In the mantle section of many ophiolite sequences, dunite dikes are present. Around dunite dikes at the Josephine and Trinity ophiolite, a sequence of lithologies consisting of plagioclase lherzolite, lherzolite, and harzburgite is present. This sequence of rocks has been interpreted to be the result of reactive porous flow. From trace element data, the mafic melt has been interpreted to flow both into and out of the dunite dikes. Whether the melt emanates from the dunite bodies or is collected by them has implications for the mechanisms of melt extraction beneath ridge systems. The determination of the flow direction based on tracer distributions is difficult and therefore additional constraints are important. Reactive transport theory predicts that lithological zonations around dunite bodies can indicate the direction of flow. To date no reactive transport model has been developed to test these hypotheses, and therefore I have built a reactive transport model using COMSOL v. 4.1. I developed a model for an orthopyroxene dissolution front based on the model of Chadam et al. (1986, Reactive infiltration instabilities, IMA Journal of Applied Mathematics, v. 36, p.207-221). This model includes the strong nonlinearity feedback that has been invoked to lead to the channelization of melt flow. The instability leads to the formation of elongated regions where orthopyroxene is depleted. This model predicts that the melt is focused into the dunite bodies, most flow is parallel to the dunite boundaries, and exits the fingers at the tip of the column. / text

Understanding the behavior of charring or decomposing materials exposed to high temperature environments is an essential aspect in rocket design. In particular, the tip of re-entry vehicles and sacrificial rocket nozzle liners are both exposed to extremely high temperatures. This thesis is specifically concerned with better understanding the reaction of sacrificial rocket nozzle liners to these high temperature environments. The sacrificial liners are designed to shield the rocket nozzle from the thermal and chemical effects of the heated exhaust gas that flows through the nozzle. However, in the design process space and weight of the rocket are at a premium. The sacrificial liners need to be designed to be as light and thin as possible, while properly shielding the nozzle from the heated exhaust gases. The sacrificial liner material is initially impermeable in its virgin state; however, as the liner is exposed to the heated exhaust gases, it chars and the liner material begins to decompose. The decomposition of the liner by heating in the absence of oxygen is known as pyrolysis. At high temperatures, the virgin material will decompose into a solid material (charred liner) and a vapor (pyrolysis gas). The pyrolysis process leads to the flow of pyrolysis gases throughout the porous charred liner. As a result, significant pressures can build within the liner. If the pressures within the liner are high enough, mechanically weak portions of the liner may fracture and break off. Fracturing of the liner could expose the nozzle to the heated exhaust gases, thus jeopardizing the structural integrity of the nozzle. Therefore, it is important to understand the pressure distribution within the sacrificial liners that occurs as a result of the pyrolysis process. This work describes the code PorePress, which solves for steady state and transient pressure distributions in 1- and 2-D axisymmetric geometries that represent sacrificial liners. The PorePress code is essentially a 1- and 2-dimensional differential equation solver for mixed, unstructured geometries. Specifically, the code is used for solving a coupled form of the Ideal Gas Law, Conservation of Mass, and Conservation of Momentum Equations, which describe the flow and resulting pressures within liner geometries. The code centers around using Taylor Series expansions to approximate derivatives needed to solve the appropriate differential equations. The derivative approximation process used in PorePress is grid transparent, meaning the same method can be used for any combination of quadrilateral (4-sided) or triangular (3-sided) elements in a mesh, without any changes to the code. Stability issues arise in both the 1- and 2-D PorePress solution processes, as a result of the non-linear nature of the coupled equations, high spatial gradients, and large variations in material properties. In the 1-D case stabilization techniques such as: upwinding, dynamic differencing, under-relaxation, and preconditioning are applied. Meanwhile, in the 2-D case, stabilization techniques such as: inverse weighting and QR factorization of the coefficient matrix, under-relaxation, and preconditioning are applied. The steady state and transient solution processes for both the 1- and 2-D pore pressure solution processes used in PorePress are covered in this thesis, as well as discussion of the resulting pressure distributions. Certain sacrificial liner design considerations that arise as a result of PorePress models for sample liner burns are also covered. / Master of Science

Melting and melt segregation are key processes in the geochemical evolution of the Earth. However, mechanism and time scale of melt transport from the source to the surface are still not well understood and are dependent on the grain-scale distribution of melt. A related question is the retention of melt in partially molten regions of the Earths upper mantle. Seismic observations from mid-ocean ridges (MOR) and subduction zones are interpreted to show in-situ melt contents up to 3%, while geochemical observations from MOR basalts are inferred to indicate very efficient extraction of melt (porosities of order 0.1%). Earlier theoretical models of the melt distribution were based on the balance of surface tension between melt and uniform crystalline grains, predicting a simple net- work of melt along three-grain edges. Analyses of experimentally produced samples of olivine and basaltic melt show that the melt geometry is much more complex, and includes wetted two-grain boundaries. I reconstructed the melt geometry of two experimentally produced samples by serial sectioning and 3-D rendering of the pore geometry which demonstrates for the first time that melt exists in thin layers on two-grain boundaries. This confirms the inferences from previous 2-D observations and has significant implications for physical properties of partially molten regions, for example seismic velocities and attenuation. The wetted two-grain boundaries are inferred to be a consequence of continuous grain growth. Due to the complexity of the 3-D melt geometry the perme- ability of partially molten rocks can not be predicted from simple models. I therefore investigated the permeability as a function of porosity for both synthetic and ex- perimentally determined pore geometries using a lattice-Boltzmann method. The calculated permeability is not a simple function of porosity, but increases rapidly at a critical fraction of wetted two-grain boundaries. In order to extrapolate the experimentally based findings to grain sizes expected in natural rocks I examined the geometry of secondary phases inferred to represent relict melt in mantle peridotites from the Krivaja massif in Bosnia. These findings corroborate the experimental observations of wetted two-grain boundaries.