Simulation Software for Flow of Fluid with Suspended Point Particles in Complex Domains: Application to Matrix Diffusion

Matrix diffusion is a phenomenon in which tracer particles convected along a flow channel can diffuse into porous walls of the channel, and it causes a delay and broadening of the breakthrough curve of a tracer pulse. Analytical and numerical methods exist for modeling matrix diffusion, but there are still some features of this phenomenon, which are difficult to address using traditional approaches. To this end we propose to use the lattice-Boltzmann method with point-like tracer particles. These particles move in a continuous space, are advected by the flow, and there is a stochastic force causing them to diffuse. This approach can be extended to include particle-particle and particle-wall…

A prospect for computing in porous materials research: Very large fluid flow simulations

Abstract Properties of porous materials, abundant both in nature and industry, have broad influences on societies via, e.g. oil recovery, erosion, and propagation of pollutants. The internal structure of many porous materials involves multiple scales which hinders research on the relation between structure and transport properties: typically laboratory experiments cannot distinguish contributions from individual scales while computer simulations cannot capture multiple scales due to limited capabilities. Thus the question arises how large domain sizes can in fact be simulated with modern computers. This question is here addressed using a realistic test case; it is demonstrated that current …

Radial phononic thermal conductance in thin membranes in the Casimir limit: Design guidelines for devices

In a previous publication, we discussed the formalism and some computational results for phononic thermal conduction in the suspended membrane geometry for radial heat flow from a central source, which is a common geometry for some low-temperature detectors, for example. We studied the case where only diffusive surface scattering is present, the so called Casimir limit, which can be experimentally relevant at temperatures below $\sim$ 10 K in typical materials, and even higher for ultrathin samples. Here, we extend our studies to much thinner membranes, obtaining numerical results for geometries which are more typical in experiments. In addition, we interpret the results in terms of a small…

A Composite Phononic Crystal Design for Quasiparticle Lifetime Enhancement in Kinetic Inductance Detectors

A nanoscale phononic crystal filter (reflector) is designed for a kinetic inductance detector where the reflection band is matched to the quasiparticle recombination phonons with the aim to increase quasiparticle lifetime in the superconducting resonator. The inductor is enclosed by a 1 um wide phononic crystal membrane section with two simple hole patterns that each contain a partial spectral gap for various high frequency phonon modes. The phononic crystal is narrow enough for low frequency thermal phonons to propagate unimpeded. With 3D phonon scattering simulations over a 40 dB attenuation in transmitted power is found for the crystal, which was previously estimated to give a lifetime e…

Specific heat of thin phonon cavities at low temperature: Very high values revealed by zeptojoule calorimetry

The specific heat of phonon cavities is investigated in order to analyze the effect of phonon confinement on thermodynamic properties. The specific heat of freestanding very thin SiN membranes in the low-dimensional limit is measured down to very low temperatures (from 6 K to 50 mK). In the whole temperature range, we measured an excess specific heat orders of magnitude bigger than the typical value observed in amorphous solids. Below 1 K, a crossover in cp to a lower power law is seen, and the value of the specific heat of thinner membranes becomes larger than that of thicker ones demonstrating a significant contribution coming from the surface. We show that this high value of the specific…

Coupling of lattice-Boltzmann solvers with suspended particles using the MPI intercommunication framework

Abstract The MPI intercommunication framework was used for coupling of two lattice-Boltzmann solvers with suspended particles, which model advection and diffusion respectively of these particles in a carrier fluid. Simulation domain was divided into two parts, one with advection and diffusion, and the other with diffusion only (no macroscopic flow). Particles were exchanged between these domains at their common boundary by a direct process to process communication. By analysing weak and strong scaling, it was shown that the linear scaling characteristics of the lattice-Boltzmann solvers were not compromised by their coupling.

Simultaneous Noise and Impedance Fitting to Transition-Edge Sensor Data using Differential Evolution

We discuss a robust method to simultaneously fit a complex model both to the complex impedance and the noise data for transition-edge sensors (TES). It is based on a differential evolution (DE) algorithm, providing accurate and repeatable results with only a small increase in computational cost compared to the standard least squares (LS) fitting method. Test fits are made using both DE and LS methods, and the results compared with previously determined best fits, with varying initial value deviations and limit ranges for the parameters. The robustness of DE is demonstrated with successful fits even when parameter limits up to a factor of 5 from the known values were used. It is shown that t…

Controlling thermal conductance using three-dimensional phononic crystals

Controlling thermal transport at the nanoscale is vital for many applications. Previously, it has been shown that this control can be achieved with periodically nanostructured two-dimensional phononic crystals for the case of suspended devices. Here, we show that thermal conductance can also be controlled with three-dimensional phononic crystals, allowing the engineering of the thermal contact of more varied devices without the need for suspension in the future. We show the experimental results obtained at sub-Kelvin temperatures for two different period three-dimensional crystals and for a bulk control structure. The results show that the conductance can be enhanced with the phononic cryst…

Numerical simulation of low temperature thermal conductance of corrugated nanofibers

Low-Temperature Coherent Thermal Conduction in Thin Phononic Crystal Membranes

In recent years, the idea of controlling phonon thermal transport coherently using phononic crystals has been introduced. Here, we extend our previous numerical studies of ballistic low-temperature heat transport in two-dimensional hole-array phononic crystals, and concentrate on the effect of the lattice periodicity. We find that thermal conductance can be either enhanced or reduced by large factors, depending on the the lattice period. Analysis shows that both the density of states and the average group velocity are strongly affected by the periodic structuring. The largest effect for the reduction seen for larger period structures comes from the strong reduction of the group velocities, …

Minimizing coherent thermal conductance by controlling the periodicity of two-dimensional phononic crystals

Periodic hole array phononic crystals (PnC) can strongly modify the phonon dispersion relations, and have been shown to influence thermal conductance coherently, especially at low temperatures where scattering is suppressed. One very important parameter influencing this effect is the period of the structure. Here, we measured the sub-Kelvin thermal conductance of nanofabricated PnCs with identical hole filling factors, but three different periodicities, 4, 8, and 16 $\mu$m, using superconducting tunnel junction thermometry. We found that all the measured samples can suppress thermal conductance by an order of magnitude, and have a lower thermal conductance than the previously measured small…

Low temperature heat capacity of phononic crystal membranes

Phononic crystal (PnC) membranes are a promising solution to improve sensitivity of bolometric sensor devices operating at low temperatures. Previous work has concentrated only on tuning thermal conductance, but significant changes to the heat capacity are also expected due to the modification of the phonon modes. Here, we calculate the area-specific heat capacity for thin (37.5 - 300 nm) silicon and silicon nitride PnC membranes with cylindrical hole patterns of varying period, in the temperature range 1 - 350 mK. We compare the results to two- and three-dimensional Debye models, as the 3D Debye model is known to give an accurate estimate for the low-temperature heat capacity of a bulk sam…

Engineering thermal conductance using a two-dimensional phononic crystal

Controlling thermal transport has become relevant in recent years. Traditionally, this control has been achieved by tuning the scattering of phonons by including various types of scattering centres in the material (nanoparticles, impurities, etc). Here we take another approach and demonstrate that one can also use coherent band structure effects to control phonon thermal conductance, with the help of periodically nanostructured phononic crystals. We perform the experiments at low temperatures below 1 K, which not only leads to negligible bulk phonon scattering, but also increases the wavelength of the dominant thermal phonons by more than two orders of magnitude compared to room temperature…

Effective medium theory for the low-temperature heat capacity of a metasolid plate

Nanopatterning can be used to strongly control the thermal properties of solids, but theoretical understanding relies often on complex numerical simulations. Here, an analytical theory is derived for the low temperature heat capacity of a nanopatterned phononic crystal plate, focusing on the geometry of a square lattice of cylindrical holes in an isotropic matrix material. Its quasistatic elastic properties were studied using an anisotropic effective medium theory, that is, considering it as a homogenized metasolid. The effective elastic parameters can then be used as an input for an anisotropic plate theory, yielding analytical expressions for the dispersion relations of the three lowest p…