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Boundary conditions required for numerical solution of the Boltzmann kinetic equation (BKE) for mass/heat transfer between evaporation and condensation surfaces are analyzed by comparison of BKE results with molecular dynamics (MD) simulations. Lennard-Jones potential with parameters corresponding to solid argon is used to simulate evaporation from the hot side, nonequilibrium vapor flow with a Knudsen number of about 0.02, and condensation on the cold side of the condensed phase. The equilibrium density of vapor obtained in MD simulation of phase coexistence is used in BKE calculations for consistency of BKE results with MD data. The collision cross-section is also adjusted to provide a thermal flux in vapor identical to that in MD. Our MD simulations of evaporation toward a nonreflective absorbing boundary show that the velocity distribution function (VDF) of evaporated atoms has the nearly semi-Maxwellian shape because the binding energy of atoms evaporated from the interphase layer between bulk phase and vapor is much smaller than the cohesive energy in the condensed phase. Indeed, the calculated temperature and density profiles within the interphase layer indicate that the averaged kinetic energy of atoms remains near-constant with decreasing density almost until the interphase edge. Using consistent BKE and MD methods, the profiles of gas density, mass velocity, and temperatures together with VDFs in a gap of many mean free paths between the evaporation and condensation surfaces are obtained and compared. We demonstrate that the best fit of BKE results with MD simulations can be achieved with the evaporation and condensation coefficients both close to unity.
RESUMO
PURPOSE: To investigate the long-term effectiveness of non-penetrating deep sclerectomy (NPDS) with xenogenically derived cancellous bone collagen glaucoma implant (XCB-CGI) implantation in patients with primary open-angle glaucoma (POAG). MATERIALS AND METHODS: Retrospective chart review of patients with POAG stages 2 and 3 was treated with NPDS and XCB-CGI. Follow-up was at 6 months, 1, 2, 3, 4 and 5 years after surgery. Main outcomes were intraocular pressure (IOP) and medication burden. Secondary outcomes were visual acuity, corneal hysteresis (CH), visual field (VF) and optical coherence tomography (OCT) parameter analysis. RESULTS: Among 71 patients (71 eyes), the mean age was 72.7 ± 9.8. Average initial IOP was 27.7 ± 7.9 and average initial med load was 2.36 ± 0.99. At 6 months, 1, 2, 3, 4 and 5 years, the average IOP was 14.9 ± 3.3 mm Hg (46.2% reduction), 15.3 ± 4.0 mm Hg (44.7% reduction), 14.2 ± 3.8 mm Hg (48.7% reduction), 15.2 ± 3.3 mm Hg (45.0% reduction), 15.5 ± 3.3 mm Hg (44.0% reduction) and 14.2 ± 2.8 mm Hg (48.7% reduction), respectively. In 5 years, the success rate was 34% and 67%, without, and with medications (1.8 ± 0.8 meds required), respectively. Visual acuity was not significantly different (P > .05) at all follow-up visits from baseline. Mean CH increased by 2.1 ± 0.8 (P = .05). No glaucomatous deterioration of the VF and OCT parameters was detected in 56 eyes at the 5-year follow-up. CONCLUSION: NPDS with XCB-CGI implantation is an effective procedure to normalize the level of IOP, stabilize glaucomatous changes and decrease the number of meds needed for glaucoma control.