A new method for the numerical solution of integral equation approximations

A new numerical technique for solving the Ornstein-Zernike equation is described. It is particularly useful in solving the Ornstein-Zernike equation for approximations and pair potentials (such as the Percus-Yevick and mean spherical approximations for finite ranged potentials) which imply a finiteranged direct correlation function since for such approximations the numerical technique is essentially exact. The only approximation involved in such cases is the discretization of direct and total correlation functions over the finite range on which the direct correlation function is nonzero. Thus, the new method avoids truncation of the total correlation function and should permit the critical point and spinodal curve to be mapped out with greater accuracy than is permitted by existing methods. Preliminary explorations on the stability and accuracy of the method are described.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Solution of the Percus-Yevick equation in the coexistence region of a simple fluid

There has been much recent interest in the behavior of integral-equation theories for the distribution functions of a fluid near the critical point and in the two-phase region. For most systems, implementation of these theories necessitates numerical solution of the integral equations. However, for two examples, the adhesive hard sphere fluid in the Percus-Yevick approximation and the hard sphere plus Yukawa tail model in the mean spherical approximation, analytical solutions of the Ornstein-Zernike equation are available. In this work we consider the comparison of results obtained via numerical methods with the analytical solution of the Percus-Yevick equation for the adhesive hard sphere fluid. This complements a recent study by us of the mean spherical approximation for the hard sphere plus Yukawa tail fluid. This allows us to examine carefully how errors arise in the numerical solutions. We examine the accuracy of numerical calculations of the critical exponents as well as the interpretation of solutions obtained in the coexistence region. We discuss the implications of this work for applications to more realistic potentials where only numerical solutions are available.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Extension to Planck''s equation for predicting freezing times of foodstuffs of simple shapes

Planck's equation for predicting freezing times ignores sensible heat and the gradual character of the phase-change process in foodstuffs. By making certain analytical approximations to take these effects into account, a simple freezing-time prediction method is obtained that uses no empirical factor, chart or advanced algebra. The freezing process is divided into cooling and phase-change periods, the latter being calculated with Planck's equation, the former with extensions to Newton's law of cooling. The gradual character of the phase-change process is taken into account by the use of a ‘mean freezing temperature’, while the thermophysical properties of the material are approximated by straight-line segments. The method agrees with published data as well as or better than any previous procedure, including finite-difference computations.     

The effect of freezing rate on the accuracy of numerical freezing calculations

The accuracy of finite difference and finite element freezing time predictions was examined. The accuracy of the predictions was shown to depend on the rate of freezing, with the extent of underprediction increasing as the rate of freezing increased. A feasible explanation for this is that the deviation of the actual physical behaviour from the models used is more significant at higher rates. The accuracy of predictions is therefore limited more by the physical approcimations than by numerical approximations. Only a marginal improvement, if any, would be expected by elaborating the numerical schemes. Until the physical behaviour of food freezing can be more accurately quantified, predictions to better than ±10% appear, therefore, impracticable. Such accuracy can be obtained by a simple prediction method.     

Determination of freezing rates of some fruit and vegetable products

Experimentally determined freezing rates of selected fruit and vegetable varieties together with samples of simulated test substances were compared with freezing rates given by Planck's equation using the computer program developed in Marmara Research Institute. The modified Charm's program was applied to the fruit and vegetable samples with predicted thermal properties. The freezing rates determined were 6.8, 6.3, 6.6, 7.5 and 6.3 cm h⁻¹ for carrot, strawberry, sour cherry, plum and leek samples respectively. Good production was achieved based on test substances with similar water content.     

A corresponding-states principle for the equation of state of hard-convex-body fluids

A theoretically based corresponding-states principle is developed for the equation of state of hard-convex-body fluids. For all the fluids considered, the excess compressibility factor, reduced by means of a parameter which can be determined analytically. lies on a single curve whose analytical expression can be obtained from the equation of state of the hard-sphere fluid.     

A corresponding-states principle for the equation of state of linear homonuclear fused-hard-sphere fluids

A theoretically based corresponding-states principle previously developed for the equation of state of hard-convex-body fluids is extended to rigid linear homonuclear fused-hard-sphere fluids. Effective volumes and shapes are introduced in order to account for the nonconvexity of the molecules. The excess compressibility factor, reduced by means of a parameter which can be determined analytically, is a common function of the effective packing fraction. The analytical expression for the function can be obtained from the equation of state of the hard-sphere fluid. Existing simulation data for diatomics, triatomics and tetraatomics show excellent agreement with the corresponding-states principle.     

The thermal conductivity of commercial brines and seawater in the freezing range

In the absence of exact data for the physical properties of the brine contents of meat and fish, the author proposes an ‘Ersatz’ brine model bases on the known properties of commercial brines. The resulting thermal conductivities of the slush and that of the dry muscle are introduced into the modified Maxwell-Eucken equation for calculating the conductivity in the freezing range for several meats and fish of varying brine contents. A series of 15 test diagrams taken from various publications is analysed and discussed.     

Photonic realization of the deformed Dirac equation via the segmented graphene nanoribbons under inhomogeneous strain

ABSTRACT

Starting from an engineered periodic optical structure formed by waveguide arrays comprised of two interleaved lattices, we simulate a deformed Dirac equation. We show that the system also simulates graphene nanoribbons under strain. This optical analogue allows us to study the phenomenon of Zitterbewegung for the modified Dirac equation. Our results show that the amplitude of Zitterbewegung oscillations changes as the deformation parameter is changed.     

Developments in chilling and freezing of fish

The report sums-up progress in the comprehension of physicochemical and microbiological processes occurring during the chilling and freezing of fish. With physicochemical reactions, three main phenomena occur during storage, namely, product drying, oxidative rancidity and muscular protein changes, particularly with myosine, this latter alteration now popularly known as freezing denaturation.Following a review of various shipboard processes for fresh fish catches, such as the use of coolants, additives, handling operations, etc, the report deals with post-shipboard functions such as freezing, storage, storage disorders and remedial action.     

The Tait equation: 100 years on

The Tait equation, which is now widely used to fit liquid density data over wide pressure ranges, is a modification of the original equation of Tait, published 100 years ago, to fit his results on the compressibility of fresh water and seawater at different pressures. The range of applicability of these different equations is discussed and it is concluded that their simplicity and accuracy in reproducing high pressure density data for dense gases, liquids, solids, and liquid mixtures will ensure their continued use.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

蓄冷板冻结与释冷的实验研究

通过实验的方式,分别研究了初始温度为30℃的Na Cl蓄冷板在-25、-35和-40℃的环境中的冻结过程以及初温度为-25℃的Na Cl蓄冷板在-10、-5和0℃环境中的释冷过程。实验结果表明:在冻结过程中,当环境温度低于Na Cl共晶液的共晶温度-21.2℃时,环境温度对共晶液开始结晶的时间有较大影响,而对共晶液从开始结晶至完全冻结过程所需时间影响较小;释冷过程中,环境温度高于Na Cl共晶液共晶温度-21.2℃时,外界环境对蓄冷板释冷所需时间以及共晶冰开始融化到完全融化的过程影响较大。     

Parametric study of economical energy usage in freezing tunnels

Large amounts of electricity are consumed in food freezing tunnels. An actual freezing tunnel at a citrus processing plant was studied experimentally to determine its operating characteristics. A computer model was also developed, and predicted temperature profiles were compared to experimental data. A parametric study was performed to determine the effect of the bed velocity, ambient temperature, internal fan loads, and can spacing on the tunnel bed. Methods for improving the effectiveness of the freezing tunnels are discussed. It is concluded that a factor, K, the ratio of fan work divided by the useful refrigeration effect, was the best indicator of economical energy usage in the freezing tunnel.     

盐冻循环条件下SBS改性沥青砂浆的力学性能分析?

在寒冷地区,冬季路面极易出现积雪结冰现象,常使用融雪盐对路面进行融雪除冰,融雪盐的使用会对沥青混合料产生侵蚀。沥青砂浆作为沥青混凝土材料的重要组成部分,在力学性能方面发挥了极其重要的作用。对 SBS 改性沥青盐冻循环前后的三大指标(针入度、软化点和延度)进行了测试,对经历不同盐冻循环的沥青砂浆试件进行单轴压缩蠕变实验,并通过扫描电镜(SEM)研究其微观结构的变化。结果表明,冻融循环和荷载应力会造成沥青砂浆力学性能的下降,因此在昼夜温差较大的北方寒冷地区的冬季应尽量限制重载车辆的通行量以及融雪盐的用量,以减少对路面结构的损坏。     

冷冻聚合法制备多孔P(NIPAm-Co-AAm)水凝胶及其性能研究

采用冷冻聚合法制备了多孔结构的P(NI-PAm-co-AAm)智能水凝胶,利用扫描电子显微镜和比表面积分析仪对水凝胶的多孔结构和表面形貌进行了测试,并测定了水凝胶的平衡溶胀比、溶胀和退溶胀动力学,研究了不同预冷冻聚合时间对水凝胶温度响应速率的影响,并且与传统方法制备的P(NIPAm-co-AAm)水凝胶进行了响应速率对...     

A method for calculating the freezing point of dairy products

Using the method of Leighton, an approximate method of predicting the freezing point of milk products, including ice cream, is developed. It takes account only of the concentrations of sugar and serum. Predictions are tested against a range of experimental measurements and the error is found to be generally less than 0.05°C.     

Analytical method for predicting freezing times of rectangular blocks of foodstuffs

For irregular geometries, the distance from the surface to the thermal centre is not uniform. This makes the calculation of freezing time impossible. The difficulty can be overcome by defining a ‘mean conducting path’ D_m/2, which can then be used to calculate Biot numbers. D_m/2 is considered to be the mean length of heat conducting paths from the surface of the body to the thermal centre. For rectangular blocks, experimental data suggest that D_m is proportional to the geometric mean of the two shorter sides. An equation for calculating the effective Biot number is presented, which incorporates one empirical coefficient. For squat-shaped bodies a good estimate of D_m can be obtained by averaging the shortest and longest dimensions. Pham's freezing time prediction method applied to brick-shaped blocks yields about the same accuracy as for the basic shapes (infinite slabs, infinite cylinders and spheres), and is more accurate than previous methods, including finite-different methods.     

液氮喷淋冷冻性能计算分析

利用模拟计算分析方法对液氮喷淋冷藏车中影响冻结物冻藏性能的因素进行研究,分析液氮喷嘴数量和喷嘴布置形式对冻结特性的影响以及循环风的强度对冷冻空间和冻结物温度变化影响、液氮喷量对冻结特性的影响,提出合理喷液量的影响因素关系.     

超声波辅助马铃薯冻结的实验研究

为了研究超声波辅助沉浸冻结的机理,将马铃薯样品分别浸入脱气冷冻液与未脱气冷冻液中冷却。每次实验时,从?1℃时开始,启动超声波发生装置,使马铃薯内的水分在超声场中冻结。利用扫描电镜比较分析不同实验条件下马铃薯组织的微观结构,实验结果表明不同冷冻液中的马铃薯样品遭受超声波辐射后,其组织在冻结过程中受到的损伤均小于无超声波作用的样品,而且超声波对浸于未脱气冷冻液中样品组织的改善作用更为显著。表明超声波诱发的冷冻液的分子振动与空化均对沉浸冻结有影响。     

An analysis of factors influencing precision of thermal property values during freezing

An unfrozen water fraction prediction equation is proposed that compensates for both unfreezable water (M_b) and the equivalent molecular weight of solids (MW_s) during the food freezing process. The parameters (M_b and MW_s), when obtained from published unfrozen water content data, demonstrate that the proposed equation describes the data very well. When unfrozen water content data is not available, MW_s can be obtained from the initial freezing point (T_f) of the food product, and M_b can be obtained using calorimetric methods. The precision of MW_s is shown to be very dependent on the precision of T_f for a frozen food with medium (75%) to high (95%) moisture content. The precision of the input variables required in the proposed equations (temperature, M_b, MW_s, solids content) along with other physical parameters of the unfrozen food product (density, specific heat, and thermal conductivity) were investigated in an effort to determine the predictability of the frozen food density, apparent specific heat, enthalpy, thermal conductivity and unfrozen water content.