Initial Water Volume Research Articles

A study on automatic optimal operation of a pump for solar domestic hot water system

The objective of this research is to determine optimal control variables of a collector pump placed on a collector loop to improve the performance of a solar domestic hot water system. A mathematical model of the system is developed to predict its operating performance under real weather conditions at Jeju Island, South Korea. The optimum control variables of the collector loop are investigated based on the relationship between the useful heat gain of the solar collector and the electricity consumption of the collector pump. In addition, the effects of various parameters such as solar collector area, initial water temperature, and volume of storage tank are analyzed. The results of the simulation showed that the optimum variable flow rate was determined at m=0.05ΔTAc/60(kg/s) (Kv=0.05). At this value, the useful heat gain of the solar collector Qu increased by about 1.54% while the electricity consumption of the collector pump Ep sharply decreased to 65.6% when the constant flow was replaced by the variable flow for the collector loop. Furthermore, the system performance is significantly affected by the change of initial water temperature and volume of the storage tank, as well as the collector area.

Optimum scheduling of micro grid connected wind-pumped storage hydro plant in a frequency based pricing environment

This paper presents a new formulation to maximize the operational profit of a micro grid connected hybrid system having wind farm and pumped storage unit for a day ahead electricity market in a frequency based pricing environment. Under frequency based pricing mechanism in India, the pricing for energy exchange is adaptive as per Availability Based Tariff (ABT) rate structure and the payment for deviation from schedule, i.e. Unscheduled Interchange (UI) charge is inversely proportional to the prevailing grid frequency. In this work, a small power system is considered as micro grid and it is expected that the hybrid system connected with the micro grid has a role to play to maintain the micro grid frequency. The pump storage hydro plant is operated to serve the dual role of minimizing the UI flow and maximizing the system economy by participating in frequency control based on energy price. The uncertainties in wind power prediction and loads are considered. The optimum operating schedule of PSH unit in coordination with wind farm is investigated. The optimization is performed by utilizing the water storage availability of pump storage hydro unit. An optimization algorithm is proposed and solved using Artificial Bee Colony algorithm. The solution of the proposed approach gives the strategies to be followed by the hybrid system to operate its pump storage unit. The effect of the initial storage water volume on the performance of the hybrid system has also been investigated. It reveals that the PSH units would not operate simply to compensate for the short fall or the surplus generation of the wind units in a frequency based pricing system. Rather, the pump storage units should take the advantage of the low price periods to maximize the profit of the hybrid system. The hourly energy management scenarios of the hybrid system with the micro grid are reported and the numerical case studies on PSH plant scheduling demonstrate the effectiveness of the proposed approach.

Numerical evaluation of tsunami debris impact loading on wooden structural walls

Water-based disasters such as tsunami, hurricane, and flood can cause significant structural damage to coastal areas and ultimately result in human and socioeconomic losses. Recent studies have highlighted the difficulties associated with estimating tsunami impact loads on residential structures with greater challenges pertaining to estimating the debris impact loads. The main challenges are associated with large variations in debris mass, shape, velocity, and impact angle. According to FEMA P-646 [1], although impact of floating debris is required to be considered by the codes, the added mass of water behind the debris and/or the potential for damming when debris is blocked by structural elements are ignored. Additionally, there is a lack of 3D numerical models that can accurately predict debris impact loads. Due to the three-dimensional dynamic nature of the problem, coupled with highly variable factors affecting debris loads, a 3D finite element (FE) analysis is necessary to determine the debris impact on structures as accurately as possible. To date, one of the major obstacles in modeling tsunami impact on structures is the intense computational demand linked with such models. This paper presents the formulation of an efficient 3D FE model with computational fluid dynamic (CFD) capabilities to study debris impact on interior and exterior wood structural panels. Several important parameters such as initial water volume, water velocity, debris shape, and debris density are varied throughout the analysis in order to determine the individual effect of each parameter as well as the overall effect on wood structural walls. The results for an interior wall panels showed that contribution from water height and velocity is more significant the debris mass in the impact force as water height and velocity increase. Additionally, as the water height increases, the impact force due to debris decreases for an interior panel when debris mass is constant. An exterior panel is significantly closer to a rigid structure, therefore, an increase in impact force due to debris is observed with the increase in water height and debris mass. The results can be used by engineers to estimate debris impact load on wood panels with similar dimension and material properties.

Hydrological modeling of typhoon-induced extreme storm runoffs from Shihmen watershed to reservoir, Taiwan

Typhoon-induced extreme storm runoffs often cause flood hazards. In this study, a hydrological model (HEC-HMS) was applied to Shihmen watershed located in Taiwan. Three typhoon-induced storm events, with return period ranging from 1 to 90 years, were used in case studies to characterize storm runoff. With a 5-year storm for model calibration, model parameters were carefully calibrated through the comparison between model simulated and observed flows at a stream gage station. The calibrated model was then verified for a 90-year storm and a 1-year storm event. Results indicate that the calibrated and verified HEC-HMS hydrological model is capable of providing satisfactory predictions of the typhoon-induced extreme storm runoff to support reservoir operation and flood hazard mitigation. Based on model simulations, typhoon-induced water table increases for different initial water volumes at Shihmen Reservoir was derived by adding storm-runoff volume to the reservoir’s initial elevation-volume rating curve. Water tables above the top elevation of the dam in the reservoir indicate the need for immediate water releases to avoid the risk of overflow over the dam.

Transient dynamic response of solar diffusion driven desalination

The dynamic response for the solar diffusion driven desalination (DDD) process has been investigated. The heat and mass transfer within the direct contact evaporator is analyzed by one-dimensional conservation equations. The heat and mass transport models account for the transient variations within the packed bed due to time varying inlet water and air temperatures and humidity. The conservation equations are solved numerically using a finite difference scheme to predict water, air/vapor mixture and packed bed temperatures and humidity ratio within the evaporator and the condenser. The system dynamic response for the packed bed materials, wettability, and liquid hold-up, sudden increase–decrease in the inlet water temperature is investigated. It is found that the response time for the outlet water to reach the steady state temperature in the evaporator is shorter for lower liquid hold-ups. The response time is not sensitive to the packing material. Higher wettability does not affect the response time, but it does result in improved heat transfer with a higher exit air temperature and lower exit water temperature. The steady state temperature in the evaporator is not dependent on the heat capacity of the packing material, and liquid hold up. A delayed operating mode for the solar DDD is introduced to enhance the fresh water production rate. It is found that increasing the initial saline water temperature and decreasing the initial water volume in the seawater tank results in a higher fresh water production rate.

A Simulation Model for Predicting the Performance of Solar Domestic Hot Water System

The article deals with the modeling and simulation aspects of the performance improvement of a solar domestic hot water system. A mathematical model of this system is carried out to predict its operating performance under specified weather conditions of Jeju Island, Korea. The optimum mass flow rate through collector based on the relationship between the useful heat gain of solar collector and the electricity consumption of solar pump is investigated. Besides, the effect of various parameters such as solar collector area, initial water temperature and volume of storage tank is analyzed. The result of the simulation shows that the optimum mass flow rate was determined at kg/s with the new coefficient . At this value, the amount of useful heat gain slightly decreased about 84.3 (Wh) corresponds to 0.16% but the amount of electricity consumption strongly decreased about 227.8 (Wh) corresponds to 48.8% compares with kg/s ( ) was proposed by . Furthermore, the system performance is affected strongly by the change of collector area, initial water temperature and volume of storage tank.

Analysis of peptide uptake and location of root hair‐promoting peptide accumulation in plant roots

Peptide uptake by plant roots from degraded soybean-meal products was analyzed in Brassica rapa and Solanum lycopersicum. B. rapa absorbed about 40% of the initial water volume, whereas peptide concentration was decreased by 75% after 24 h. Analysis by reversed-phase HPLC showed that number of peptides was absorbed by the roots during soaking in degraded soybean-meal products for 24 h. Carboxyfluorescein-labeled root hair-promoting peptide was synthesized, and its localization, movement, and accumulation in roots were investigated. The peptide appeared to be absorbed by root hairs and then moved to trichoblasts. Furthermore, the peptide was moved from trichoblasts to atrichoblasts after 24 h. The peptide was accumulated in epidermal cells, suggesting that the peptide may have a function in both trichoblasts and atrichoblasts.

Comparison of Fluid Compartments and Fluid Responsiveness in Septic and Non-Septic Patients

Our objective was to study the response to a fluid load in patients with and without septic shock, the relationship between the response and baseline fluid distributions and the ratios of the various compartments. A total of 18 patients with septic shock and 14 control patients without pathologies that increase capillary permeability were evaluated prospectively. We used transpulmonary thermodilution to measure the extravascular lung water index, intrathoracic blood volume index and pulmonary blood volume. For the measurement of the initial distribution volume of glucose, plasma volume and extracellular water we used dilutions of glucose, indocyanine green and sinistrin respectively. Transpulmonary thermodilution and dilutions of glucose were repeated 75 minutes after the beginning of the fluid load. The patients in the septic group had higher volumes of extracellular water (median 295 vs. 234 ml/kg, P < 0.001), lower intrathoracic blood volume index (median 894 vs. 1157 ml/m2, P < 0.003), higher pulmonary permeability ratios (extravascular lung water/pulmonary blood volume) (P < 0.003) and higher systemic permeability ratios (interstitial/plasma volume) (P < 0.04). The intrathoracic blood volume index increase after fluid loading was lower in the septic group (10 vs. 145 ml/m2). The pulmonary permeability ratios did not correlate with the systemic permeability ratios, and in the septic group, the percentage volume retained in the intrathoracic blood volumes after fluid loading did not correlate with the systemic permeability ratios. Septic shock can cause a redistribution of fluids. Fluid administration in these patients produced a minimal increase in intrathoracic blood volume, and the percentage of volume retained in this space was not correlated with the interstitial/plasma volume ratio.

Determination of Water Saturation in Relatively Dry Porous Media Using Gas‐Phase Tracer Tests

Soil desiccation (drying), induced by dry air injection and moist air extraction, is a potentially robust remediation process to slow migration of inorganic or radionuclide contaminants through the vadose zone. The application of gas‐phase partitioning tracer tests has been proposed as a means to estimate initial water volumes and to monitor the progress of the desiccation process at pilot tests and field sites. In this study, tracer tests were conducted in porous medium columns with various water saturations using SF6 as the conservative tracer and trichlorofluoromethane and difluoromethane as the water‐partitioning tracers. For porous media with minimal silt or organic matter fractions, tracer tests provided reasonable saturation estimates for saturations close to zero. For sediments with significant silt or organic matter fractions, however, tracer tests only provided satisfactory results when the water saturation was greater than 0.1 to 0.2. For drier conditions, the apparent tracer retardation increased due to air–soil sorption, which is not included in traditional retardation coefficients derived from advection–dispersion equations accounting only for air–water partitioning and water–soil sorption. Based on these results, gas‐phase partitioning tracer tests may be used to determine initial water volumes in sediments, provided that the initial water saturations are sufficiently large. Tracer tests are not suitable for quantifying moisture content in relatively dry sediments, however, especially if significant amounts of organic matter or silt are present.

Facile preparation of monodisperse micrometer-sized hollow silica spheres with tunable size and commendable surface topography

The fabrication of hollow silica spheres (HSS) is of great importance due to its plenty of implications. Till now, several methods to prepare HSS have been reported, which existed some drawbacks. Herein, a facile and efficient approach was developed to successfully fabricate micrometer-sized monodisperse HSS based on templating method. The approach was achieved by changing the initial water volume and using ethylene glycol dimethacrylate (EGDMA) as the crosslinking agent. The alteration of water volume was the key factor in controlling the size of HSS, and EGDMA was used to accessorily enlarge the bulk of template spheres. In this way, the uniform HSS were controlled in micrometer scale, which simultaneously possessed the favorable surface topography. This method could achieve high reproducibility and would become a general method to systematically manipulate the size and shape of inorganic spheres as we expected. Most importantly, the formation mechanism for HSS was presented and some key influencing factors were analyzed.

Experimental measurement of the solubility of bismuth phases in water vapor from 220°C to 300°C: Implications for ore formation

Abstract Preliminary measurements were carried out of the solubility of the O 2- buffering assemblage bismuth + bismite (Bi 2 O 3 ) in aqueous liquid–vapor and vapor-only systems at temperatures of 220, 250 and 300 °C. All experiments were carried out in Ti reaction vessels and were designed such that the Bi solids were contained in a silica tube that prevented contact with liquid water at any time during the experiment. Two blank (no Bi solids present) liquid–vapor experiments at 220 °C yielded Bi concentrations (±1 σ ) in the condensed liquid of 0.22 ± 0.02 mg/L, whereas the solubility measurements at this temperature yielded an average value of approximately 6 ± 9 mg/L, with replicate experiments ranging from 0.3 to 26 mg/L. Although the 6 mg/L value is associated with a considerable degree of uncertainty, the experiments do indicate transport of Bi through the vapor phase. Measured Bi concentrations in the condensed liquid at 250 °C were in the same range as those at 220 °C, whereas those at 300 °C were significantly lower (i.e., all below the blank value). Vapor-only experiments necessarily contained much smaller initial volumes of water, thereby making the results more susceptible to contamination. Single blank runs at 220 and 300 °C yielded Bi concentrations of 82 and 16 mg/L, respectively. Measured concentrations (±1 σ ) of Bi in the vapor-only solubility experiments at 220 °C were 235 ± 78 mg/L for an initial water volume of 0.5 mL, and at 300 °C were 56 ± 30 mg/L and 33 ± 21 for initial water volumes of 1 and 2 mL, respectively, suggesting strong preferential partitioning of Bi into the vapor. The results indicate a negative dependence of Bi solubility on temperature, but are inconclusive with respect to the dependence of Bi solubility on water density or fugacity. The experiments reported here suggest that significant Bi transport is possible in the vapor phase. Comparison of the liquid–vapor and vapor-only experiments further suggests that, at the conditions studied, the solubility of Bi in the vapor is significantly higher than that in the liquid phase (calculated distribution coefficients, i.e., C Vapor / C Liquid at 220 °C ranged from 81 to 168, where C is concentration in mg/L). The concentrations measured in the vapor-only experiments at 220 °C are approximately 11 orders of magnitude higher than those calculated from available thermodynamic data assuming no interaction between volatile Bi species and water molecules. This finding indicates that hydration of volatile Bi species probably occurs to a significant extent; similar to behavior observed previously in published vapor phase solubility studies of other metals. However, the interpretation of the results was complicated by the formation of Bi silicate phases and the lack of certainty that O 2 fugacity buffering was effective throughout the experiments.

Initial Water Absorption Characteristics and Volume Changes at Different Deterioration Levels in Welsh Onion Seed (Allium fistulosum L.)

The germination activity and the initial water absorption characteristics of Welsh onion seeds were examined at different levels of deterioration. Using data on the changes in moisture content of Welsh onion seeds, a non-linear least squares method was applied to an approximate solution of the diffusion equation. The constant for a given solid shape values (B1) of the diffusion model were estimated to be about 0.8. The data were fitted to the exact solution for the infinite plane sheet diffusion model using a non-linear least squares method. The measured results agreed with the calculated results. The specific volume changes of the sample were determined using particle density measurements at several moisture contents by a liquid-displacement method using a pycnometer. Using an empirical equation with three parameters that related moisture content and temperature to specific volume, the measured data agreed with the values calculated from the equation. The results of the comparison of aging effects among the three deterioration levels of Welsh onion seed showed that the water absorption rate of aged seeds was lower than the fresh seeds at all tested temperatures. Moreover, the aging effect appeared as lower volume expansions by water absorption, besides the increase of abnormal and non-germination seeds in the germination test.

Procedure to Enhance the Recovery Rate of Fungus Gnat, Bradysia sp. nr. coprophila Lintner (Diptera: Sciaridae) Adults from Growing Medium

Fungus gnats, Bradysia spp., are major insect pests in greenhouses and interiorscapes. Management typically involves the use of either insecticides or biological control agents such as entomopathogenic nematodes. Efficacy trials provide information to greenhouse producers on the effectiveness of these management options. However, a simple procedure that rapidly evaluates the performance of control products against fungus gnat larvae is needed. Because fungus gnat larvae inhabit the growing medium, excess or deficient growing medium moisture may reduce adult fungus gnat emergence, thus confounding effects from efficacy trial treatments. Therefore, it is important to determine the amount of moisture and moisture content that results in the highest recovery of fungus gnat adults. We conducted two replicated experiments in a completely randomized design using a range of initial water volumes (treatments) and two larval stages (second and third) of the fungus gnat, Bradysia sp. nr. coprophila. The success of the procedure was based on the number of fungus gnat adults that emerged per treatment. In the first experiment, initial water volumes of 0, 25, 50, 75, 100, 150, and 200 mL were applied to 300 mL of a soilless growing medium consisting of 50% composted pine bark, 20% Canadian sphagnum peatmoss, 10% perlite, and 20% medium coarse vermiculite (SB300 Universal Mix). In general, the highest mean numbers (range, 11.2 to 14.6) of fungus gnat adults were recovered from growing medium treated with 50, 75, and 100 mL of water. In the second experiment, initial water volumes (treatments) of 50, 55, 60, 65, 70, and 75 mL were applied to 300 mL of the soilless growing medium (SB300 Universal Mix). There were no significant differences in the mean number of fungus gnat adults recovered regardless of the larval instar (second instar: 15.8 to 17.7; third instar: 14.4 to 17.4). The final percent moisture content ranged from 65% to 68% for the second instars and 56% to 66% for third instars. This study demonstrates that the highest number of fungus gnat adults may be recovered from soilless growing medium (SB300 Universal Mix) treated with between 50 and 75 mL of water, thus enhancing the confidence in any data set generated when evaluating insecticides or biological control agents for control of fungus gnats.

Water transport in epididymal and ejaculated rhesus monkey ( Macaca mulatta) sperm during freezing

In the present study, we report the effects of cooling ejaculated and epididymal rhesus monkey ( Macaca mulatta) sperm with and without the presence of a cryoprotective agent, glycerol. Water transport data during freezing of ejaculated and epididymal sperm cell suspensions were obtained at a cooling rate of 20 °C/min in the absence of any cryoprotective agents and in the presence of 0.7 M of glycerol, as well. Using previously published values, the macaque sperm cell was modeled as a cylinder of length 73.83 μm with a radius of 0.40 μm and an osmotically inactive cell volume, V b, of 0.772 V o, where V o is the isotonic cell volume. This translated to a surface area, SA to initial water volume, WV ratio of ∼22 μm −1. By fitting a model of water transport to the experimentally determined volumetric shrinkage data, the best-fit membrane permeability parameters (reference membrane permeability to water at 0 °C, L pg or L pg [ cpa] and the activation energy, E Lp or E Lp [ cpa]) were found to range from: L pg or L pg [ cpa] = 0.0020–0.0029 μm/min-atm; E Lp or E Lp [ cpa]) = 10.6–18.3 kcal/mole. By incorporating these membrane permeability parameters in a recently developed equation (optimal cooling rate, B opt = 1009.5 · exp ( - 0.0546 · E Lp ) · ( L pg ) · ( SA WV ) ; where the units of B opt are °C/min, E Lp or E Lp [ cpa] are kcal/mole, L pg or L pg [ cpa] are μm/min-atm and SA/WV are μm −1), we determined the optimal rates of freezing macaque sperm to be ∼23 °C/min (ejaculated sperm in the absence of CPAs), ∼29 °C/min (ejaculated sperm in the presence of glycerol), ∼24 °C/min (epididymal sperm in the absence of CPAs) and ∼24 °C/min (epididymal sperm in the presence of glycerol). In conclusion, the subzero water transport response and consequently the subzero water transport parameters are not significantly different between the ejaculated and epididymal macaque spermatozoa under corresponding cooling conditions.

Detection and isolation of H5N1 influenza virus from large volumes of natural water

Various species of aquatic or wetlands birds can be the natural reservoir of avian influenza A viruses of all hemagglutinin (HA) subtypes. Shedding of the virus into water leads to transmission between waterfowl and is a major threat for epidemics in poultry and pandemics in humans. Concentrations of the influenza virus in natural water reservoirs are often too low to be detected by most methods. The procedure was designed to detect and isolate low concentrations of the influenza virus in large volumes of water without the need for costly installations and reagents. The virus was adsorbed onto formalin-fixed erythrocytes and subsequently isolated in chicken embryos. Sensitivity of the method was determined using a reverse-genetic H5N1 virus. A concentration as low as 0.03 of the 50% egg infection dose per milliliter (EID 50/ml) of the initial volume of water was effectively detected. The probability of detection was ∼13%, which is comparable to that of detecting the influenza virus M-gene by PCR amplification. The method can be used by field workers, ecologists, ornithologists, and researchers who need a simple method to isolate H5N1 influenza virus from natural reservoirs. The detection and isolation of virus in embryonated chicken eggs may help epidemiologic, genetic, and vaccine studies.

Maximization of Water Storage in Backfilled and Lined Channels and Dimples Subject to Evaporation and Leakage

A channel or axisymmetric dimple filled with a coarse porous material and aimed at a temporary storage of infiltrated water as a perched water table aquifer is studied. The bottom shape is varied based on the criterion of maximal water storage after a certain period of drainage and evaporation. Leakage into the vadose zone through a thin liner occurs with a specific discharge proportional to the pressure drop across the liner. Evaporation through a horizontal shrinking water table is spatially uniform. An ordinary differential equation, which follows from the mass balance condition, is solved either explicitly or numerically. The class of triangular, polynomial, and conical sections is studied. The shape of maximal water retention is calculated for a given initial stored water volume or water table width, evaporation intensity, liner thickness and conductivity, vadose zone pressure beneath the liner, and selected time interval between two sequential infiltration events.

Medium optimization of antifungal lipopeptide, iturin A, production by Bacillus subtilis in solid-state fermentation by response surface methodology

Iturin A, a lipopeptide antibiotic produced by Bacillus subtilis RB14-CS, suppresses the growth of various plant pathogens. Here, enhancement of iturin A production in solid-state fermentation (SSF) on okara, a soybean curd residue produced during tofu manufacturing, was accomplished using statistical experimental design. Primary experiments showed that the concentrations of carbon and nitrogen sources were the main factors capable of enhancing iturin A production, whereas initial pH, initial water content, temperature, relative humidity, and volume of inoculum were only minor factors. Glucose and soybean meal were the most effective among tested carbon and nitrogen sources, respectively. Based on these preliminary findings, response surface methodology was applied to predict the optimum amounts of the carbon and nitrogen sources in the medium. The maximum iturin A concentration was 5,591 mug/g initial wet okara under optimized condition. Subsequent experiments confirmed that iturin A production was significantly improved under the predicted optimal medium conditions. The SSF product generated under the optimized conditions exhibited significantly higher suppressive effect on the damping-off of tomato caused by Rhizoctonia solani K-1 compared with the product generated under the non-optimized conditions.

Subzero water permeability parameters and optimal freezing rates for sperm cells of the southern platyfish, Xiphophorus maculatus

This study reports the subzero water transport characteristics (and empirically determined optimal rates for freezing) of sperm cells of live-bearing fishes of the genus Xiphophorus, specifically those of the southern platyfish Xiphophorus maculatus. These fishes are valuable models for biomedical research and are commercially raised as ornamental fish for use in aquariums. Water transport during freezing of X. maculatus sperm cell suspensions was obtained using a shape-independent differential scanning calorimeter technique in the presence of extracellular ice at a cooling rate of 20 °C/min in three different media: (1) Hanks’ balanced salt solution (HBSS) without cryoprotective agents (CPAs); (2) HBSS with 14% (v/v) glycerol, and (3) HBSS with 10% (v/v) dimethyl sulfoxide (DMSO). The sperm cell was modeled as a cylinder with a length of 52.35 μm and a diameter of 0.66 μm with an osmotically inactive cell volume ( V b) of 0.6 V 0, where V 0 is the isotonic or initial cell volume. This translates to a surface area, SA to initial water volume, WV ratio of 15.15 μm −1. By fitting a model of water transport to the experimentally determined volumetric shrinkage data, the best fit membrane permeability parameters (reference membrane permeability to water at 0 °C, L pg or L pg [cpa] and the activation energy, E Lp or E Lp [cpa]) were found to range from: L pg or L pg [cpa] = 0.0053–0.0093 μm/min atm; E Lp or E Lp [cpa] = 9.79–29.00 kcal/mol. By incorporating these membrane permeability parameters in a recently developed generic optimal cooling rate equation (optimal cooling rate, B opt = 1009.5 exp ( - 0.0546 E Lp ) ( L pg ) ( SA WV ) where the units of B opt are °C/min, E Lp or E Lp [cpa] are kcal/mol, L pg or L pg [cpa] are μm/min atm and SA/WV are μm −1), we determined the optimal rates of freezing X. maculatus sperm cells to be 28 °C/min (in HBSS), 47 °C/min (in HBSS + 14% glycerol) and 36 ° C/min (in HBSS + 10% DMSO). Preliminary empirical experiments suggest that the optimal rate of freezing X. maculatus sperm in the presence of 14% glycerol to be ∼25 °C/min. Possible reasons for the observed discrepancy between the theoretically predicted and experimentally determined optimal rates of freezing X. maculatus sperm cells are discussed.

A Simplified Procedure to Determine the Optimal Rate of Freezing Biological Systems

The effect of several cell-level parameters on the predicted optimal cooling rate B(opt) of an arbitrary biological system has been studied using a well-defined water transport model. An extensive investigation of the water transport model revealed three key cell level parameters: reference permeability of the membrane to water L(pg), apparent activation energy E(Lp), and the ratio of the available surface area for water transport to the initial volume of intracellular water (SA/WV). We defined B(opt) as the "highest" cooling rate at which a predefined percent of the initial water volume is trapped inside the cell (values ranging from 5% to 80%) at a predefined end temperature (values ranging from -5 degrees C to -40 degrees C). Irrespective of the choice of the percent of initial water volume trapped and the end temperature, an exact and linear relationship exists between L(pg), SA/WV, and B(opt0. However, a nonlinear and inverse relationship is found between E(Lp) and B(opt). Remarkably, for a variety of biological systems a comparison of the published experimentally determined values of B(opt) agreed quite closely with numerically predicted B(opt) values when the model assumed 5% of initial water is trapped inside the cell at a temperature of -15 degrees C. This close agreement between the experimental and model predicted optimal cooling rates is used to develop a generic optimal cooling rate chart and a generic optimal cooling rate equation that greatly simplifies the prediction of the optimal rate of freezing of biological systems.

Determining Rate of Flow through a Funnel

This inquiry-based Activity illustrates kinetics concepts using the rate of the flow of water through several funnels made from plastic beverage bottles and rubber stoppers with varyings numbers and sizes of holes. The amount of time it takes different volumes of water to pass through different funnels is recorded. A graph of time and volume data from the Activity results in a curve whose slope equals the rate of water flow. Students are asked to anticipate what conditions control the rate of water flow, and are given a variety of stoppers to test their hypothesis. Sample experimental data is included as online supplemental material. Data is shown for the emptying rate of 1) one-, two-, and three-hole stoppers; 2) different hole sizes for stoppers; and 3) different column heights for the same initial volume of water.