectiveness of the proposed algorithm and also show good agreement of the numerical solution with laboratory experimental results.

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Poor fit has become one of reasons for high non-compliance in the use of garments made of compression textiles in venous deficiency treatments. A novel methodology to categorize lower body shapes and sizes has been established via three-dimensional digital anthropometric technology in this study based on 208 Hong Kong subjects aged 40–60 years. Three new parameters were introduced to classify body shapes, namely the “A-angle” for assessing the “alignment” of lower extremities, the “cosine values of the key angle” at the turning point for below-knee shape determination, and “gradient” for above-knee shape categories. The mathematical simulation via the interpolation function was employed to explore the characteristics of shape variation trends with the involvement of dynamic interactions of both circumferences (Cir) and heights (Hei) of lower extremities. The clustering analysis quantitatively segmented the sample population into three stratified leg morphologies (i.e. diamond, inverted trapezoid, and balanced leg shapes) in terms of the determined anthropometric landmarks along the lower extremities, in which the Cir(s) of the brachial (cB1), calf (cC), and thigh (cF) exhibited most obvious differences among the clustered lower limbs. The created stratified shape-driven sizing system and methodologies further involved the body shape classifications into the Cir-based size categories to cater for diverse body morphologies in product size selection, thus improving dimensional fitness and accurate treatment using compression textiles in practice.

A biphase mixture continuum mechanics model is derived for neutral heat-shrinkable thermo-sensitive hydrogels in this paper. The mixing free energy of the special mixture is recalculated based on the partition function of Bose system, and it evaluates the contribution of the hydrophilic, hydrophobic interaction and hydrogen bonding to the volume phase transition behaviors. The ideas of the Flory lattice theory and the UNIFAC group contribution method are employed to get the expression of the mixing free energy. Then we deduce a particular model by combining this mixing free energy with the conservation laws equations and constitutive relations of both phases to predict the volume transition behaviors of these special hydrogels.

First and second order numerical schemes for the fourth order parabolic equation with Peng-Robinson equation of state, which are based on recently proposed invariant energy quadratisation method are developed. Both schemes are linear, unconditionally energy stable and uniquely solvable. The reduced linear systems are symmetric and positive definite, so that their solutions can be efficiently found. Numerical results demonstrate the good performance of the schemes, consistent with experimental data.

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