The contact angle in inviscid fluid mechanics

We show that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited conditions under which such a specification is permissible are derived; however, these include cases where the static meniscus is not flat. In view of this situation, the status of the many `solutions' in the literature which prescribe a contact angle in potential flows comes into question. We suggest that these solutions which attempt to incorporate a phenomenological, but incompatible, condition are in some, imprecise sense `weak-type solutions'; they satisfy or are likely to satisfy, at least in the limit, the governing equations and boundary conditions everywhere except in the neighbourhood of the contact line. We discuss the implications of the result for the analysis of inviscid flows with free surfaces.Comment: 13 pages, no figures, no table

Kinetic Theory of Transient Condensation and Evaporation at a Plane Surface

The phenomenon of transient condensation onto, or evaporation from, a liquid sheet in contact with its pure vapor is treated from a kinetic theory viewpoint. The Maxwell moment method is used to formulate the detailed transient problem. A steady surface mass flux rate exists for times large in comparison with the collision time, that is, in the continuum regime, and explicit formulas are given for this limit. The complete gasdynamic field, however, is nonsteady for all times. The calculations are carried out utilizing four moments, and the effects of incorporating additional moments are negligible. Finally, the analysis is extended to incorporate imperfect mass and temperature accommodation. Examination of the transient solution and a matched asymptotic "quasisteady" solution shows that the gasdynamic field consists of a diffusion process near the liquid surface coupled through an expansion or compression wave to the constant far field state

The motion of bubbles inside drops in containerless processing

A theoretical model of thermocapillary bubble motion inside a drop, located in a space laboratory, due to an arbitrary axisymmetric temperature distribution on the drop surface was constructed. Typical results for the stream function and temperature fields as well as the migration velocity of the bubble were obtained in the quasistatic limit. The motion of bubbles in a rotating body of liquid was studied experimentally, and an approximate theoretical model was developed. Comparison of the experimental observations of the bubble trajectories and centering times with theoretical predictions lends qualified support to the theory

Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip

Recent experiments on triangular lattice organic Mott insulators have found evidence for a 2D spin liquid in proximity to the metal-insulator transition. A Gutzwiller wavefunction study of the triangular lattice Heisenberg model with appropriate four-spin ring exchanges has found that the projected spinon Fermi sea state has a low variational energy. This wavefunction, together with a slave particle gauge theory, suggests that such spin liquid possesses spin correlations that are singular along surfaces in momentum space ("Bose surfaces"). Signatures of this state, which we refer to as a "Spin Bose-Metal" (SBM), are expected to be manifest in quasi-1D ladder systems: The discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg strip (zigzag chain). Using DMRG, variational wavefunctions, and a Bosonization analysis, we map out the full phase diagram. Without ring exchange the model is equivalent to the J_1 - J_2 Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess particular singular wavevectors and allow us to identify this phase as the hoped for quasi-1D descendant SBM state. We derive a low energy theory and find three gapless modes and one Luttinger parameter controlling all power laws. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 VBS or a period-4 Chirality order, which we discover in the DMRG; we also find an interesting SBM state with partial ferromagnetism.Comment: 30 pages, 23 figure

Physical phenomena in containerless glass processing

Experiments were conducted on bubble migration in rotating liquid bodies contained in a sphere. Experiments were initiated on the migration of a drop in a slightly less dense continuous phase contained in a rotating sphere. A refined apparatus for the study of thermocapillar flow in a glass melt was built, and data were acquired on surface velocities in the melt. Similar data also were obtained from an ambient temperature fluid model. The data were analyzed and correlated with the aid of theory. Data were obtained on flow velocities in a pendant drop heated from above. The motion in this system was driven principally by thermocapillarity. An apparatus was designed for the study of volatilization from a glass melt

Balancing food waste and sustainability goals in online food delivery: Towards a comprehensive conceptual framework

Increasing food waste is a major threat to sustainability and food security. Recognizing the issue, the United Nations Sustainable Development Goal (SDG) 12 mandates reducing global food waste by 50 percent by 2030. This situation has also given impetus to academic research on consumer food waste in both household and out-of-home settings. However, food delivery apps (FDAs) remain under-researched from this perspective. This is a serious gap because operating under a business model that inherently facilitates food over-ordering, FDAs can be a major source of food waste. Understanding the demand-side factors that drive consumers to order more food than required to satiate their hunger can be useful in mitigating such wasteful indulgences. Noting this, we extend the seminal theory of planned behavior (TPB) to propose direct and intervening mechanisms that can better explicate why consumers indulge in a ‘shopping routine’ of ordering more food than required. We analyzed data from 487 FDA users to test the proposed hypotheses. Our results reveal the positive associations of (a) attitude and subjective norms with usage intentions and (b) trust, intentions, and leftover reuse routine with shopping routine. In addition, both proposed moderators—i.e., willingness to pay for eco-friendly packaging and number of years of FDA usage—do, in fact, moderate the associations of leftover reuse routine with both usage intentions and shopping routine. These findings can help marketers and policymakers devise appropriate strategies to promote pro-environmental green behaviors among FDA users without harming the commercial interests of the sector

Structure of 9α,19-dihydroxy-4-androstene-3,17-dione

C19H26O4, M1 = 318.41, orthorhombic, P212121, a = 10.591 (1), b = 11.133 (1), c = 13.657 (2) Å, V – 1610.29 Å3, Z = 4, Dm (flotation in KI) = 1.301, Dx = 1.313 g cm-3, Mo Kα, Å = 0.7107 Å, μ = 0.85 cm-1, F(000) = 688, T = 293 K, R – 0.057 for 1253 significant reflections. The Å ring is disordered with atoms C(2) and O(19) occupying two possible sites. The molecules are held together by a hydrogen bond [O(9)…O(17) = 2.89 Å]

Autosomal Dominant Retinal Dystrophies Caused by a Founder Splice Site Mutation, c.828+3A>T, in PRPH2 and Protein Haplotypes in trans as Modifiers.

PurposeWe determined the phenotypic variation, disease progression, and potential modifiers of autosomal dominant retinal dystrophies caused by a splice site founder mutation, c.828+3A>T, in the PRPH2 gene.MethodsA total of 62 individuals (19 families) harboring the PRPH2 c.828+3A>T mutation, had phenotype analysis by fundus appearance, electrophysiology, and visual fields. The PRPH2 haplotypes in trans were sequenced for potential modifying variants and generalized estimating equations (GEE) used for statistical analysis.ResultsSeveral distinct phenotypes caused by the PRPH2 c.828+3A>T mutation were observed and fell into two clinical categories: Group I (N = 44) with mild pattern dystrophies (PD) and Group II (N = 18) with more severe cone-rod dystrophy (CRD), retinitis pigmentosa (RP), and central areolar chorioretinal dystrophy (CACD). The PRPH2 Gln304-Lys310-Asp338 protein haplotype in trans was found in Group I only (29.6% vs. 0%), whereas the Glu304-Lys310-Gly338 haplotype was predominant in Group II (94.4% vs. 70.4%). Generalized estimating equations analysis for PD versus the CRD/CACD/RP phenotypes in individuals over 43 years alone with the PRPH2 haplotypes in trans and age as predictors, adjusted for correlation within families, confirmed a significant effect of haplotype on severity (P = 0.03) with an estimated odds ratio of 7.16 (95% confidence interval [CI] = [2.8, 18.4]).ConclusionsThe PRPH2 c.828+3A>T mutation results in multiple distinct phenotypes likely modified by protein haplotypes in trans; the odds of having the CACD/RP-like phenotype (versus the PD phenotype) are 7.16 times greater with a Glu304-Lys310-Gly338 haplotype in trans. Further functional studies of the modifying haplotypes in trans and PRPH2 splice variants may offer therapeutic targets