We present in detail a theoretical framework for representing hydrodynamic systems through a systematic discretization of the Boltzmann kinetic equation. The work is an extension of a previously proposed formulation. Conventional lattice Boltzmann models can be shown to be directly derivable from this systematic approach. Furthermore, we provide here a clear and rigorous procedure for obtaining higher-order approximations to the continuum Boltzmann equation. The resulting macroscopic moment equations at each level of the systematic discretization give rise to the Navier–Stokes hydrodynamics and those beyond. In addition, theoretical indications to the order of accuracy requirements are given for each discrete approximation, for thermohydrodynamic systems, and for fluid systems involving long-range interactions. All these are important for complex and micro-scale flows and are missing in the conventional Navier–Stokes order descriptions. The resulting discrete Boltzmann models are based on a kinetic representation of the fluid dynamics, hence the drawbacks in conventional higher-order hydrodynamic formulations can be avoided.

These findings suggest that while MSCs do generate constructs with substantial cartilaginous properties, further optimization must be done to achieve levels similar to those produced by chondrocytes.

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Replicating the nanostructured components of extracellular matrix is a target for dermal tissue engineering and regenerative medicine. Electrospinning Bombyx mori silk fibroin (BMSF) allows the production of nano- to microscale fibrous scaffolds. For BMSF electrospun scaffolds to be successful, understanding and optimizing the cellular response to material morphology is essential. Primary human dermal fibroblast response to nine variants of BMSF scaffolds composed of nano- to microscale fibers ranging from ~250 to ~1200 nm was assessed in vitro with regard to cell proliferation, viability, cellular morphology, and gene expression. BMSF support of epithelial migration was then assessed through utilization of a novel ex vivo human skin wound healing model. Scaffolds composed of the smallest diameter fibers, ~250 -300 nm, supported cell proliferation significantly more than fibers with diameters approximately 1 μm (p < 0.001). Cell morphology was observed to depart from a stellate morphology with numerous cell -fiber interactions to an elongated, fiber-aligned morphology with interaction predominately with single fibers. The expressions of extracellular matrix genes, collagen types I and III (p < 0.001), and proliferation markers, proliferating cell nuclear antigen (p < 0.001), increased with decreasing fiber diameter. The re-epithelialization of ex vivo wound models was significantly improved with the addition of BMSF electrospun scaffolds, with migratory keratinocytes incorporated into scaffolds. BMSF scaffolds with nanofibrous architectures enhanced proliferation in comparison to microfibrous scaffolds and provided an effective template for migratory keratinocytes during re-epithelialization. The results may aid in the development of effective BMSF electrospun scaffolds for wound healing applications

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Shear banding of wormlike micelle solution has been studied in the context of constitutive instability of the Johnson-Segalman (JS) model plus Newtonian stress. We have incorporated a higher-order gradient term of the deformation-rate tensor into the JS model for investigating the dynamics of a mechanical interface in shear-banded flow. Two-dimensional modelling of the new model has been carried out by a general Lagrangian-Eulerian scheme. Within the unstable region, our results show that the new term plays an important role in selecting steady-state shear stress and the selected stress is independent of the nominal shear rate. The transit period of reaching the steady state can be much longer than the intrinsic relaxation time of the JS fluid. We have verified the experimental evidence on the existence of mechanical metastable regime, over which hysteresis in flow curve might occur. The model captures many features of experimental results on shear banded flow.

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