A novel methodology for simulating contact-line behavior in capillary-driven flows

Despite the wide swath of applications where multiphase fluid contact lines exist, there is still no consensus on an accurate and general simulation methodology. Most prior numerical work has imposed one of the many dynamic contact-angle theories at solid walls. Such approaches are inherently limited by the theory accuracy. In fact, when inertial effects are important, the contact angle may be history dependent and, thus, any single mathematical function is inappropriate. Given these limitations, the present work has two primary goals: 1) create a numerical framework that allows the contact angle to evolve naturally with appropriate contact-line physics and 2) develop equations and numerical methods such that contact-line simulations may be performed on coarse computational meshes.

Fluid flows affected by contact lines are dominated by capillary stresses and require accurate curvature calculations. The level set method was chosen to track the fluid interfaces because it is easy to calculate interface curvature accurately. Unfortunately, the level set reinitialization suffers from an ill-posed mathematical problem at contact lines: a ``blind spot'' exists. Standard techniques to handle this deficiency are shown to introduce parasitic velocity currents that artificially deform freely floating (non-prescribed) contact angles. As an alternative, a new relaxation equation reinitialization is proposed to remove these spurious velocity currents and its concept is further explored with level-set extension velocities.

To capture contact-line physics, two classical boundary conditions, the Navier-slip velocity boundary condition and a fixed contact angle, are implemented in direct numerical simulations (DNS). DNS are found to converge only if the slip length is well resolved by the computational mesh. Unfortunately, since the slip length is often very small compared to fluid structures, these simulations are not computationally feasible for large systems. To address the second goal, a new methodology is proposed which relies on the volumetric-filtered Navier-Stokes equations. Two unclosed terms, an average curvature and a viscous shear VS, are proposed to represent the missing microscale physics on a coarse mesh.

All of these components are then combined into a single framework and tested for a water droplet impacting a partially-wetting substrate. Very good agreement is found for the evolution of the contact diameter in time between the experimental measurements and the numerical simulation. Such comparison would not be possible with prior methods, since the Reynolds number Re and capillary number Ca are large. Furthermore, the experimentally approximated slip length ratio is well outside of the range currently achievable by DNS. This framework is a promising first step towards simulating complex physics in capillary-dominated flows at a reasonable computational expense.

Development of semicrystalline morphology of poly(L-lactic acid) during processing of a vascular scaffold

New and promising treatments for coronary heart disease are enabled by vascular scaffolds made of poly(L-lactic acid) (PLLA), as demonstrated by Abbott Vascular’s bioresorbable vascular scaffold. PLLA is a semicrystalline polymer whose degree of crystallinity and crystalline microstructure depend on the thermal and deformation history during processing. In turn, the semicrystalline morphology determines scaffold strength and biodegradation time. However, spatially-resolved information about the resulting material structure (crystallinity and crystal orientation) is needed to interpret in vivo observations.

The first manufacturing step of the scaffold is tube expansion in a process similar to injection blow molding. Spatial uniformity of the tube microstructure is essential for the consistent production and performance of the final scaffold. For implantation into the artery, solid-state deformation below the glass transition temperature is imposed on a laser-cut subassembly to crimp it into a small diameter. Regions of localized strain during crimping are implicated in deployment behavior.

To examine the semicrystalline microstructure development of the scaffold, we employed complementary techniques of scanning electron and polarized light microscopy, wide-angle X-ray scattering, and X-ray microdiffraction. These techniques enabled us to assess the microstructure at the micro and nano length scale. The results show that the expanded tube is very uniform in the azimuthal and axial directions and that radial variations are more pronounced. The crimping step dramatically changes the microstructure of the subassembly by imposing extreme elongation and compression. Spatial information on the degree and direction of chain orientation from X-ray microdiffraction data gives insight into the mechanism by which the PLLA dissipates the stresses during crimping, without fracture. Finally, analysis of the microstructure after deployment shows that it is inherited from the crimping step and contributes to the scaffold’s successful implantation in vivo.