Solid-liquid Mass Transfer Resistance Research Articles

Shedding light on mechanisms leading to convex-upward van Deemter curves on a cellulose tris(4-chloro-3-methylphenylcarbamate)-based chiral stationary phase

An unusual convex-upward van Deemter curve was observed for the more retained enantiomer of a chiral sulfoxide (2-(benzylsulfinyl)benzamide) on a cellulose tris(4-chloro-3-methylphenylcarbamate)-based chiral stationary phase (CSP), prepared on silica particles of 1000 Å pore size. In contrast, the firstly eluted enantiomer of the same molecule exhibited the traditional convex-downward van Deemter curve.A detailed kinetic and thermodynamic investigation has revealed that this unusual phenomenon, which however has already been observed in chiral chromatography, originates when the adsorption of the compound is very strong and the solid-phase diffusion negligible. Experimentally, the intraparticle diffusion of the more retained enantiomer of the sulfoxide was found to be one order of magnitude smaller than that of the first eluted one. Overall, this translates into very little longitudinal diffusion (b-term of van Deemter curve) accompanied by high solid-liquid mass transfer resistance (c-term). Finally the comparison with another, differently-substituted chiral sulfoxide (whose enantiomers both exhibit traditional van Deemter curve behavior) has allowed to correlate these findings to the specific characteristics of the molecule.

Impact of straight, unconnected, radially-oriented, and tapered mesopores on column efficiency: A theoretical investigation

Superficially porous particles (SPPs) can be prepared from a pseudomorphic transformation (PMT) which produces straight, unconnected, and radially-oriented mesopores (ROMs). ROMs can be either both ends open in fully porous particles (FPPs) or one-end-closed in SPPs. The impact of ROMs on the longitudinal diffusion (B/u), solid–liquid mass transfer resistance (Csu), and on the eddy dispersion (A(u)) height equivalent to a theoretical plate (HETP) of 3D randomly packed columns was investigated based on theoretical viewpoints. Torquato's theory of effective diffusion in packed beds (B term), Giddings’ coupling theory of eddy dispersion (A term), and Giddings’ generalized nonequilibrium theory (Cs term) are applied to make predictions. First, it is found that the A term is nearly independent on the internal structure of the particle. Secondly, in the absence of flow, infinitely narrow and both ends open (no constriction effect) ROMs induce an internal hindrance factor of 23 regarding diffusion along the axial direction. Experimental data reveal that one-end-closed and 80Å wide ROMs in SPPs lead to a measurable internal hindrance factor of 27 regarding diffusion in the porous shell. Thirdly, above the optimum speed, the Cs coefficient is dependent on the geometry (cylinders, cones, etc.) of the ROMs: when ROMs are conical in SPPs, Cs is expected to decrease by 80% with respect to cylindrical ROMs. From an application perspective, PMT-SPPs prepared with narrow ROMs are well suited for the analysis of small molecules at or below optimum speed (lowest B term) while PMT-SPPs made of wide and conical ROMs are ideal for the analysis of large molecules above optimum speed (smallest Cs term).

The quantitative impact of the mesopore size on the mass transfer mechanism of the new 1.9 μm fully porous Titan-C18 particles. I: Analysis of small molecules

Previous data have shown that could deliver a minimum reduced plate height as small as 1.7. Additionally, the reduction of the mesopore size after C18 derivatization and the subsequent restriction for sample diffusivity across the Titan-C18 particles were found responsible for the unusually small value of the experimental optimum reduced velocity (5 versus 10 for conventional particles) and for the large values of the average reduced solid–liquid mass transfer resistance coefficients (0.032 versus 0.016) measured for a series of seven n-alkanophenones. The improvements in column efficiency made by increasing the average mesopore size of the Titan silica from 80 to 120Å are investigated from a quantitative viewpoint based on the accurate measurements of the reduced coefficients (longitudinal diffusion, trans-particle mass transfer resistance, and eddy diffusion) and of the intra-particle diffusivity, pore, and surface diffusion for the same series of n-alkanophenone compounds. The experimental results reveal an increase (from 0% to 30%) of the longitudinal diffusion coefficients for the same sample concentration distribution (from 0.25 to 4) between the particle volume and the external volume of the column, a 40% increase of the intra-particle diffusivity for the same sample distribution (from 1 to 7) between the particle skeleton volume and the bulk phase, and a 15–30% decrease of the solid–liquid mass transfer coefficient for the n-alkanophenone compounds. Pore and surface diffusion are increased by 60% and 20%, respectively. The eddy dispersion term and the maximum column efficiency (295000plates/m) remain virtually unchanged. The rate of increase of the total plate height with increasing the chromatographic speed is reduced by 20% and it is mostly controlled (75% and 70% for 80 and 120Å pore size) by the flow rate dependence of the eddy dispersion term.

Evaluation of the kinetic performance of new prototype 2.1 mm × 100 mm narrow-bore columns packed with 1.6 μm superficially porous particles

The mass transfer mechanism in three prototype narrow-bore columns (2.1mm×100mm format) packed with 1.6μm superficially porous particles was investigated using different instruments. The heights equivalent to a theoretical plate of three small molecules were measured using a mixture of acetonitrile and water as the eluent. The values reported include the contributions of longitudinal diffusion, eddy dispersion, and the solid–liquid mass transfer resistance. The bulk diffusion coefficients of the analytes were measured using the capillary method, calibrated with thiourea in pure water. The reduced longitudinal diffusion coefficient was determined from the results of a series of peak parking experiments. The solid–liquid mass transfer resistance coefficient and the intra-particle diffusivities of the analytes in the porous region of the particles were estimated from Garnett–Torquato's model of effective diffusion in dense beds packed with core–shell particles. The eddy dispersion term, mostly due to trans-column and border effects, was obtained by subtracting the longitudinal diffusion and the solid–liquid mass transfer resistance terms from the total HETP obtained from the first and second central peak moments calculated by numerical integration (Simpson's approach) after baseline correction and systematic left and right cuts of the peak profiles. The results show that the eddy dispersion controls at least 66% of the overall column HETP for small molecules beyond the optimum velocity. This work illustrates how important it is to use ultra-low dispersive very high pressure liquid chromatography (vHPLC) systems to properly measure and to practically use the high efficiencies of narrow-bore columns packed with 1.6μm core–shell particles since these columns provide intrinsic efficiencies higher than 400,000 plates per meter.

Mass transfer mechanism in chiral reversed phase liquid chromatography

The mechanism of mass transfer in chiral chromatography was investigated using an experimental protocol already applied in RPLC and HILIC chromatography. The different contributions to the reduced height equivalent to a theoretical plate (HETP) include the longitudinal diffusion HETP term, the solid–liquid mass transfer resistance HETP term, the short-range eddy dispersion HETP term, and the long-range eddy dispersion HETP term. Their accurate measurement permits the determination of the adsorption rate constant kads of trans-stilbene enantiomers on a column packed with Lux 5μm Cellulose-1 particles. The experimental results demonstrate that the number of adsorption–desorption steps per unit time of chiral compounds on polysaccharide-based chiral stationary phases is four orders of magnitude smaller than that of achiral compounds.

Effect of parallel segmented flow chromatography on the height equivalent to a theoretical plate II – Performances of 4.6 mm × 30 mm columns packed with 2.6 μm Accucore-C18 superficially porous particles

The reduced trans-column (or long-range eddy dispersion) height equivalent to a theoretical plate (HETP) of short and wide 4.6mm×30mm columns packed with 2.6μm Accucore-C18 superficially porous particles was measured under conventional (no split flow) and parallel segmented (outlet and inlet) flow chromatography. The overall reduced HETP was derived from the true moments of the recorded concentration profiles. The longitudinal diffusion HETP term was measured at a very small flow rate (0.05mL/min). The solid–liquid mass transfer resistance was derived from the shell diffusivity, using the composite Garnett–Torquato model of effective diffusion in a heterogeneous system made of a dense packing of core–shell particles immersed in a continuous matrix (the eluent). The trans-channel and short-range interchannel eddy dispersion HETP terms were assumed to be equal to the calculated h data after solving the Navier–Stokes equation and simulating the advection–diffusion transport process. Experimental results confirmed that the optimum efficiency of these short columns was increased by a factor of about two. The ratio of the detection sensitivities on the PSFC stream and on a regular stream increased from 1 to 1.45 when the retention factor decreases from about 10 to 0.5. These phenomena are due to a strong reduction of the trans-column eddy dispersion HETP term. The system loses about 60% of the sample mass when only outlet skimming is carried out when the flow rate ratio of 55% is applied, as was done in this work. It loses about 50% of the sample when inlet/outlet segmentation is applied. In gradient elution, the peak capacity is increased by only 15%, due to post-column band spreading, which should imperatively be minimized when the outlet flow is split.

Mass transfer mechanism in hydrophilic interaction chromatography

The mass transfer mechanism in HILIC was investigated in depth. The reduced heights equivalent to a theoretical plate (HETP) of five low molecular weigh compounds with retention factors of −0.05 (slight exclusion from the surface due to the presence of a water-rich layer in which naphthalene is insoluble) to 3.64 were measured at room temperature for a 4.6mm×100mm column packed with 3.5μm 140Å XBridge HILIC particles in a wide range of flow velocities. The mobile phase was a buffered acetonitrile–water mixture (92.5/7.5, v/v). Using a physically reliable model of effective diffusion in binary composite media (Torquato's model), the longitudinal diffusion and solid–liquid mass transfer resistance reduced HETP terms were measured. The reduced short-range eddy dispersion HETP was taken from the literature data. The long-range reduced HETP was directly measured from the subtraction of these HETP terms to the overall HETP measured from moment analysis. In contrast to RPLC, the plots of the reduced HETP versus the reduced velocity depend weakly on the retention factor, due to the constant, low intra-particle diffusivity observed in HILIC. So, the reduced longitudinal diffusion HETP is smaller and the reduced solid–liquid mass transfer resistance HETP is larger in HILIC than in RPLC. Whereas border effects can be concealed in RPLC for retained analytes due to fast radial equilibration across the column diameter, a residual long-range eddy dispersion term persists in 4.6mm I.D. HILIC columns, even at very slow flow rates. Experiments show that the minor differences in the long-range eddy dispersion term between analytes having different retention factors is directly correlated to the reciprocal of their bulk diffusion coefficient. The performance of HILIC columns packed with fine particles is then more sensitive to the inlet sample distribution and to the outlet sample collection than RPLC columns due to the relatively poor radial mixing controlled by lateral diffusion.

Comparison between the intra-particle diffusivity in the hydrophilic interaction chromatography and reversed phase liquid chromatography modes. Impact on the column efficiency

The effective diffusion coefficients of five low molecular weigh compounds (naphthalene, uracil, uridine, adenosine, and cytosine) were measured at room temperature in a 4.6mm×100mm column packed with 3.5μm XBridge HILIC particles. The mobile phase was an acetonitrile–water mixture (92.5/7.5, v/v) containing 10mM ammonium acetate and 0.02% acetic acid. Using a physically reliable model of effective diffusion in binary composite media (Torquato's model), accurate estimates of the intra-particle diffusivities in the HILIC particles were obtained as a function of the retention of these analytes. The HILIC diffusion coefficients were compared to those previously obtained for endcapped RPLC-C18 particles (5.0μm Gemini-C18). The experimental results confirm that adsorption sites are not localized in RPLC whereas they are so in the HILIC mode. In contrast to RPLC columns, HILIC columns provide longitudinal diffusion B/u terms that increase very little with increasing retention factors. This confirms the absence of surface diffusion in HILIC. The impact of intra-particle diffusivity on the column efficiency was projected in HILIC and RPLC on the basis of the measured intra-particle diffusivities and on the well established theory of band broadening in particulate columns. Accordingly, RPLC columns generate short-range eddy dispersion and solid–liquid mass transfer resistance Cu terms that increase less than do HILIC column with increasing retention factors. The HETP contribution caused by the trans-column structure heterogeneity is smaller in the HILIC than in the RPLC modes because the transverse excursion length is smaller in HILIC. Even though the overall column efficiencies are comparable in HILIC and RPLC, this study shows that the individual mass transfer phenomena are inherently different in the HILIC and the RPLC retention modes.

Effect of parallel segmented flow chromatography on the height equivalent to a theoretical plate. I—Performance of 4.6 mm × 30 mm columns packed with 3.0 μm Hypurity-C18 fully porous particles

The mass transfer kinetics in short and wide 4.6mm×30mm columns packed with 3.0μm Hypurity-C18 fully porous particles were measured for three different configurations of the inlet sample distribution and outlet sample collection: (1) both the inlet and outlet column endfittings are standard, (2) the inlet endfitting is standard while the outlet endfitting allows parallel segmentation of the exiting flow between a central and a peripheral region across the column diameter, and (3) both the inlet and outlet endfittings allow a parallel segmentation of the flow entering and exiting the column, respectively. The total reduced heights equivalent to a theoretical plate (HETP) were carefully measured, using the first and second central moments of the elution band profiles, obtained by its accurate numerical integration. The longitudinal diffusion term was measured at the lowest experimental reduced velocity applied. The solid–liquid mass transfer resistance was estimated from measurements of the intra-particle diffusivity using the Torquato's model of effective diffusion in packed beds. The trans-channel and short-range interchannel eddy diffusion HETP terms were taken from data obtained by solving numerically the Navier–Stokes equations and simulating advective-diffusive transport in computer-generated random sphere packings. The results clearly show that the trans-column eddy diffusion HETP term can account for up to 85% of the total intrinsic HETP (corrected for extra-column contributions) of the standard columns. Parallel segmented flow chromatography can reduce this contribution by half at high velocities, by eliminating most of the baseline peak tailing. This holds true irrespective of the retention factor of the analyte. It was found also that segmenting the inlet/outlet flow increases detection sensitivity by 25–50% for peaks with large to small retention factors, respectively. In practice, the advantage of parallel segmented flow chromatography in gradient elution (thin peak widths) is essentially limited by post-column bandspreading and diffusion in the dwell volume of the instrument used. Analyst should minimize post-column bandspreading (caused by connectors and detection cell volume) and synchronize the eluent composition in the peripheral and central inlet ports of the column, by using two separate pumps with appropriate dwell volumes.

Limit of the speed-resolution properties in adiabatic supercritical fluid chromatography

Kinetic Poppe plots for small retained compounds were calculated in HPLC (using pure acetonitrile) and SFC (using pure carbon dioxide) for columns having twenty one different lengths (between 3cm and 30m), operated under strict adiabatic conditions (no heat exchange was allowed between the column and the external environment), with a constant pressure drop of 200bar. The outlet pressures were set at 1 and 160bar in HPLC and SFC, respectively. The eluent inlet temperature was set at 312K. The hold-up time t0 and the apparent column efficiency 〈N〉 were calculated by taking into account the longitudinal variations of the eluent pressure, its temperature, density, viscosity, heat capacity, thermal expansion coefficient, equilibrium constant, and diffusion coefficient along the column length. Three different classes of stationary phase were considered: fully porous particles and core–shell particles of different diameter and structure, and silica monolithic columns of the second generation. The reduced plate heights of these stationary phases were taken from experimental data obtained with liquid eluents (acetonitrile/water mixtures). The columns were assumed to be radially homogeneous. The Henry's constant of the compound was fixed at Ka=2.0 at the column inlet. The results demonstrate the potential advantage of using sub-3μm core–shell particles for fast analysis in both LC and SFC, regardless of the intra-particle diffusivity through the stationary phase. In RPLC conditions, the contribution of surface diffusion to intra-particle diffusivity is important and the 4.6 μm core–shell particles can perform as well as sub-2 μm fully porous particles and silica monolithic columns of the second generation. In the absence of surface diffusion or for localized adsorption onto the stationary phase, sub-2 μm particles and silica monolithic column of the second generation outperform the 4.6 μm core–shell particles because the solid–liquid mass transfer resistance controls the column efficiency at high speeds. Eventually, for the same stationary phase and speed of analysis, SFC methods using pure CO2 may provide at least a twice column efficiency than LC methods using pure acetonitrile. For a constant pressure drop and resolution power, SFC methods may generate four times faster analyses than LC methods. Ultimately, a standard commercial 4.6mm × 50mm long column packed with 2.6μm core–shell particles, operated with an inlet flow rate of 25mL/min in fast SFC (200bar back pressure, 40°C) may provide a hold-up time of about 1s requiring data acquisition at a frequency of 400Hz, with a variance of 0.35μL2. This performance will require the use of new, ultra-low dispersion SFC system.

How changing the particle structure can speed up protein mass transfer kinetics in liquid chromatography

The mass transfer kinetics of a few compounds (uracil, 112Da), insulin (5.5kDa), lysozyme (13.4kDa), and bovine serum albumin (BSA, 67kDa) in columns packed with several types of spherical particles was investigated under non-retained conditions, in order to eliminate the poorly known contribution of surface diffusion to overall sample diffusivity across the porous particles in RPLC. Diffusivity across particles is then minimum. Based on the porosity of the particles accessible to analytes, it was accurately estimated from the elution times, the internal obstruction factor (using Pismen correlation), and the hindrance diffusion factor (using Renkin correlation). The columns used were packed with fully porous particles 2.5μm Luna-C18 100Å, core–shell particles 2.6μm Kinetex-C18 100Å, 3.6μm Aeris Widepore-C18 200Å, and prototype 2.7μm core–shell particles (made of two concentric porous shells with 100 and 300Å average pore size, respectively), and with 3.3μm non-porous silica particles. The results demonstrate that the porous particle structure and the solid–liquid mass transfer resistance have practically no effect on the column efficiency for small molecules. For them, the column performance depends principally on eddy dispersion (packing homogeneity), to a lesser degree on longitudinal diffusion (effective sample diffusivity along the packed bed), and only slightly on the solid–liquid mass transfer resistance (sample diffusivity across the particle). In contrast, for proteins, this third HETP contribution, hence the porous particle structure, together with eddy dispersion govern the kinetic performance of columns. Mass transfer kinetics of proteins was observed to be fastest for columns packed with core–shell particles having either a large core-to-particle ratio or having a second, external, shell made of a thin porous layer with large mesopores (200–300Å) and a high porosity (≃0.5–0.7). The structure of this external shell seems to speed up the penetration of proteins into the particles. A stochastic model of the penetration of bulky proteins driven by a concentration gradient across an infinitely thin membrane of known porosity and pore size is suggested to explain this mechanism. Yet, under retained conditions, surface diffusion speeds up the mass transfer into the mesopores and levels the kinetic performance of particles built with either one or two porous shells.

Repeatability of the efficiency of columns packed with sub-3 μm core–shell particles: Part I. 2.6 μm Kinetex-C18 particles in 4.6 mm and 2.1 mm × 100 mm column formats

The column-to-column repeatability of the mass transfer mechanism in columns packed with sub-3μm shell particles was investigated. The parameters of this mechanism were measured for twelve columns (six 2.1mm×100mm and six 4.6mm×100mm) packed with the same batch of 2.6μm Kinetex-C18 particles (Phenomenex, CA, USA). For both series, the manufacturer provided columns at different positions in the efficiency distribution given by the quality test control. Three compounds were used, uracil, naphthalene and insulin. The reduced longitudinal diffusion term was measured with the peak parking (PP) method, the reduced solid–liquid mass transfer resistance term was given by a combination of the PP results and a model of effective diffusion in ternary composite materials (non-porous cores, concentric porous shell, and eluent matrix), validated previously. The overall eddy diffusion term was obtained by subtraction of these two HETP terms from the overall reduced HETP measured by numerical integration of the entire peak profiles. The results demonstrate that the dispersion of the column efficiencies is only due to the random nature of the packing process. At the highest reduced velocity achieved, the relative standard deviations (RSDs) of the eddy diffusion term for the 2.1mm I.D. columns were ca. 7% and 3% for the low molecular weight compounds and for insulin, respectively. For the 4.6mm I.D. columns, these RSDs were 15% and 5%, respectively. The larger RSDs for the 4.6mm I.D. columns is explained by the exceptionally low value of the eddy diffusion term.

Repeatability of the efficiency of columns packed with sub-3 μm core–shell particles: Part III. 2.7 μm Poroshell 120 EC-C18 particles in 4.6 mm and 2.1 mm × 100 mm column formats

As part of an investigation of the column-to-column repeatability of the efficiency of columns packed with sub-3μm shell particles, the parameters of the mass transfer kinetics of twelve columns packed with the same batch of 2.7μm Poroshell 120 EC-C18 particles (Agilent Technologies, Little Fall, DE, USA) were sequentially measured, using columns provided by the manufacturers that were representative of the efficiency distribution given by the quality test control. The reduced longitudinal diffusion term (B) was measured using the peak parking (PP) method; the reduced solid–liquid mass transfer resistance term (C) was given by a combination of the PP results and the most accurate model of effective diffusion in ternary composite materials. The overall eddy diffusion term (A) was obtained by subtraction of these two HETP terms from the overall reduced HETP derived from the peak moments measured by numerical integration of the entire peak profiles. The results demonstrate that the dispersion of the column efficiencies is a result of the random nature of the packing process and the eddy diffusion term resulting from the lack of homogeneity of the column bed. At the highest reduced velocity achieved for small analytes, the relative standard deviations (RSD) of the eddy diffusion term for the 2.1mm I.D. columns were ca. 3 and 11% (with average values heddy= 2.5 and 13.5) for naphthalene (k=3) and uracil (k=0), respectively. For the 4.6mm I.D. columns, these RSDs were 5 and 13%, respectively, with average values heddy= 1.4 and 2.9. For insulin at reduced velocities as high as 160, the RSDs of the total reduced plate heights were 3 and 8% for the 2.1 and 4.6mm I.D. columns, respectively.

Repeatability of the efficiency of columns packed with sub-3 μm core–shell particles: Part II. 2.7 μm Halo-ES-Peptide-C18 particles in 4.6 mm and 2.1 mm × 100 mm column formats

The column-to-column repeatability of the mass transfer kinetics in columns packed with sub-3μm shell particles was investigated. The parameters of this kinetics were measured for twelve columns (six 2.1mm×100mm and six 4.6mm×100mm) packed with the same batch of 2.7μm Halo-ES-Peptide-C18 particles (Advanced Material Technologies, Wilmington, DE, USA). For both series, the manufacturer provided columns at different positions in the efficiency distribution given by the quality test control. Three compounds were used, uracil, naphthalene and insulin. The reduced longitudinal diffusion term was measured with the peak parking (PP) method; the reduced solid–liquid mass transfer resistance term was given by a combination of the PP results and the most accurate model of effective diffusion in ternary composite materials (non-porous cores, concentric porous shell, and eluent matrix), validated previously. The overall eddy diffusion term was obtained by subtraction of these two HETP terms from the overall reduced HETP measured by numerical integration of the entire peak profiles. The results demonstrate that the dispersion of the column efficiencies is mostly due to the random nature of the packing process and the associated eddy diffusion term. At the highest reduced velocity achieved, the relative standard deviations (RSDs) of the eddy diffusion term for the 2.1mm I.D. columns were ca. 5 and 10% (with average values A(ν)=2.3 and 8.5) for naphthalene and uracil, respectively. For the 4.6mm I.D. columns, these RSDs were 3 and 5%, respectively, with average values A(ν)=1.5 and 2.7.

On the relationship between band broadening and the particle-size distribution of the packing material in liquid chromatography: Theory and practice.

The influence of the particle size distribution (PSD) on the band broadening and the efficiency of packed columns is investigated on both theoretical and practical viewpoints. Each of the classical contributions to mass transfer kinetics, those due to longitudinal diffusion, eddy dispersion, and solid–liquid mass transfer resistance are measured and analyzed in terms of their expected and observed intensity as a function of the PSD of mixtures of the commercially available packing materials, 5 and 3 μm Luna-C 18(2) particles (Phenomenex, Torrance, CA, USA). Six 4.6 mm × 150 mm columns were packed with different mixtures of these two materials. The efficiencies of these columns were measured for a non-retained and a retained analytes in a mixture of acetonitrile and water. The longitudinal diffusion coefficient was directly measured by the peak parking method. The solid–liquid mass transfer coefficient was measured from the combination of the peak parking method, the best model of effective diffusion coefficient and the actual PSDs of the different particle mixtures measured by Coulter counter experiments. The eddy diffusion term was measured according to a recently developed protocol, by numerical integration of the peak profiles. Our results clearly show that the PSD has no measurable impact on any of the coefficients of the van Deemter equation. On the contrary and surprisingly, adding a small fraction of large particles to a batch of small particles can improve the quality of the packing of the fine particles. Our results indirectly confirm that the success of sub-3 μm shell particles is due to the roughness of their external surface, which contributes to eliminate most of the nefarious wall effects.

Non-invasive measurement of eddy diffusion in very efficient liquid chromatography columns packed with sub-3 μm shell particles

Mass transfer kinetics in a particular column packed with 2.6 μ m Kinetex-C 18 particles was measured using a series of non-invasive methods. According to the manufacturer, this column was the most efficient one in a lot of 133 columns of the same dimensions, packed with particles of the same batch, with an efficiency about 6% larger than the lot average. The total eddy diffusion term of this column was determined by subtracting from the experimental HETP data (1) the longitudinal diffusion term (given by the peak parking method); (2) the trans-particle solid–liquid mass transfer resistance term (given by the peak parking method and an axial diffusion model); and (3) the external film mass transfer resistance term (derived from the Wilson and Geankoplis correlation). The results are analyzed based on the general coupling theory of eddy diffusion of Giddings and are compared to those previously obtained with a column packed with 2.7 μ m Halo-C 18 column, which also has a low eddy diffusion term. The particular column investigated shows no trans-column velocity bias and a smaller reduced short-range inter-channel eddy diffusion term than the Halo column. This result explains the unusual efficiency of this exceptionally well packed column.

Removal of SO2from Low Sulfur Coal Combustion Gases by Limestone Scrubbing

An analysis of the limestone scrubbing process for SO/sub 2/ removal was carried out. It was found that low concentrations of SO/sub 2/ in power plart flue gas (<1,000 ppM) tend to minimize the solidliquid mass transfer resistance, and the S02 absorption process approaches gas phase cortrol. Gas phase cortrol has a favorable effect on the important parameters of limestone blinding, scaling, slurry pH stability, sulfite oxidation, solids settling, and slurry recirculation rate. It is concluded that operational reliability increases for lower SO/sub 2/ gas concentrations. A discussion of scrubber designs and corresponding mass transfer coefficients for limestone scrubbing is given, and a process design procedure is presented. (auth)