Lattice-Boltzmann-based two-phase thermal model for simulating phase change.

A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A nonideal equation of state (EOS) is introduced by using a pseudopotential LB model. The evolution equation for the pseudotemperature variable is constructed in such a manner that in the continuum limit one recovers the well known macroscopic energy conservation equation for the mixtures. Heats of reaction, the enthalpy change associated with the phase change, and the diffusive transport of enthalpy are all taken into account; but the dependence of enthalpy on pressure, which is usually a small effect in most nonisothermal flows encountered in chemical reaction systems, is ignored. The energy equation is coupled to the LB equations for species transport and pseudopotential interaction forces through the EOS by using the filtered local pseudotemperature field. The proposed scheme is validated against simple test problems for which analytical solutions can readily be obtained.

Avoiding crystallization of lorazepam during infusion.

Lorazepam is a strong sedative for intensive care patients and a commonly used method of administering it to the patient is by infusion of a freshly prepared lorazepam solution. During lorazepam infusion often unwanted lorazepam crystallization occurs, resulting in line obstruction and reduced lorazepam concentrations. With the aid of solubility measurements a solid-liquid phase diagram for lorazepam in mixtures of a commercially available lorazepam solution and an aqueous glucose solution was determined. This confirmed that the glucose solution acts as an anti-solvent, greatly reducing the lorazepam solubility in the infusion solution. Three approaches are proposed to obtain stable lorazepam solutions upon mixing both solutions and thus to prevent crystallization during infusion: (1) using a high lorazepam concentration, and thus a lower glucose solution volume fraction, in the mixed solution; (2) using an elevated temperature during solution preparation and administration; (3) reducing the lorazepam concentration in the commercial lorazepam solution.

Improved bounce-back methods for no-slip walls in lattice-Boltzmann schemes: theory and simulations.

A detailed analysis is presented for the accuracy of several bounce-back methods for imposing no-slip walls in lattice-Boltzmann schemes. By solving the lattice-BGK (Bhatnagar-Gross-Krook) equations analytically in the case of plane Poiseuille flow, it is found that the volumetric approach by Chen et al. is first-order accurate in space, and the method of Bouzidi et al. second-order accurate in space. The latter method, however, is not mass conservative because of errors associated with interpolation of densities residing on grid nodes. Therefore, similar interpolations are applied to Chen's volumetric scheme, which indeed improves the accuracy in the case of plane Poiseuille flow with boundaries parallel to the underlying grid. For skew boundaries, however, it is found that the accuracy remains first order. An alternative volumetric approach is proposed with a more accurate description of the geometrical surface. This scheme is demonstrated to be second-order accurate, even in the case of skew channels. The scheme is mass conservative in the propagation step because of its volumetric description, but still not in the collision step. However, the deviation in the mass is, in general, found to be small and proportional to the second-order terms in the standard BGK equilibrium distribution. Consequently, the scheme is a priori mass conservative for Stokes flow.

Volumetric method for calculating the flow around moving objects in lattice-Boltzmann schemes.

A method for calculating the fluid flow around moving objects is presented, based on a volumetric representation of the lattice-Boltzmann scheme and surfaces defined by facets. It enables us to move objects of arbitrary shape and orientation independent of the position of the grid nodes. To represent the motion of the object, additional momentum is added to the reflected particles from each facet in the propagation step. These particles are redistributed on nodes in the vicinity of the surface, depending on the position and orientation of the facet. Because the surface is considered to be closed, additional techniques need to be used to guarantee the conservation of mass. The flow field of a moving periodic cubic array of cubes at two Re numbers (Re=0.5 and Re=50) is compared with that of a fixed array. For Re=0.5, no significant deviations are found for the velocity field, pressure field, and the drag force. For Re=50, the drag and pressure field exhibit small fluctuations that relate to the position of the surface relative to the position of the grid. However, the influence of the pressure fluctuations on the velocity field is very small. Results on the velocity for a moving array of cubes show second-order accuracy in the lattice spacing. For physical consistency, the drag force on a periodic cubic array of moving spheres at Re=0.5 is compared with Hasimoto's analytical solution. The dependence on the grid spacing, the resolution of the surface of the object, and the viscosity have been studied. The discrepancies between simulations and the analytical results are smaller than 1.5%. For Re=50, the drag force, the streamline pattern, and the pressure field around a moving sphere in a large periodic domain showed good agreement with data from literature on a single sphere in an infinitely large flow field.