Hold-up Times Research Articles

Generalized flow calculation of the gas flow in a network of capillaries used in gas chromatography.

A general method for the calculation of the flow and pressure of a gas in a network of cylindrical capillaries is presented. This method is used specifically for gas chromatographic systems in this work. With this approach, it is possible to easily calculate flow and pressures in complex gas chromatographic systems, like flow-modulated or thermal-modulated multidimensional gas chromatographic systems, or systems with multiple outlets at different pressures. A mathematic abstraction using graph theory is used to represent the system of capillaries. With this graph, the flow balance equations at the connections of the capillaries can easily be set up. Using a computer algebra system, the system of flow balance equations can be solved for the pressures at the connection points. For simple systems, this approach is presented, and calculated flows, pressures, and hold-up times are compared with measured values. In addition, two complex systems (4-Way-Splitter, Deans Switch system) of capillaries are presented with calculations only. For these systems, certain conditions were formulated, that is, a certain difference in hold-up times and a defined split ratio between different paths of these systems. Using a numeric non-linear solver, configurations of these systems were found, that fulfill these conditions.

Global characterization of hydrodynamics and gas-liquid mass transfer in a thin-gap bubble column in presence of Newtonian or non-Newtonian liquid phase

Bubble columns are commonly used as photobioreactors (PBRs) due to their good mixing and mass transfer capabilities. Modification in design and operating parameters are nevertheless needed to intensify volumetric productivity. Thin-gap bubble column can be used in this context to operate with high biomass concentration, up to conditions where the culture becomes non-Newtonian. In the present study, the global hydrodynamics and gas–liquid mass transfer inside a 4 mm thickness thin-gap bubble column are characterized in presence of low viscosity Newtonian fluid (water) and two aqueous solutions of Carboxymethyl Cellulose and Xanthan Gum. These shear-thinning solutions are used to mimic high concentration cultures of Chlorella Vulgaris at 42 g.L−1. A range of superficial gas velocities and different capillary diameters are explored to investigate the effect of sparging on hydrodynamics and gas–liquid mass transfer. Studied parameters are flow regimes, mixing, and gas–liquid mass transfer. Results are compared with literature results in classical bubble columns to put into evidence the original effects of both confinement and liquid rheology. Among others, these results show that compared to Newtonian media, non-Newtonian media result in higher gas holdup and mixing times and a lower gas–liquid mass transfer coefficient. The findings suggest that the presence of smaller bubbles would improve mass transfer due to the increased interfacial area, while the presence of larger bubbles would improve mixing performance due to increased vorticity in their wake and relatively greater species transport.

Residence Time Distribution Analysis of Drip-Irrigated Beds—The Effect of Material and Fluid Properties with Implications for Heap Leaching Practice

The quantitative effect of particle shape, porosity, wettability, particle size, and solution viscosity on the residence time distribution (RTD) profiles of non-reactive, steady-state, drip-irrigated ore beds characteristic of heap leaching systems is presented. Results were obtained using step-up tracer tests and allowed for the analysis of preferential flow behaviour within the systems. The key findings were as follows. Increased particle sphericity enhanced channelling in beds of smaller particles, but not for larger particle sizes. Higher particle wettability caused greater liquid dispersion during both initial wetting studies and at steady-state fluid flux. Higher porosity levels and the inclusion of fines in mixed sized beds resulted in longer average solute residence times, higher liquid hold-up, longer solution and tracer breakthrough times, and increases in drain-down moisture percentages. Increasing the irrigation fluid’s viscosity, reflective of the increase in ionic concentrations in leach solutions, reduced both the solution and tracer breakthrough times and increased dispersion with signs of more discontinuous or isolated fluid volumes at steady-state. These results highlighted the importance of the inclusion of fines in agglomerated beds to improve uniform wetting especially those with low to moderate particle porosities (<2.5 m2/g specific surface area). The viscosity results suggest that there may be changes in preferential flow extent, due to variations in viscosity owing to the increasing sulphate concentration within the liquid phase in heaps and with time.

Experimental investigation of the residence time behavior of a wiped film evaporator

Wiped film evaporators (WFEs) are characterized by small hold-up and short residence times, making them well suited for the separation of thermally sensitive substances and for fast chemical reactions. Since fluid dynamics and heat transfer in WFEs are highly interdependent, the effects of different wiper geometries, operating parameters and physical properties on the residence time behavior are manifold and poorly understood. In this work, the influence of liquid load, wiper speed and liquid viscosity on the residence time distribution (RTD) of a wiped liquid film was investigated. Tracer experiments were conducted without evaporation in a stainless steel WFE alternatively equipped with a spring-loaded comb wiper and a roller wiper. A detailed comparison of both wipers demonstrated that at a high liquid load and an increased viscosity, shorter residence times were achieved with the roller wiper, which could be explained by a strongly pronounced bow wave with an increased vertical flow velocity. Using a comb wiper, an increase in dispersion with rising liquid load at higher viscosity was demonstrated.

Investigation of flow dynamics of porous clinkers in a ball mill using technitium-99m as a radiotracer

A radiotracer investigation was carried out in a ball mill of a cement plant in Kenya. Residence time distribution (RTD) of raw feed to the mill was measured using Technetium-99m adsorbed on the clinkers as a radiotracer. From the measured RTDs, solid holdup and mean residence times (MRTs) in the ball mill and associated separator were determined. The measured RTDs were modelled using axial dispersion model (ADM) and tank-in-series model both connected with a plug flow component in series. The results of the modelling indicated significant degree of backmixing within the ball mill and no axial mixing in the separator.

Influence of the acid-base ionization of drugs in their retention in reversed-phase liquid chromatography

The effect of the ionization in the RP-HPLC retention of 66 acid-base compounds, most of them drugs of pharmaceutical interest, is studied. The retention time of the compounds can be related to the pH measured in the mobile phase (pwsH) through the sigmoidal equations derived from distribution of the neutral and ionic forms of the drug into the stationary and mobile phases. Fitting of the obtained retention vs. pH profiles provides the retention times of the ionic and neutral forms and the pKa values of the drugs in the mobile phase (pwsKa).The obtained pwsKa values are linearly correlated to the pKa values in water (pwwKa) with two different correlations, one for neutral acids and another for neutral bases that reflect the different influence of the dielectric constant of the medium in ionization of acids and bases. The retention of the neutral species is well correlated to the octanol-water partition coefficient of the drugs as measure of the lipophilicity of the drug, which affects chromatographic retention. Also, the retention time of the ionized forms is related to the retention time of the neutral forms by two different linear correlations, one for anions and the other for cations. These last correlations point out the different retention behaviour of anions and cations: anions are less retained than cations of the same lipophilicity, as measured by the octanol-water partition coefficient of the neutral form.The different retention behaviour of anionic, cationic and neutral forms is confirmed by the hold-up times obtained from different approaches: pycnometry and retention times of anionic (KBr and KI) and neutral (DMSO) markers. Hold-up times obtained by pycnometric measurements agree with those obtained by retention of neutral markers (0.83–0.85 min), whereas hold-up time for anions is mobile phase pH dependent. At acidic pH it is similar to the hold-up time for neutral markers (0.83 min), but then it decreases with the increase of mobile phase pH to 0.65 min at pH 11. The decrease can be explained by the ionization of the silanols of the column and exclusion of anions by charge repulsion. Although not directly measured, the obtained retention data and correlations indicate hold-up time for cations are similar or slightly lower than hold-up time for neutral compounds (0.77–0.83 min).The model proposed and the correlations obtained can be very useful for its implementation in retention prediction algorithms for optimization of separation purposes.

Development and validation of a pneumatic model for the reversed-flow differential flow modulator for comprehensive two-dimensional gas chromatography

The development of the reversed fill/flush modulator represents a significant advancement in flow-modulated, comprehensive two-dimensional gas chromatography (GC × GC). Compared to the forward flush/fill modulator, the reversed-flow modulator is less susceptible to baseline anomalies and peak tailing as a result of modulator channel overfilling or insufficient purging of high concentration analytes. Flow reversal requires the addition of a bleed capillary not present in the forward-flow modulator. Selecting the appropriate restriction of the bleed capillary is critical. If the bleed capillary is too restrictive, eluate from the first-dimension column can split between the modulator channel and second-dimension column, which also results in baseline artifacts. To gain a better understanding of the reversed-flow modulator, a comprehensive pneumatic model was developed. The model was validated by comparing calculated and measured hold-up times. The errors in calculated hold-up times were less than 1% of the measured values. The model can be used to predict first-dimension eluate splitting and determine the optimal bleed capillary dimensions to prevent its occurrence. Calculation of the modulator hold-up time can be used to determine the maximum collection time to ensure comprehensive analysis and optimal flush times for partial fill operation.

Chasing the elusive hold-up time from an LFER approach

A homologous series approach derived from the Abraham’s solvation model was developed for the determination of hold-up times. Firstly, it was tested from reversed-phase liquid chromatography data obtained in the literature involving several series of homologues, followed by its application in a polymeric zwitterionic HILIC column using two different homologous series (n-alkyl benzenes and n-alkyl phenones). Acetonitrile and methanol were selected as organic modifiers in a composition range between 80% and 100% in volume. Results obtained for both series were consistent, and hold-up times were found to be strongly dependent on the water content and the organic modifier nature of the mobile phase.

Designing an Autonomous Integrated Downstream Sequence From a Batch Separation Process - An Industrial Case Study.

This work is a proof of concept of how a sequence of industrial batch separation steps together are used to form an integrated autonomous downstream process. The sequence in this case study consisted of an anion chromatography step, virus inactivation and finally a hydrophobic chromatography step. Moving from batch to integrated separation minimizes hold-up times, storage tanks, and required equipment. The conversion from batch to integrated mode is achieved by extracting operating points and separation data from batch chromatograms. The integrated separation process is realized on an ÄKTA Pure controlled by an open research software called Orbit, making it possible to operate complex process configurations including multiple steps. The results from this case study is the principle and method of the steps taken to automation, achieving a more continuous and efficient downstream process.

Effect of axial temperature gradient on chromatographic efficiency under adiabatic conditions

The effect of axial temperature gradient on the chromatographic efficiency was studied under adiabatic conditions by a modeling approach. The equilibrium-dispersive model of chromatography was used for the calculations. The model was extended by taking into account the axial temperature gradient. The results show that due to the temperature gradient, there are retention and migration velocity gradients in the column. Since the retention factor, k, is not constant in the column, k cannot be calculated as the ratio of net retention and hold-up times. As a result of the gradual increase of migration velocity, the retention times of solutes decrease as the slope of temperature gradient increases. In addition, the band in the column have extra broadening due to larger migration velocity of the front of band. The width of bands becomes larger at larger change of temperature. In the same time, however, the release velocity of the compounds from the column is increasing as ΔT increases. Accordingly, an apparent peak compression effect makes the peaks thinner. As a result of the two counteracting effects (peak expansion, apparent peak compression) the column efficiency does not change significantly in case of axial temperature gradient under adiabatic conditions. The resolutions, however, decrease slightly due to the decrease of retention times.

Enantioselective gas chromatography with functionalized cyclodextrins as chiral selectors. Fundamentals of the measurement of absolute association constants using capillary columns

Chiral capillary GC columns containing different amounts of octakis(6-O-tert-butyldimethylsilyl-2,3-di-O-acetil)-γ-cyclodextrin as chiral selector dissolved in a polymeric matrix were constructed with the aim of determining enantiomeric association constants between a group of well resolved chiral N-trifluoroacetyl amino acid methyl esters and this specific selector at different temperatures. The most relevant sources of uncertainties in the experimental data (hold-up and retention times, and column phase ratios at each temperature) were assessed. These cyclodextrin-based columns are known to enantioseparate a wide variety of chemical compounds, thus, the measurement of the absolute enantioselective constants of a group of solutes with this selector can be useful for systematic studies aimed to a general understanding about how these selectors work. These absolute association constants were estimated from data collected from very simplified experimental systems, and by using the fundamental gas-liquid chromatography equations.

Process analytical technologies in food industry - challenges and benefits: A status report and recommendations.

Process analytical technologies in food industry - challenges and benefits: A status report and recommendations.

Factors Influencing the Isothermal Retention Indices of 51 Solutes on 12 Stationary Phases of Different Polarity: Applicability of the Solvation Parameter Model

Isothermal retention indices (I) at 333–413 K on 12 stationary phases (SPs) covering a wide polarity range of a variety of volatile solutes belonging to 7 one-heteroatom chemical function series and 10 non-series solutes have been determined. The I values were computed with a method (LQG method) which does not require the determination of holdup times of the chromatographic column. I values of some compounds never before studied are reported. The influence on the retention indices of the column temperature, methylene number, and polarity of both the stationary phase and the solute has been studied. The solvation parameter model (SPM) as a function of I has been used for predicting I values, and for unraveling the influence of the polarity of stationary phase and solute on the retention indices. Seeley et al.’s formulation of the SPM has been used for quantifying the influence of polar and non-polar interactions on the I, and for checking the agreement between calculated and experimental values. According to our results, the I values obtained by the modified SPM can be considered equal to the experimental I values at the 99 % confidence level.

Measurements of association constants between enantiomers and chiral selectors by capillary gas chromatography. Theoretical and practical considerations

The association constants of several volatile enantiomers with octakis(3-O-butanoyl-2,6-di-O-pentyl)-γ-cyclodextrin at temperatures between 50 and 100°C were measured by gas–liquid chromatography using capillary columns coated with different amounts of chiral selector dissolved in polysiloxane OV-1701 and prepared with a precisely determined phase ratio. Simple expressions were deduced to estimate the apparent distribution constants from accurate hold-up and retention times along with that known phase ratio at each temperature. The enantiomer-chiral selector association constants were then calculated from the linear regression of the apparent constants as a function of the chiral selector concentration. One aim of this study consisted in discussing all the experimental uncertainties inherent in the determination of enantiomer/selector association constants with chiral analytes, and how these fundamental measurements can be performed precisely without resorting to the use of reference solutes.

Determinations of gas–liquid partition coefficients using capillary chromatographic columns. Alkanols in squalane

This study focused on an investigation into the experimental quantities inherent in the determination of partition coefficients from gas–liquid chromatographic measurements through the use of capillary columns. We prepared several squalane – (2,6,10,15,19,23-hexamethyltetracosane) – containing columns with very precisely known phase ratios and determined solute retention and hold-up times at 30, 40, 50 and 60°C. We calculated infinite dilution partition coefficients from the slopes of the linear regression of retention factors as a function of the reciprocal of the phase ratio by means of fundamental chromatographic equations. In order to minimize gas–solid and liquid–solid interface contributions to retention, the surface of the capillary inner wall was pretreated to guarantee a uniform coat of stationary phase. The validity of the proposed approach was first tested by estimating the partition coefficients of n-alkanes between n-pentane and n-nonane, for which compounds data from the literature were available. Then partition coefficients of sixteen aliphatic alcohols in squalane were determined at those four temperatures. We deliberately chose these highly challenging systems: alcohols in the reference paraffinic stationary phase. These solutes exhibited adsorption in the gas–liquid interface that contributed to retention. The corresponding adsorption constant values were estimated. We fully discuss here the uncertainties associated with each experimental measurement and how these fundamental determinations can be performed precisely by circumventing the main drawbacks.The proposed strategy is reliable and much simpler than the classical chromatographic method employing packed columns.

Speed-resolution properties of columns packed with new 4.6 μm Kinetex-C18 core–shell particles

The achievable separation speed and resolution of columns packed with the new 4.6μm Kinetex particles were characterized by their permeability and their plate heights, measured meticulously. Their specific permeabilities range between 1.81 and 1.95×10−10cm2 and their external porosities between 0.394 and 0.405. The efficiencies of the eluted peaks measured by numerical integration of the whole band concentration provided minimum reduced plate heights for uracil (non-retained) and naphthalene (retained) between 1.3 and 1.5 (H=6.0–6.9μm) for two 4.6mm×150mm replicate columns of Kinetex and between 1.6 and 2.0 (H=7.4–9.2μm) for two narrow-bore 2.1mm×150mm replicate columns. The most efficient 4.6mm×150mm Kinetex column shows a deviation of one reduced plate height h unit with respect to the infinite diameter column (no wall, no inlet, no outlet endfitting) at high speed. Eventually, the separation speed and the resolution of columns packed with 4.6μm core–shell Kinetex particles are better or equivalent to those of columns packed with 2.5μm fully porous particles for hold-up times larger than only 10s. These core–shell materials are virtually equivalent to the second generation of silica monolithic columns with the advantage of operating well at pressure drops larger than 200bar.

A Membrane Cell for On-line Hydrogen/Deuterium Exchange to Study Protein Folding and Protein-Protein Interactions by Mass Spectrometry

A membrane cell for hydrogen and deuterium exchange on-line with mass spectrometry has been developed to monitor protein-protein interactions and protein conformations. It consists of two channels separated by a semipermeable membrane, where one channel carries the protein sample and the other deuterium oxide. The membrane allows transfer of deuterium oxide into the sample flow. The labeling time is controlled via the flow rate in the sample channel. This cell was validated against three models commonly used in hydrogen-deuterium exchange mass spectrometry: monitoring of folded and unfolded states in a protein, mapping the protein secondary structure at the peptide level, and detection of protein and antibody interactions. The system avoids the conventionally used sample dilution and handling, allowing for potential automation.

Continuous‐time random walk models of DNA electrophoresis in a post array: Part I. Evaluation of existing models

Several continuous-time random walk (CTRW) models exist to predict the dynamics of DNA in micropost arrays, but none of them quantitatively describes the separation seen in experiments or simulations. In Part I of this series, we examine the assumptions underlying these models by observing single molecules of λ DNA during electrophoresis in a regular, hexagonal array of oxidized silicon posts. Our analysis takes advantage of a combination of single-molecule videomicroscopy and previous Brownian dynamics simulations. Using a custom-tracking program, we automatically identify DNA-post collisions and thus study a large ensemble of events. Our results show that the hold-up time and the distance between collisions for consecutive collisions are uncorrelated. The distance between collisions is a random variable, but it can be smaller than the minimum value predicted by existing models of DNA transport in post arrays. The current CTRW models correctly predict the exponential decay in the probability density of the collision hold-up times, but they fail to account for the influence of finite-sized posts on short hold-up times. The shortcomings of the existing models identified here motivate the development of a new CTRW approach, which is presented in Part II of this series.

Hydrodynamics and mass transfer in a novel multi-airlifting membrane bioreactor

A novel multiple-airlifting membrane bioreactor is built with four sintered stainless steel tubular filters as the risers and downcomers. This work investigates the hydrodynamics including gas holdup, liquid velocity, liquid circulation and mixing times by aerating different number of risers (one to three) at superficial gas velocities of 0.02–0.07 m/s The mass transfer phenomena, including oxygen mass transfer ( k L a ) and effective molecular diffusivity of lactic and acetic acids through the walls of tubular filters, are also investigated. It is found that gas holdup in individual risers increases linearly with the superficial gas velocity, and performs independently under multiple-airlifting conditions. The vessel-based gas holdup and liquid velocity in downcomer(s) increase with aeration rate of individual risers as well as the number of risers. The liquid velocity in downcomers reaches an upper limit (about 0.6 m/s), because of flow resistance or energy loss of liquid circulation. The oxygen mass transfer coefficient ( k L a ) is primarily affected by gas holdup and the number of risers, and to some extent influenced by liquid velocity. The novel airlifter configuration results in good liquid mixing in the bioreactor that quickly reaches new steady state in response to a sudden pH change from acid addition.

A Comparative Study of Methods for Determining Gas Hold-Up Time

It has been proved mathematically that there exists an identity between the various published methods for determining the hold-up times in gas chromatography. All of these methods are based on the equation: ln t'(R) = ln (t(R) - t(M)) = a + bZ, where t(R), t'(R), and t(M) are retention times, adjusted retention times, and hold-up times, respectively; a and b are coefficients that depend on the experimental conditions, and Z is the numbers of carbon atom of a homologue. So long as there are no errors in the values of the retention times, the hold-up times obtained by different methods based on this equation will be the same. The calculated results of experimental data reported in the literature support the viewpoints presented here.