Maximum Enrichment Ratio Research Articles

Investigation of parameters and porous plug enhanced enrichment with field-amplified sample stacking in microchip

With the recent great interest in microfluidic devices, a better understanding of preconcentration technology has become increasingly important. Herein, concentration enrichment of charged samples is achieved by using field-amplified sample stacking (FASS) technology in the microchannel. This paper aims to develop a fundamental understanding of FASS and to propose a method to enhance the enrichment quality of FASS. First, numerical investigations are carried out to systematically study the effects of various parameters including the applied voltage, the charged properties of the sample, the buffer concentration ratio, the injection length, and the microchannel width on FASS enrichment performance. The results show that reducing the width of the microchannel is an effective way to improve the enrichment quality. The maximum enrichment ratio can be improved by 67.35% by reducing the width of the microchannel to less than 10 μm due to the inhibition of background buffer diffusion. Second, to improve traditional FASS performance, a high-conductance gradient boundary is established by photoinitiating fabrication of a porous plug at the enriched interface position. This structure provides a region that reduces the local size of the internal channel to less than 5 μm and has high flow resistance, but allows the electromigration of the charged analyte. Experimental results show that an electropherogram signal increases by a maximum factor of 329 in electrophoretic enrichment of fluorescein–Na with 5 × 10−7 M initial concentrations, and the enrichment quality of traditional FASS is greatly improved.

Effect of pyro-processing conditions on impurity removal and precious metal enrichment in waste printed circuit board (WPCB) recycling process

The combinatorial effects of slag composition and O2-blowing conditions on silicon (Si) and iron (Fe) removal as well as gold (Au) and silver (Ag) enrichment from waste printed circuit boards (WPCBs) were investigated to optimize pyrometallurgical WPCBs recycling process. Regardless of the experimental conditions, the removal rate for Si and Fe was approximately 100%, except in slag-free operation. The Si removal rate was generally higher than the Fe removal rate at a given reaction time irrespective of experimental variables because the O2 affinity of Si is higher than that of Fe in molten copper, thermodynamically. The removal rate of impurities was clearly dependent on blowing conditions and slag composition, and a combinatorial operation of bottom-blowing and highly fluid slag favored the efficient removal of impurities. The maximum enrichment ratio of Au and Ag (CAu,AgMax) was about 10% and the possession rates of Au and Ag, RAu,Ag at CAu,AgMax were greater than 96%. The loss of Au and Ag can be minimized, i.e., RAu,Ag can be maximized by stopping O2-blowing before metal droplets are physically entrapped by molten slag, because metal droplet's entrainment is affected by slag viscosity, which contributes to the settling velocity of metal droplets. Consequently, it is very critical to appropriately control not only the slag composition but also O2-blowing conditions for both impurities removal and maximizing precious metals enrichment and possession.

Flotation as a separation technology for recovering pulp fines and sustainable nanocellulose production

• Fines from refined pulp were separated and enriched by froth flotation. • Flotation was controlled by pulp suspension rheology and fluid flow hydrodynamics. • Fines separation was quantified by fines enrichment ratio and fines recovery. • Fines recovery and fines enrichment ratio balance enables process optimisation. • Quality of fines and fines sheets was comparable to nanocellulose. Nanocellulose has great potential in the pulp and paper industry, but current nanocellulose production methods require high energy. One way to achieve energy efficient production of nanocellulose is to develop a large-scale process of separating small fibers (fines) from large fibers. In this study, a laboratory mill was used to produce moderately refined (30.8% fines) and highly refined (81.8% fines) Bleached Eucalyptus Kraft (BEK) pulp. Refined samples were subjected to flotation separation, and separation efficiency was quantified by fines recovery and fines enrichment ratio. At high pH (11.9), with a surfactant concentration of 0.15 mM, the surface tension of the air–water interface was 44 mN/m and the Sauter mean diameter of the bubbles in the froth was 0.948 mm. These conditions provide the required froth stability and low bubble size to achieve selective separation of fines. Maximum recoveries of 80.4% and 43.0% were achieved at pH 11.9 and 1.0 wt% for moderately refined and highly refined pulp, respectively. Maximum enrichment ratios of 4.33 and 4.37 were observed for moderately refined and heavily refined pulp at pH 11.9 and 1.5 wt%, respectively. The aspect ratio of float fibers increased by 14% and 18% for moderately and highly refined BEK, respectively. Flotation was shown to be controlled by the viscosity and surface charge of the pulp suspension. Viscosity and zeta potential values were maximised at pH 11.9 and 1.0–1.5 wt% pulp solids, promoting agglomeration of long fibers and enhanced fines separation. Experimental results were found to be statistically significant via ANOVA. Fines were shown to have analogous properties to commercial nanocellulose. This study demonstrates that size-selective fiber flotation is governed by pulp suspension rheology and fluid flow hydrodynamics, and that flotation represents a promising technology for fines separation and production of a sustainable nanocellulose substitute.

On the Challenges of Soil Phosphorus Prospections in Heterogeneous Environments\u2014a Case Study on the Iron Age Altenburg Hillfort (Niedenstein, Hesse, Germany)

Heterogeneous environments might be considered inadequate for geoarchaeological soil phosphorus (P) prospections due to the manifold potential alterations of archaeologically relevant soil P contents. To elucidate if this assumption is correct, we conducted a case study in the heterogeneous environment of the Iron Age Altenburg hillfort near Niedenstein (Hesse, Germany). We introduce the least influenced area (LIA) approach to deduce the native soil P contents of the local soils inductively from own soil P data. The native P contents are crucial for further data evaluation in any P prospection. Moreover, we develop two parameters to quantify and compare soil P enrichment in pedogenically heterogeneous areas: the mean enrichment ratio (MER) and the maximum enrichment ratio (XER). Finally, we modify and discuss the approach of Lorch (The Science of Nature 28(40/41):633–640, 1940) to interpret spatial patterns of soil P enrichment with regard to prehistoric land use. Our study shows that soil P prospections can be conducted in heterogeneous environments. Still, they require a systematic field work strategy and soil scientific support. Moreover, instead of absolute soil P contents, alternative parameters must be derived from the data to evaluate soil P enrichment adequately for a heterogeneous area. Using such alternative parameters on the basis of our data, the Iron Age Altenburg hillfort was significantly larger than formerly assumed. Only the Altenburg plateau and the directly adjacent slopes seem to have been densely covered with buildings. The neighboring areas might have been used for different purposes including agriculture, livestock grazing, and economic activities.

Characterization, partitioning, and potential ecological risk quantification of trace elements in coal fly ash.

Coal-based thermal power plants are the major source of power generation in India. Combustion of coal gives rise to by-products such as fly ash (FA) in huge quantities. The current study focuses on physico-chemical and mineralogical characterization and risk evaluation of FA, generated from five thermal power plants (TPPs) of India. The coal, and corresponding FA and bottom ash (BA) were further analyzed for trace elements in order to observe the enrichment and partitioning behavior of elements. The environmental risk assessment of trace elements in FA was performed in accordance with geoaccumulation index (I geo) and potential ecological risk index (PERI). The results demonstrated that FA was enriched predominantly in SiO2, Al2O3, and Fe2O3 along with small concentrations of CaO and MgO. The mineral phases identified in FA were quartz, mullite, hematite, and magnetite. Elemental characterization indicated that the metals were more enriched in FA as compared to coal and BA. The concentrations of trace elements, Cr, Pb, Hg, and As in FA (TPPs), varied from 12.59-24.28, 22.68-43.19, <0.0001-2.29, and 0.08-3.39 mg/kg, respectively. Maximum enrichment ratio (ER) was observed for Pb (5.21) in TPP3 FA. Hg in TPP1 showed the highest partition ratio (PR) value. I geo values for metals were mostly below zero. The PERI values indicated moderate risk from TPP4 FA and low risk from TPP1, TPP2, TPP3, and TPP5 FA to the environment, according to the threshold values provided.

Spatial distribution of heavy metals in the surface soil of source-control stormwater infiltration devices - Inter-site comparison.

Stormwater runoff infiltration brings about some concerns regarding its potential impact on both soil and groundwater quality; besides, the fate of contaminants in source-control devices somewhat suffers from a lack of documentation. The present study was dedicated to assessing the spatial distribution of three heavy metals (copper, lead, zinc) in the surface soil of ten small-scale infiltration facilities, along with several physical parameters (soil moisture, volatile matter, variable thickness of the upper horizon). High-resolution samplings and in-situ measurements were undertaken, followed by X-ray fluorescence analyses and spatial interpolation. Highest metal accumulation was found in a relatively narrow area near the water inflow zone, from which concentrations markedly decreased with increasing distance. Maximum enrichment ratios amounted to >20 in the most contaminated sites. Heavy metal patterns give a time-integrated vision of the non-uniform infiltration fluxes, sedimentation processes and surface flow pathways within the devices. This element indicates that the lateral extent of contamination is mainly controlled by hydraulics. The evidenced spatial structure of soil concentrations restricts the area where remediation measures would be necessary in these systems, and suggests possible optimization of their hydraulic functioning towards an easier maintenance. Heterogeneous upper boundary conditions should be taken into account when studying the fate of micropollutants in infiltration facilities with either mathematical modeling or soil coring field surveys.

FOAM FRACTIONATION AS A MEANS TO RECOVER AND FRACTIONATE BIOACTIVES

In this research, the optimum conditions for the separation of polyphenols from apple juice (AJ) and the separation of BSA from a BSA/water solution were found by looking at the enrichment ratio (ER) and recovery. A mixture of the AJ and BSA was also studied to see how the different conditions affect separation of either compound. For AJ only, maximum ER was achieved at a feed concentration of 0.00184mg/mL of polyphenols (10.9˚Brix), air flowrate of 10mL/min, pH of 6.03 and temperature of 4.1˚C. For the BSA only solution, maximum ER was achieved at a feed concentration of 2.5g/L, air flowrate of 7mL/min, pH of 5-6 and temperature either above or below 20˚C. For the mixture, maximum polyphenol ER was at a feed polyphenol concentration of 0.0018mg/mL, feed BSA concentration of 5g/L and a pH of 3.7. Whereas maximum BSA ER was achieved when the feed polyphenol concentration was again 0.00184mg/mL, but a minimum was seen at 5g/L BSA feed concentration and pH of 3.7. These results show that there are interactions between the polyphenol and proteins that affects the separation of compounds. The bubble size distribution and gas hold-up of the AJ and BSA solutions were then compared and the BSA solution had larger bubbles present and a greater gas hold-up, which is attributed to the greater surface activity of BSA protein. Finally basic modelling – linear regression, was performed to link the ER to the different conditions tested. The models were judged by comparing R 2 values, the F-statistic and the p-value and all showed weak relationships between the ER and the independent variables. Further data is required to improve the model as from previous literatures these variables have been seen to contribute to adsorption, which in turn affects the ER.

Parametric Study on the Enrichment of Immunoglobulin from Milk by Foam Fractionation

Foam fractionation is a promising method for separation and concentration of biochemicals. It is simple, easily scalable, inexpensive, and environment friendly. Foam fractionation thus represents an alternative to the traditional methods used for immunoglobulin enrichment. However, little, if any, literature exists documenting the utilization of foam fractionation in the enrichment of immunoglobulins. Milk were utilized as an immunoglobulin source to serve as examples of a real system in this study. The investigation examined the effects of varying five different process parameters: the initial pH value, the initial concentration of immunoglobulin, the nitrogen flow rate, the column height, and the foaming time. Experimental results demonstrated that immunoglobulin could effectively be enriched from milk by foam fractionation. The maximum enrichment ratio with pretreatment (using pH 4.6 precipitation) was 6.30 along with a more than 92 % recovery for IgG and an enrichment ratio of 5.1 with 85 % recovery for IgM.

Effects of temperature and trehalose on foam separation of nisin from the culture broth produced by Lactococcus lactis subspecies lactis W28

Nisin is an antimicrobial peptide, an important biopreservative, and it is produced by certain strains of Lactococcus lactis ssp. lactis. In this paper, a foam separation technique was used for the separation of nisin from its culture broth, and the effects of temperature and trehalose on the performance of foam separation of nisin were studied to increase the enrichment ratio and recovery percentage of nisin and decrease the inactivity percentage of nisin. The results showed that temperature and trehalose significantly affected the performance of foam separation of nisin. Under the optimum conditions of 50°C temperature, 150-mL/min air flow rate, 400-mL initial loading liquid volume, and 1-g/L trehalose concentration, the maximum enrichment ratio, recovery percentage, and the minimum inactivity percentage of nisin reached 23.7, 84.1%, and 5.9%, respectively, which were, respectively, 5.04, 0.93, and 1.03 times more than those under the conditions of 20°C temperature, 150-mL/min air flow rate, 400-mL initial loading liquid volume, and no trehalose addition. These results indicated that the change of temperature and the addition of trehalose could improve the performance of foam separation of nisin.

Effect of ionic strength on the foam separation of nisin from the fermentation broth

Nisin is a 34-residue peptide and it is widely used as food preservative. Different strategies for nisin purification from the complex broth have been investigated. But these methods increase the cost of nisin production, and its wide application is limited. Foam separation is an economical and effective technology for protein concentration and separation. In this paper, we utilized foam separation technology to recover nisin from fermentation broth, and studied the effect of ionic strength on the experimental system. The results showed that with ionic strength increasing, surface tension and inactivation ratio first decreased and then increased, and, however, foaming ability, foam stability, enrichment ratio and recovery first increased and then decreased. Under the conditions of the titer of nisin fermentation broth 4200 IU/ml, pH 3.0, feed liquid 250 ml, air flow rate 30 ml/min and temperature 25 °C, the maximum enrichment ratio and recovery and the minimum inactivation ratio of nisin reached 6.4, 86.44% and 9.89%, respectively, when the ionic strength was 0.41 mol/kg. Furthermore, we obtained higher nisin recovery and activity using sodium rather than potassium salt.

Effect of ionic strength on the foam fractionation of BSA with existence of antifoaming agent

Foam fractionation is an economical and effective technology for protein concentration and separation. However, the presence of antifoaming agent in the fermentation broth restricts the application of this technology. In this paper surfactant-assisted foam process was conducted with a mimic system using bovine serum albumin (BSA) as target protein, polyoxypropylene polyoxyethylene glylerin ether (PGE) as antifoaming agent and cetyltrimethyl ammonium bromide (CTAB) as surfactant, putting emphasis on study of the effect of ionic strength on the separation process. The experimental results showed that with ionic strength increasing, the mixed-system foaming ability gradually increased. Under the conditions of C BSA 100 mg/L, C CTAB 20 mg/L, C PGE 8 mg/L and pH 7.4, feed liquid 250 mL, air flow rate 100 mL/min at 25 °C, the maximum enrichment ratio of BSA reached 27 when the ionic strength was 0.0500 mol/kg and the maximum recovery of BSA reached 80.5% when the ionic strength was 0.1696 mol/kg. Furthermore, K + had better separate efficiency than Na + under the same ionic strength.

Protein Removal from Whey Waste by Foam Fractionation in a Batch Process

The work investigates the separation of proteins from whey waste collected from a local confectionery by the foam fractionation technique in batch mode. The purpose of this work was to evaluate performance criteria of protein separation. The effects of pH, the concentration of initial feed solution, the nitrogen flow rate, the % gas hold up, the bubble diameter, the breaking time of foam, and the optimization of the protein–surfactant ratio (1.5:1) were investigated in detail. Maximum enrichment ratio (48.189), %Rp (96.378) were observed at a gas flow rate of 330 ml/min and pH 5 that is closest to isoelectric point of observed proteins (Bovine serum albumin, β-Lactoglobulin, α-lactalbumin).

Study on Riboflavin Recovery from Wastewater by a Batch Foam Separation Process

A batch recovery of riboflavin via foam separation from industrial simulative wastewater was studied using a cationic surfactant, cetyltrimethyl ammonium bromide (CTAB). The experimental parameters examined were the surfactant concentration, air flow rate, pH, and foam height. Under optimal operating conditions obtained through an orthogonal experiment, the maximum enrichment ratio of 48.7 was achieved for riboflavin along with 99.3% removal efficiency. The optimal operating conditions had the concentration of CTAB at 0.3 g/L, air flow rate at 400 ml/min, foam height at 90 cm, and pH at 12. Therefore foam separation proved to be an effective method to recover the riboflavin in terms of the good enrichment and removal efficiency.

Mercury Sedimentation in Lakes in Western Whatcom County, Washington, USA and its Relation to Local Industrial and Municipal Atmospheric Sources

Concentrations of mercury (Hg) were measured in six dated cores from four lakes in western Whatcom County, Washington, USA, that were at various bearings from a chlor-alkali plant, two municipal waste incinerators and a municipal sewage sludge incinerator. The importance of atmospheric emissions of Hg from these local municipal and industrial sources was evaluating by comparing the temporal trends in sedimentation of the lake cores with the emission history of each Hg species and by examining the geographical distribution of Hg sedimentation in relation to the region’s primary wind pattern. Local municipal and industrial sources of atmospheric Hg were not responsible for the majority of the Hg in the upper layer of sediments of Whatcom County lakes because of (1) the significant enrichment of Hg in lake sediments prior to emissions of local industrial and municipal sources in 1964, (2) smaller increases in Hg concentrations occurred after 1964, (3) the similarity of maximum enrichments found in Whatcom County lakes to those in rural lakes around the world, (4) the inconsistency of the temporal trends in Hg sedimentation with the local emission history, and (5) the inconsistency of the geographic trends in Hg sedimentation with estimated deposition. Maximum enrichment ratios of Hg in lake sediments between 2 and 3 that are similar to rural areas in Alaska, Minnesota, and New England suggest that global sources of Hg were primarily responsible for increases of Hg in Whatcom County lakes beginning about 1900.

Platinum-group elements (Ir, Pd, Pt and Rh) in road-deposited sediments in two urban watersheds, Hawaii

This study represents the first detailed investigation of platinum-group elements (PGEs) in road-deposited sediment (RDS) in Hawaii, USA. Thirty-three sample locations, in two urban watersheds in Honolulu, Oahu, Hawaii were sampled. The <63 μm fraction of RDS was digested with aqua regia, followed by matrix separation with Dowex AG50-X8 cation exchange resin. PGEs were analyzed with inductively coupled plasma-mass spectrometry (ICP-MS) equipped with a desolvating nebulizer. Concentrations of Rh, Pd and Pt in residential streets reached 64, 105 and 506 ng/g, respectively. Maximum enrichment ratios, computed as RDS concentrations relative to baseline values, exceeded 400, indicating a significant anthropogenic signal with the sequence Rh > Pt > Pd. Iridium concentrations were uniformly low <1 ng/g, and enrichment ratios support a geogenic source. Significant interelement PGE correlations (Pd–Pt–Rh), combined with the magnitude of PGE pair-wise ratios (Pt/Pd, Pt/Rh and Pd/Rh), and relative percentages comparable to European RDS and roadside soil in Indiana, USA all suggest an automobile source. Attrition of PGE-loaded automobile catalytic converters and subsequent loss to the environment by exhaust emissions explains the significant environmental signal of PGEs in road environments of Hawaii. Further PGE work is required to quantify urban transport paths as PGEs are known to bioaccumulate, cause cellular damage and may have detrimental human health effects.

Zinc Isotope Fractionation on Benzo-15-crown-5 Resin by Liquid Chromatography

Chromatographic fractionation of zinc isotopes was performed on the synthesized benzo-15-crown-5 resin as a column packing material at 323K in the breakthrough manner for both a frontal and a rear bands. Zinc adsorption capacity was affected by anion chloride concentration and solvent dielectric constant. The heavier zinc isotopes were found enriched to the solution phase and the lighter zinc isotope was concentrated on the resin phase. The frontal maximum enrichment ratio for isotopic pair of 68Zn/64Zn was 1.0081. The isotope separation coefficients for isotopic pair of 68Zn/64Zn for frontal and rear band, were 5.3 × 10−4, 4.5 × 10−4, respectively.

Zinc Isotope Fractionation on Benzo-15-crown-5 Resin by Liquid Chromatography

Chromatographic fractionation of zinc isotopes was performed on the synthesized benzo-15-crown-5 resin as a column packing material at 323K in the breakthrough manner for both a frontal and a rear bands. Zinc adsorption capacity was affected by anion chloride concentration and solvent dielectric constant. The heavier zinc isotopes were found enriched to the solution phase and the lighter zinc isotope was concentrated on the resin phase. The frontal maximum enrichment ratio for isotopic pair of 68Zn/64Zn was 1.0081. The isotope separation coefficients for isotopic pair of 68Zn/64Zn for frontal and rear band, were 5.3 × 10−4, 4.5 × 10−4, respectively.

Cu, Pb and Zn contamination in Nuuanu watershed, Oahu, Hawaii

Trace metal contamination in urban aquatic ecosystems in Hawaii is a significant problem, especially in terms of Cu, Pb, and Zn. These trace metals are linked to automobile usage. An in-depth study was designed to determine the influence of road sediments and storm sewers on bioavailable (0.5 M HCl) trace metal concentrations in bed sediments of Nuuanu stream, Oahu. Lead was the most enriched trace metal in the watershed. Compared to baseline Pb concentrations of <3 mg/kg, road sediments averaged 186 mg/kg, with a maximum value of 3140 mg/kg. Stream bed sediments had average Pb values of 122 mg/kg, with a maximum of 323 mg/kg. Al-normalized enrichment ratios (ERs) for the <63 μm fraction indicated that the watershed was significantly polluted in the lower, urbanized reaches, with maximum ER values of 560 and 94 for Pb in road sediments and stream sediments, respectively. Median ER values for Cu, Pb, and Zn in stream sediments were 2, 36, and 5, respectively. Rainfall events prior to sediment sampling masked any influence that storm sewer outlets might have had on the localized spatial distribution of metals associated with bed sediments. However, there was a general pattern of increasing trace metal concentrations downstream as the fluvial network traversed residential areas and commercial, highly trafficked areas in the lower portions of the watershed.

Continuous foaming for protein recovery: part II. Selective recovery of proteins from binary mixtures.

Foam separation may have potential for protein recovery. However, for foam separation to be a viable protein recovery technique it is important to demonstrate, not only that high enrichments and recoveries can be achieved for single proteins, but also that high enrichments and recoveries, together with selectivity of partition, can be achieved for recovery from multi-component mixtures. Most process streams which require purification are indeed complex multi-component mixtures, for example, fermentation broths. In this study, three binary protein mixtures were chosen for continuous foam separation: beta-casein:lysozyme; Bovine serum albumin (BSA):lysozyme and beta-casein:BSA (mixtures 1, 2, and 3, respectively). For each of these mixtures, the expected outcome of each experiment, based on a previous knowledge and determination of relevant protein physical properties, was that the first protein should be preferentially separated into the foam phase. On the basis of results reported in Part I of this study for the continuous foam separation of beta-casein, conditions found to favor maximum enrichment were selected. For each mixture a range of concentrations of both proteins was considered. For mixture 1, maximum protein recoveries in the foam phase were 85.6% and 25% for beta-casein and lysozyme, respectively; and for mixture 2, maximum recoveries of 77. 6% and 18.9% were obtained for BSA and lysozyme, respectively. Maximum enrichment ratios in the foam phase were 79.4 and 2.5 for beta-casein and lysozyme respectively in mixture 1; and 74.0 and 1.4 for BSA and lysozyme respectively in mixture 2. Selective partitioning of beta-casein and BSA into the foam phase was obtained in mixtures 1 and 2, respectively, particularly for protein concentrations at which dilute protein films are known to form at the gas-liquid interface in the foam. Maximum partition ratios for mixtures 1 and 2 were 31.8 and 52.8, respectively. For mixture 3, both BSA and beta-casein were enriched into the foam phase. Maximum enrichments were 42.9 and 24.7 for BSA and beta-casein, respectively; however, selective partitioning in mixture 3 was limited (maximum partition ratio being 1.8).

Foam fractionation of colloid‐surfactant systems

AbstractThe presence of colloidal particulates has a significant effect upon the foam fractionation of aqueous solutions of surface‐active agents. An experimental investigation is presented of the foam fractionation‐flotation of the stannic oxide‐cetyltrimethylammonium bromide (CTAB) and stannic oxide‐alkyl benzene sulfonate (ABS) systems. The average diameter of the stannic oxide particles was 180Å, and particle concentrations were determined by turbidmetry. For stannic oxide‐CTAB a froth flotation mechanism controls, and upon foaming feed sols of fixed concentration, fractional residuals of particulates and surfactant are approximately equal. Maximum enrichment ratios are obtained at maximum aeration time, minimum air rate, and maximum foam height. Increasing the feed concentration of particulates increases the collapsed foam volume, while the CTAB concentration in the residual sol first decreases and then becomes virtually constant. For stannic oxide‐ABS sols, no particulates are removed preferentially in the foam. A foam fractionation mechanism controls, and compared with ABS solutions the addition of stannic oxide decreases the foam volume and residual ABS concentration, producing a pronounced increase in the enrichment ratio.