Minimal surfaces over stars

A JS surface is a minimal graph over a polygonal domain that becomes infinite in magnitude at the domain boundary. Jenkins and Serrin characterized the existence of these minimal graphs in terms of the signs of the boundary values and the side-lengths of the polygon. For a convex polygon, there can be essentially only one JS surface, but a non-convex domain may admit several distinct JS surfaces. We consider two families of JS surfaces corresponding to different boundary values, namely JS₀ and JS₁, over domains in the form of regular stars. We give parameterizations for these surfaces as lifts of harmonic maps, and observe that all previously constructed JS surfaces have been of type JS₀. We give an example of a JS₁ surface that is a new complete embedded minimal surface generalizing Scherk's doubly periodic surface, and show also that the JS₀ surface over a regular convex 2n-gon is the limit of JS₁ surfaces over non-convex stars. Finally we consider the construction of other JS surfaces over stars that belong neither to JS₀ nor to JS₁.     

A Pore-Scale Investigation of Low-Salinity Waterflooding in Porous Media: Uniformly Wetted Systems

The potential of low-salinity (LS) water injection as an oil recovery technique has been the source of much recent debate within the petroleum industry. Evidence from both laboratory and field-level studies has indicated significant benefits compared to conventional high-salinity (HS) waterflooding, but many conflicting results have also been reported and, to date, the underlying mechanisms remain poorly understood. In this paper, we aim to address this uncertainty by developing a novel, steady-state pore network model in which LS brine displaces oil from a HS-bearing network. The model allows systematic investigation of the crude oil/brine/rock parameter space, with the goal of identifying features that may be critical to the production of incremental oil following LS brine injection. By coupling the displacement model to a salinity-tracking tracer algorithm, and assuming that a reduction of water salinity within the pore network leads to localised wettability alteration, substantial perturbations to standard pore filling sequences are predicted. The results clearly point to two principal effects of dynamic contact angle modification at the pore scale: a “pore sequence” effect, characterised by an alteration to the distribution of displaced pore sizes, and a “sweep efficiency” effect, demonstrated by a change in the overall fraction of pores invaded. Our study indicates that any LS effect will depend on the relative (scenario-dependent) influence of each mechanism, where factors such as the initial wettability state of the system and the pore size distribution of the underlying network are found to play crucial roles. In addition, we highlight the important role played by end-point capillary pressure in determining LS efficacy.     

A magnetic resonance (MR) microscopy system using a microfluidically cryo-cooled planar coil

We present the development of a microfluidically cryo-cooled planar coil for magnetic resonance (MR) microscopy. Cryogenically cooling radiofrequency (RF) coils for magnetic resonance imaging (MRI) can improve the signal to noise ratio (SNR) of the experiment. Conventional cryostats typically use a vacuum gap to keep samples to be imaged, especially biological samples, at or near room temperature during cryo-cooling. This limits how close a cryo-cooled coil can be placed to the sample. At the same time, a small coil-to-sample distance significantly improves the MR imaging capability due to the limited imaging depth of planar MR microcoils. These two conflicting requirements pose challenges to the use of cryo-cooling in MR microcoils. The use of a microfluidic based cryostat for localized cryo-cooling of MR microcoils is a step towards eliminating these constraints. The system presented here consists of planar receive-only coils with integrated cryo-cooling microfluidic channels underneath, and an imaging surface on top of the planar coils separated by a thin nitrogen gas gap. Polymer microfluidic channel structures fabricated through soft lithography processes were used to flow liquid nitrogen under the coils in order to cryo-cool the planar coils to liquid nitrogen temperature (-196 °C). Two unique features of the cryo-cooling system minimize the distance between the coil and the sample: (1) the small dimension of the polymer microfluidic channel enables localized cooling of the planar coils, while minimizing thermal effects on the nearby imaging surface. (2) The imaging surface is separated from the cryo-cooled planar coil by a thin gap through which nitrogen gas flows to thermally insulate the imaging surface, keeping it above 0 °C and preventing potential damage to biological samples. The localized cooling effect was validated by simulations, bench testing, and MR imaging experiments. Using this cryo-cooled planar coil system inside a 4.7 Tesla MR system resulted in an average image SNR enhancement of 1.47 ± 0.11 times relative to similar room-temperature coils.