THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.

ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

APPLICATION POSSIBILITY OF BINARY NONAZEOTROPIC REFRIGERANT IN JET REFRIGERATION *

This paper analyzes the possibility of applying binary nonazeotropic refrigerants in the jet refrigeration cycle. The thermodynamic cycle performance of two kinds of working pairs (R30/R142b, R30/R124) are calculated using the EOS of PR equation of state, and the results are discussed. The theoretical calculations indicate that refrigerating quality can be improved if the binary mixtures evaporate just in the low temperature region. The character of the rejecter to compress two phase medium supports the possibility of this kind of cycle.

Interaction between compressibility and particulate suspension on peristaltically driven flow in planar channel

The peristaltic pumping of a viscous compressible liquid mixed with rigid spherical particles of the same size in a channel is theoretically investigated. The momentum equations for the compressible flow are solved with a perturbation analysis. The analysis is carried out by duly accounting for the nonlinear convective acceleration terms for the fluid part on the wavy wall. The zeroth-order terms yield the Poiseuille flow, and the first-order terms give the Orr-Sommerfeld equation. The explicit expression for the net axial velocity is derived. The effects of the embedded parameters on the axial fluid velocity are studied through different engineering applications. The features of the flow characteristics are analyzed and discussed in detail. The obtained results are evaluated for various parameters associated with the blood flow in the blood vessels with diameters less than 5 500 μm, whereas the particle diameter has been taken to be 8 μm. This study provides a scope to evaluate the effect of the theory of two-phase flow characteristics with compressible fluid problems, and is helpful for understanding the role of engineering applications of pumping solid-fluid mixture by peristaltically driven motion.

INCOMPRESSIBLE LIMIT OF A COMPRESSIBLE LIQUID CRYSTALS SYSTEM

This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space R^N and a bounded domain of R^N with Dirichlet boundary conditions. Here we set the number of dimension N = 2 or 3.

EFFECTS OF LIQUID COMPRESSIBILITY ON RADIAL OSCILLATIONS OF GAS BUBBLES IN LIQUIDS

For forced radial oscillations of gas bubbles in liquids, a more rigorous expression of the acoustic damping constant based on Keller＇s equation is developed. Comparison with those in published papers is also made. The expression offered in this paper will improve the predictions of total damping constant in particular for high frequencies and large bubbles, i.e., large ωR0 / c1 （ ω is the frequency of driving sound field, Ro is the equilibrium bubble radius, c1 is the sound speed in the liquid）. Examples in ultrasound imaging and acoustical oceanography are demonstrated.

Incompressible Limit of the Compressible Q-tensor System of Liquid Crystals

We study the connection between the compressible Navier-Stokes equations coupled by the Qtensor equation for liquid crystals with the incompressible system in the periodic case, when the Mach number is low. To be more specific, the convergence of the weak solutions of the compressible nematic liquid crystal model to the incompressible one is proved as the Mach number approaches zero, and we also obtain the similar results in the stochastic setting when the equations are driven by a stochastic force. Our approach is based on the uniform estimates of the weak solutions and the martingale solutions, then we justify the limits using various compactness criteria.

Effects of liquid compressibility on bubble-bubble interactions between oscillating bubbles

The mutual interaction between cavitation bubbles plays an important role in the physical processes of cavitation. In this paper, a complete model is developed for modelling the mutual interaction between cavitation bubbles with the effects of liquid compressibility fully included. It is found that the liquid compressibility is an important parameter in the determination of the direction of the force （the attraction or repulsion force）, as well as the magnitude of the force. The influences of the liquid compre- ssibility on the mutual interaction force can be categorized into three terms： the first is a new term added on the mutual interaction force in incompressible liquids and this term will vanish if the sizes of two bubbles are equal, the second is the radiation damping term, the third one can be considered as a correction of the mutual interaction force in incompressible liquids with a coefficient and this correction will be prominent for small bubbles and a high ambient pressure.

GLOBAL EXISTENCE AND LONG-TIME BEHAVIOR FOR THE STRONG SOLUTIONS IN H2 TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.

Comparison of short-term and long-term performances for polymer-stabilized sand and clay

A series of tests were carried out on sulfate rich, high-plasticity clay and poorly-graded natural sand to study the effectiveness of a methylene diphenyl diisocyanate based liquid polymer soil stabilizer in improving the unconfined compressive strength （UCS） of freshly stabilized soils and aged sand specimens. The aged specimens were prepared by exposing the specimens to ultraviolet radiation, freeze-thaw, and wet-dry weathering. The polymer soil stabilizer also mitigated the swelling of the expansive clay. For clay, the observations indicated that the sequence of adding water and liquid polymer had great influence on the gained UGS of stabilized specimens. However, this was shown to be of little importance for sand. Furthermore, sand samples showed incremental gains in UCS when they were submerged in water. This increase was significant for up to 4 days of soaking in water after 4 days of ambient air curing. Conversely, the clay samples lost a large fraction of their UCS when soaked in water; however, their remaining strength was still considerable. The stabilized specimens showed acceptable endurance under weathering action, although sample yellowing due to ultraviolet radiation was evident on the surface of the specimens. Except for moisture susceptibility of the clay specimens, the results of this study suggested the liquid stabilizer could be successfully utilized to provide acceptable strength, durability and mitigated swelling.