The Geology of Mount Desert Island

Revised and reprinted from the Bulletin of the Geographical Society of Philadelphia, vol. XVII, No. 4, October 1919

Loss of solutions in shear banding fluids in shear banding fluids driven by second normal stress differences

Edge fracture occurs frequently in non-Newtonian fluids. A similar instability has often been reported at the free surface of fluids undergoing shear banding, and leads to expulsion of the sample. In this paper the distortion of the free surface of such a shear banding fluid is calculated by balancing the surface tension against the second normal stresses induced in the two shear bands, and simultaneously requiring a continuous and smooth meniscus. We show that wormlike micelles typically retain meniscus integrity when shear banding, but in some cases can lose integrity for a range of average applied shear rates during which one expects shear banding. This meniscus fracture would lead to ejection of the sample as the shear banding region is swept through. We further show that entangled polymer solutions are expected to display a propensity for fracture, because of their much larger second normal stresses. These calculations are consistent with available data in the literature. We also estimate the meniscus distortion of a three band configuration, as has been observed in some wormlike micellar solutions in a cone and plate geometry.Comment: 23 pages, to be published in Journal of Rheolog

Toughening mechanisms in elastomer-modified epoxies

The toughening mechanisms of elastomer-modified epoxies are examined by scanning electron microscopy, transmission electron microscopy, and optical microscopy, DGEBA epoxies toughened by various levels of several types of carboxyl terminated copolymers of butadiene-acrylonitrile (CTBN) liquid rubber are studied. The materials are deformed in uniaxial tension and in three-point bending with an edge notch. Scanning electron microscopy of fracture surfaces indicate cavitation of the rubber particles to be a major deformation mechanism. Particle-particle interaction is also found. Optical microscopy of thin sections perpendicular to the fracture surface shows that the cavitated particles generate shear bands. The toughening effect is hypothesized to be due to cavitation, which relieves the triaxial tension at the crack tip, and shear band formation, which creates a large plastic zone.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44686/1/10853_2005_Article_BF01114294.pd

The Role of Historical Narrative in Biblical Thought:the Tendencies Underlying Old Testament Historiography

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68403/2/10.1177_030908928100602102.pd

The importance of constraint relief caused by rubber cavitation in the toughening of epoxy

Many rubber-toughened epoxies are thought to derive the bulk of their toughness through the processes of rubber cavitation and plastic shear-yielding in the epoxy matrix. Constraint relief has been considered to be a key mechanism which allows extra plastic shear deformation to occur. The present work attempts to provide direct experimental evidence of the constraint relief effect by combining testing geometries that vary the degree of constraint with microscopic observations. The results show that the success of a rubber as a toughening agent for epoxies is closely related to its ability to cavitate. Evidence for local constraint relief is presented. Upon cavitation of the rubber, the stress state in a specimen with initial constraint is found to change to a plane stress state. The constraint relief circumvents or delays the crack initiation in the matrix, which allows more plastic deformation to occur.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44723/1/10853_2005_Article_BF01352202.pd

Influence of particle size and particle size distribution on toughening mechanisms in rubber-modified epoxies

The principal toughening mechanism of a substantially toughened, rubber-modified epoxy has again been shown to involve internal cavitation of the rubber particles and the subsequent formation of shear bands. Additional evidence supporting this sequence of events which provides a significant amount of toughness enhancement, is presented. However, in addition to this well-known mechanism, more subtle toughening mechanisms have been found in this work. Evidence for such mechanisms as crack deflection and particle bridging is shown under certain circumstances in rubber-modified epoxies. The occurrence of these toughening mechanisms appears to have a particle size dependence. Relatively large particles provide only a modest increase in fracture toughness by a particle bridging/crack deflection mechanism. In contrast, smaller particles provide a significant increase in toughness by cavitation-induced shear banding. A critical, minimum diameter for particles which act as bridging particles exists and this critical diameter appears to scale with the properties of the neat epoxy. Bimodal mixtures of epoxies containing small and large particles are also examined and no synergistic effects are observed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44701/1/10853_2005_Article_BF01184979.pd

Turbulent flow as a cause for underestimating coronary flow reserve measured by Doppler guide wire

BACKGROUND: Doppler-tipped coronary guide-wires (FW) are well-established tools in interventional cardiology to quantitatively analyze coronary blood flow. Doppler wires are used to measure the coronary flow velocity reserve (CFVR). The CFVR remains reduced in some patients despite anatomically successful coronary angioplasty. It was the aim of our study to test the influence of changes in flow profile on the validity of intra-coronary Doppler flow velocity measurements in vitro. It is still unclear whether turbulent flow in coronary arteries is of importance for physiologic studies in vivo. METHODS: We perfused glass pipes of defined inner diameters (1.5 – 5.5 mm) with heparinized blood in a pulsatile flow model. Laminar and turbulent flow profiles were achieved by varying the flow velocity. The average peak velocity (APV) was recorded using 0.014 inch FW. Flow velocity measurements were also performed in 75 patients during coronary angiography. Coronary hyperemia was induced by intra-coronary injection of adenosine. The APV maximum was taken for further analysis. The mean luminal diameter of the coronary artery at the region of flow velocity measurement was calculated by quantitative angiography in two orthogonal planes. RESULTS: In vitro, the measured APV multiplied with the luminal area revealed a significant correlation to the given perfusion volumes in all diameters under laminar flow conditions (r(2 )> 0.85). Above a critical Reynolds number of 500 – indicating turbulent flow – the volume calculation derived by FW velocity measurement underestimated the actual rate of perfusion by up to 22.5 % (13 ± 4.6 %). In vivo, the hyperemic APV was measured irrespectively of the inherent deviation towards lower velocities. In 15 of 75 patients (20%) the maximum APV exceeded the velocity of the critical Reynolds number determined by the in vitro experiments. CONCLUSION: Doppler guide wires are a valid tool for exact measurement of coronary flow velocity below a critical Reynolds number of 500. Reaching a coronary flow velocity above the velocity of the critical Reynolds number may result in an underestimation of the CFVR caused by turbulent flow. This underestimation of the flow velocity may reach up to 22.5 % compared to the actual volumetric flow. Cardiologists should consider this phenomena in at least 20 % of patients when measuring CFVR for clinical decision making