Tube Volume Research Articles

Electrohydraulic Transmission System for Minimally Invasive Robotics

It is a well-known fact that minimally invasive surgery (MIS) has many benefits, e.g., unnecessary trauma and blood loss can be minimized by opening tiny surgery scars, recovery process of patients can be lessened, and the possibilities of complications can be decreased. Although robots are widely used in MIS due to their fundamental superiorities such as high precision, current surgery robots mainly suffer from absence/limitation of haptic feedback during operation. This paper proposes a novel electrohydraulic haptic transmission system to improve the haptic feedback of a surgery robot. This new device replaces the highly nonlinear mechanical friction of thrust wire by viscous friction and avoids the backlash due to the incompressibility of fluid. Moreover, since the fluid is constantly occupying the entire volume of the hydraulic tube, the system behavior during bending of the tube can be modeled much easier than the thrust wire, for which position, shape, and bending angles of the inner wire inside the outer tube are hardly predictable. The validity of the proposal and its superiorities over conventional transmission mechanisms, such as thrust wire, are experimentally verified.

A model of force balance in Jupiter's magnetodisc including hot plasma pressure anisotropy

AbstractWe present an iterative vector potential model of force balance in Jupiter's magnetodisc that includes the effects of hot plasma pressure anisotropy. The fiducial model produces results that are consistent with Galileo magnetic field and plasma data over the whole radial range of the model. The hot plasma pressure gradient and centrifugal forces dominate in the regions inward of ∼20 RJ and outward of ∼50 RJ, respectively, while for realistic values of the pressure anisotropy, the anisotropy current is either the dominant component or at least comparable with the hot plasma pressure gradient current in the region in between. With the inclusion of hot plasma pressure anisotropy, the ∼1.2 and ∼2.7° shifts in the latitudes of the main oval and Ganymede footprint, respectively, associated with variations over the observed range of the hot plasma parameter Kh, which is the product of hot pressure and unit flux tube volume, are comparable to the shifts observed in auroral images. However, the middle magnetosphere is susceptible to the firehose instability, with peak equatorial values of βh∥e−βh⊥e≃1 − 2, for Kh=2.0 − 2.5 × 107 Pa m T−1. For larger values of Kh,βh∥e−βh⊥e exceeds 2 near ∼25 RJ and the model does not converge. This suggests that small‐scale plasmoid release or “drizzle” of iogenic plasma may often occur in the middle magnetosphere, thus forming a significant mode of plasma mass loss, alongside plasmoids, at Jupiter.

Posterior pedicle screw fixation followed by anterior decompression and fusion for the treatment of thoracolumbar burst fractures

Objective To investigate the clinical effect of posterior pedicle screw fixation combined with anterior decompression and fusion for the treatment of thoracolumbar burst fractures. Methods The clinical data of 53 patients underwent posterior pedicle screw fixation and anterior decompression and fusion were retrospectively analyzed.The vertebral height, Cobb angle, vertebral tube volume, the Frankel gradient and Fugl-Meyer score were recorded and compared before and after treatment. Results 49 patients were followed up.At the last time of follow-up, the vertebral height, Cobb angle, vertebral tube volume all significantly improved (t=24.047, P<0.001; t=21.815, P<0.001; t=31.699, P<0.001). The Frankel gradient before treatment was: A 6 cases, B 18 cases, C 15 cases, D 10 cases, E 4 cases.After treatment, it came to 3 cases, 8 cases, 11 cases, 17 cases, 10 cases, respectively.There was significant difference before and after treatment (Z=2.997, P=0.003). There was significant difference in Fugl-Meyer score before and after treatment[(74.65±8.42)points, (90.26±9.17)points, respectively, P<0.001]. Conclusion There is excellent effect on posterior pedicle screw fixation followed by anterior decompression and fusion for the treatment of thoracolumbar burst fractures.It is good for the recovery of motion and spinal function. Key words: Spinal fractures; Fracture fixation; Decompression, surgery

Abstract 18061: Supplementation to Treat Antithrombin Deficiency Improves Sensitivity to Heparin, Anticoagulation and Decreased Thrombogenecity in Neonates and Infants Undergoing Cardiac Surgery With Cardiopulmonary Bypass

Introduction: Preoperative antithrombin (AT) deficiency is common in infants undergoing cardiac surgery with cardiopulmonary bypass (CPB), and is associated with heparin resistance, difficulties achieving optimal intraoperative anticoagulation and post-operative thrombosis. Methods: We performed a pilot randomized trial of pooled human AT supplementation for children &lt;1 year with preoperative AT &lt;0.85U/ml. Subjects received a split (patient and CPB prime) dose of AT before heparinization. AT was dosed to reach a predicted AT activity of 1.2U/ml during CPB calculated from preoperative AT level and patient weight. Results: We randomized 18 subjects; 17 completed the study (9 controls, 8 AT). Mean preoperative AT level was similar between groups (Control: 0.65±0.10 vs. AT: 0.68±0.15 U/mL, p=0.66). AT group subjects had higher AT than controls immediately after start of CPB (Control: 0.44±0.10 vs. AT: 1.15±0.20 U/mL, p&lt;0.001) and at the end of CPB (Control: 0.67±0.14 vs. AT: 1.19±0.16 U/mL, p&lt;0.001). AT supplementation was associated with increased activated clotting time (ACT) post-heparinization (Control: 500±72 vs. AT: 639±172 seconds, p=0.02), increased heparin sensitivity (Control: 89±23 vs. AT: 114±22 ACT seconds per 100U/kg heparin, p=0.02), and decreased heparin dose given during CPB (Control: 1126±344 vs. AT: 845±165 U/kg, p=0.03). After primary heparinization, 56% of control subjects did not achieve ACT target vs. 25% of AT subjects. At the end of CPB, AT group subjects had lower prothrombin levels (Control: 746±372 vs. AT: 460±102 ng/mL, p=0.02) and lower levels of inflammatory cytokines (IL-1α, IL-1β, IL-6, IL-8 and TNFα). Supplementation with AT was not associated with increased chest tube volume loss or blood product requirements. One subject in each group had severe bleeding, and one in each group had post-operative infection. Thrombosis was noted for 3 controls and 1 AT subjects. Conclusions: AT supplementation to treat preoperative AT deficiency in young children is associated with decreased heparin resistance, improved anticoagulation and decreased thrombogenecity. Safety profile regarding bleeding and infections appears favorable. Equipoise exists for a larger definitive outcome trial.

Effect of Automated Attenuation-based Tube Voltage Selection on Radiation Dose at CT: An Observational Study on a Global Scale.

To evaluate the effect of automated tube voltage selection (ATVS) on radiation dose at computed tomography (CT) worldwide encompassing all body regions and types of CT examinations. No patient information was accessed; therefore, institutional review board approval was not sought. Data from 86 centers across the world were analyzed. All CT interactions were automatically collected and transmitted to the CT vendor during two 6-week periods immediately before and 2 weeks after implementation of ATVS. A total of 164 323 unique CT studies were analyzed. Studies were categorized by body region and type of examination. Tube voltage and volume CT dose index (CTDIvol) were compared between examinations performed with ATVS and those performed before ATVS implementation. Descriptive statistical methods and multilevel linear regression models were used for analysis. Across all types of CT examinations and body regions, CTDIvol was 14.7% lower in examinations performed with ATVS (n = 30 313) than in those performed before ATVS implementation (n = 79 275). Relative reductions in mean CTDIvol were most notable for temporal bone CT (-56.1%), peripheral runoff CT angiography (-48.6%), CT of the paranasal sinus (-39.6%), cerebral or carotid CT angiography (-36.4%), coronary CT angiography (-25.1%), and head CT (-23.9%). An increase in mean CTDIvol was observed for renal stone protocols (26.2%) and thoracic or lumbar spine examinations (6.6%). In the multilevel model with fixed effects ATVS and examination type, and the interaction of these variables and the random effect country, a significant influence on CTDIvol for all fixed efects was revealed (ATVS, P = .0031; examination type, P < .0001; interaction term, P < .0001). ATVS significantly reduces radiation dose across most, but not all, body regions and types of CT examinations.

Halloysite Clay Nanotubes for Loading and Sustained Release of Functional Compounds.

Halloysite is an alumosilicate tubular clay with a diameter of 50 nm, an inner lumen of 15 nm and a length of 600-900 nm. It is a natural biocompatible nanomaterial available in thousands of tons at low price, which makes it a good candidate for nanoarchitectural composites. The inner lumen of halloysite may be adjusted by etching to 20-30% of the tube volume and loading with functional agents (antioxidants, anticorrosion agents, flame-retardant agents, drugs, or proteins) allowing for formulations with sustained release tuned by the tube end-stoppers for hours and days. Clogging the tube ends in polymeric composites allows further extension of the release time. Thus, antioxidant-loaded halloysite doped into rubber enhances anti-aging properties for at least 12 months. The addition of 3-5 wt% of halloysite increases the strength of polymeric materials, and the possibility of the tube's orientation promises a gradient of properties. Halloysite nanotubes are a promising mesoporous media for catalytic nanoparticles that may be seeded on the tube surface or synthesized exclusively in the lumens, providing enhanced catalytic properties, especially at high temperatures. In vitro and in vivo studies on biological cells and worms indicate the safety of halloysite, and tests for efficient adsorption of mycotoxins in animals' stomachs are also carried out.

Thermal efficiency maximization for H- and X-shaped heat exchangers based on constructal theory

Constructal optimizations of H- and X-shaped heat exchangers are carried out by taking the maximum thermal efficiency (the ratio of the dimensionless heat transfer rate to the dimensionless total pumping power) as optimization objective. The constraints of total tube volumes and spaces occupied by heat exchangers are considered in the optimizations. For the H-shaped heat exchanger, the thermal efficiency decreases when the dimensionless mass flow rate increases. For the higher order of the X-shaped heat exchanger, when the order number is 3, the thermal efficiency of the heat exchanger with Murry law is increased by 68.54% than that with equal flow velocity in the tubes, and by 435.46% than that with equal cross section area of the tubes.

Anharmonic oscillatory flow braking in the Earth's magnetotail

AbstractPlasma sheet bursty bulk flows often oscillate around their equilibrium position at about 10 RE downtail. The radial magnetic field, pressure, and flux tube volume profiles usually behave differently earthward and tailward of this position. Using data from five Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes, we reconstruct these profiles with the help of an empirical model and apply thin filament theory to show that the oscillatory flow braking can occur in an asymmetric potential. Thus, the thin filament oscillations appear to be anharmonic, with a power spectrum exhibiting peaks at both the fundamental frequency and the first harmonic. Such anharmonic oscillatory braking can explain the presence of the first harmonic in Pi2 pulsations (frequency doubling), which are simultaneously observed by magnetometers on the ground near the conjugate THEMIS footprints.

Theoretical and experimental investigation of pressure drop and refrigeration effect in pulse tube cryocooler

The design of a highly efficient pulse tube cryocooler (PTC) is a subject of recent research activities. The PTC performance depends on various operating and design parameters. Regenerator is one of the very important components of the PTC which decides the low temperature that the PTC can attain. Efficiency of regenerator should be high enough, 96% or above, in order to reach very low temperature while the pressure drop in the regenerator is one of the parameters which needs to be analysed in detail. In the present work, theoretical and experimental investigations are carried out on two different single stage U type PTC. The volumes of regenerators and pulse tubes, in both the cases are kept same while the length to diameter (L/D) ratios of regenerators are changed. Investigations are carried out on these PTC with respect to pressure drop in the regenerator and net refrigeration effect obtained from the PTC at 80 K. The pressure drop increases from 0.29 bar to 2.07 bar with an increase in L/D ratio from 1.93 to 9, resulting in decrease in refrigeration effect from 6.1 W to 1.7 W at 80 K with 300 W input power. The study is further extended to understand the effect of coarse size stainless steel mesh size in the regenerator. Coarse size meshes filled up to 60% of regenerator length improved the refrigeration effect from 1.7 W to 2.8 W; however, further filling degrades the performance of the PTC. The experimental results are compared with theoretical results obtained by Sage software and Isothermal model.

Effects of Radiative Diffusion on Thin Flux Tubes in Turbulent Solar-like Convection

We study the combined effects of convection and radiative diffusion on the evolution of thin magnetic flux tubes in the solar interior. Radiative diffusion is the primary supplier of heat to convective motions in the lower convection zone, and it results in a heat input per unit volume of magnetic flux tubes that has been ignored by many previous thin flux tube studies. We use a thin flux tube model subject to convection taken from a rotating spherical shell of turbulent, solar-like convection as described by Weber, Fan, and Miesch (2011, Astrophys. J., 741, 11; 2013, Solar Phys., 287, 239), now taking into account the influence of radiative heating on flux tubes of large-scale active regions. Our simulations show that flux tubes of less than or equal to 60 kG subject to solar-like convective flows do not anchor in the overshoot region, but rather drift upward due to the increased buoyancy of the flux tube earlier in its evolution as a result of the inclusion of radiative diffusion. Flux tubes of magnetic field strengths ranging from 15 kG to 100 kG have rise times of less than or equal to 0.2 years, and exhibit a Joy's Law tilt-angle trend. Our results suggest that radiative heating is an effective mechanism by which flux tubes can escape from the stably stratified overshoot region, and that flux tubes do not necessarily need to be anchored in the overshoot region to produce emergence properties similar to those of active regions on the Sun.

The Shock/Shear platform for planar radiation-hydrodynamics experiments on the National Ignition Facility

An indirectly-driven shock tube experiment fielded on the National Ignition Facility (NIF) was used to create a high-energy-density hydrodynamics platform at unprecedented scale. Scaling up a shear-induced mixing experiment previously fielded at OMEGA, the NIF shear platform drives 130 μm/ns shocks into a CH foam-filled shock tube (∼ 60 mg/cc) with interior dimensions of 1.5 mm diameter and 5 mm length. The pulse-shaping capabilities of the NIF are used to extend the drive for &amp;gt;10 ns, and the large interior tube volumes are used to isolate physics-altering edge effects from the region of interest. The scaling of the experiment to the NIF allows for considerable improvement in maximum driving time of hydrodynamics, in fidelity of physics under examination, and in diagnostic clarity. Details of the experimental platform and post-shot simulations used in the analysis of the platform-qualifying data are presented. Hydrodynamic scaling is used to compare shear data from OMEGA with that from NIF, suggesting a possible change in the dimensionality of the instability at late times from one platform to the other.

Gas Analysis Using Raman Spectroscopy Demonstrates the Presence of Intraperitoneal Air (Nitrogen and Oxygen) in a Cohort of Children Undergoing Pediatric Laparoscopic Surgery

Clinically significant gas embolism during laparoscopy is a rare but potentially catastrophic event. Case reports suggest that air, in addition to the insufflation gas, may be present. We studied the effects of equipment design and flushing techniques on the composition of gas present under experimental and routine pediatric surgical conditions. Concentrations of nitrogen (N2), oxygen (O2), and carbon dioxide (CO2) were measured by Raman spectroscopy in gas delivered to and retrieved from a mock peritoneum during simulated laparoscopy. We then analyzed the composition of insufflated and recovered gases during elective laparoscopic procedures conducted with CO2-preflushed and unflushed tubing to determine the presence of significant (10%) quantities of air. In vitro, CO2 was not detected at the distal end of insufflator tubing until after delivery of approximately 0.2 L of gas, and N2 persisted until >0.4 L was delivered, with 40% ± 8% (mean ± SD, range 33%-49%) recovered from the mock peritoneum at the termination of initial insufflation. In clinical studies, preflushing reduced the initial concentration of N2 from 78% ± 0.5% to 23% ± 15%, but >10% air was detected in all subsequent samples, regardless of insufflation technique. Laparoscopic equipment and practice routinely permit delivery of air to the insufflated cavity. Purging the equipment with CO2 reduces but does not eliminate air (N2, O2) within the peritoneal cavity during laparoscopy. Thus, when vascular injury occurs, embolized gases will contain variable quantities of N2, O2, and CO2. As the initial insufflation volume diminishes and approaches the volume of the insufflation tubing, which occurs in infants and young pediatric patients, the concentration of N2 will approximate that of room air in an unflushed system. Small insufflation volumes containing high N2 concentrations can contribute to catastrophic air emboli in neonates and small pediatric patients.

Study on a Glucose Concentration Measurement System Based on Microwave Perturbation Technique

The relationship of frequency shift and glucose concentration was determined by microwave perturbation theory, and a measurement system was designed. The sensing device is a cylindrical cavity working at 7 GHz with TE011 mode. The glucose solution is placed in a capillary tube that is in the middle of the cavity. The geometrical parameters of the coupling device are optimized to make the system perform better. The radius of the capillary is 2 mm, which guarantees the volume of the capillary tube, being small enough to be neglected when concentration changes. Three modules: detecting, tracking and measuring module based on FPGA help monitor frequency change. The resolution of the system reaches up to 10 mg/dl which is promising for measuring blood glucose in the future.

Influence of the Gas Volume in the Void Tube Connecting Compressor and Inertance Tube on the Oscillating Flow in an Inertance Tube Phase Shifting System

Influencesof thegas volumein the void tube (connecting tube), connecting compressor and inertance tube, on the oscillating flowcharacteristics are experimentally investigated. Four void tubes, whose volumes are different from each other, are chosen to connect the compressor and the inertance tube respectively. Piston displacement of the compressor and dynamic pressure at the outlet of the compressor are measured by a laserdisplacement sensor and a quartz pressure sensor respectively. This investigation focuses on the piston displacement and mass flows at three special positions of the experimental system.The change of the amplitudes and phase angles of the piston displacement and the three mass flows caused by varying the void tubes with different dynamic pressures and frequencies are studied. This investigation is helpful to study the influence ofthe gas volumein the connecting parts of an inertance tube pulse tube cryocooler, such as transfer tube, cold finger and pulse tube, on oscillating characteristics of the cooler.

The influence of radiative heat exchange on the character of gasdynamic flows under conditions of pulsed discharge in high-pressure cesium vapor

The gasdynamics of pulse-periodic radiative discharge in high-pressure cesium vapor has been studied in the framework of a two-temperature multifluid model. It is established that, at a limited volume of the gas-discharge tube, the character of gasdynamic flows depends on the conditions of radiative heat exchange in discharge plasma. In cases in which the main contribution to radiative energy losses is related to a spectral region with optical thickness τR(λ) ∼ 1, there is nonlocal radiative heat exchange in discharge plasma, which is uniformly heated over the entire tube volume and moves from the discharge axis to tube walls during the entire pulse of discharge current. Under the conditions of radiative losses determined by the spectral region where τR(λ) ≪ 1, the reabsorption of radiation is absent and discharge plasma is nonuniformly heated by the current pulse. This leads to the appearance of reverse motions, so that the heated plasma is partly pushed toward the tube walls and partly returned to the discharge axis.

Tube volumes via functional equations

Tube formulas for convex sets and for smooth submanifolds of Euclidean spaces have long been of interest for geometers. In the last two decades there has been great progress on tube formulas for badly behaved spaces such as fractals, sprays and strings. We give a new, simple proof of an interesting tube formula of M. Lapidus and E. Pearse for self-similar sprays using a natural functional equation satisfied by tube volumes of them.

Physical apparatus parameters and model for vibrating tube densimeters at pressures to 140 MPa and temperatures to 473 K.

Vibrating tube densimeters are well-established tools for measuring fluid densities precisely at elevated temperatures and pressures. However, the conventional method of calibrating them utilises a model in which the apparatus parameters are represented as polynomials of temperature and pressure that contain a variable number of terms. Here a robust, physically-based model is presented and demonstrated for six different instruments at temperatures from (273 to 473) K, pressures from (0 to 140) MPa, and densities from (0 to 1050) kg m(-3). The model's physical basis ensures that only seven apparatus parameters are required to relate the measured resonant period to fluid mass density with an average r.m.s. deviation of ±0.23 kg m(-3) across all six densimeters. Estimates for each of the apparatus parameters were made based on the geometry and material properties of the vibrating tubes, and these estimates were consistent with the parameter values determined by calibration with reference fluids. Three of the apparatus parameters describe the temperature dependence of the resonant period: for the six vibrating tubes tested, the relative standard deviations of these parameters were all within the range of values estimated from the thermoelastic properties of the Hastelloy tubes. Two distinct parameters are required to describe the pressure dependence of the vibrating tube's volume and effective spring constant, both of which are estimable from equations describing the elastic deformation of thick-walled tubes. The extensive calibrations conducted demonstrate that, for these densimeters, the variations with pressure of the tube's spring constant and its volume have a ratio that is neither 0 nor 1, as has been assumed previously. The model's physical basis allows vibrating tube densimeters to be calibrated accurately using fewer reference fluid measurements than required by the conventional method. Furthermore, use of the physically-based model reduces the uncertainty of measurements made at densities, temperatures, or pressures beyond the range of the calibration.

Characterisation of organic contaminants in the CLOUD chamber at CERN

Abstract. The CLOUD experiment (Cosmics Leaving OUtdoor Droplets) investigates the nucleation of new particles and how this process is influenced by galactic cosmic rays in an electropolished, stainless-steel environmental chamber at CERN (European Organization for Nuclear Research). Since volatile organic compounds (VOCs) can act as precursor gases for nucleation and growth of particles, great efforts have been made to keep their unwanted background levels as low as possible and to quantify them. In order to be able to measure a great set of VOCs simultaneously in the low parts per trillion (pptv) range, proton-transfer-reaction mass spectrometry (PTR-MS) was used. Initially the total VOC background concentration strongly correlated with ozone in the chamber and ranged from 0.1 to 7 parts per billion (ppbv). Plastic used as sealing material in the ozone generator was found to be a major VOC source. Especially oxygen-containing VOCs were generated together with ozone. These parts were replaced by stainless steel after CLOUD3, which strongly reduced the total VOC background. An additional ozone-induced VOC source is surface-assisted reactions at the electropolished stainless steel walls. The change in relative humidity (RH) from very dry to humid conditions increases background VOCs released from the chamber walls. This effect is especially pronounced when the RH is increased for the first time in a campaign. Also the dead volume of inlet tubes for trace gases that were not continuously flushed was found to be a short but strong VOC contamination source. For lower ozone levels (below 100 ppbv) the total VOC contamination was usually below 1 ppbv and therewith considerably cleaner than a comparable Teflon chamber. On average about 75% of the total VOCs come from only five exact masses (tentatively assigned as formaldehyde, acetaldehyde, acetone, formic acid, and acetic acid), which have a rather high vapour pressure and are therefore not important for nucleation and growth of particles.

Waste Heat Recovery Using Matrix Heat Exchanger from the Exhaust of an Automobile Engine for Heating Car’s Passenger Cabin

The main objective of our work is to analysis the heat transfer rate for various fluids with different matrix heat exchanger (MHE) models and flow characteristic in matrix heat exchanger by using computational fluid dynamics (CFD) package with small car. The amount of heat carried by the cold fluid from hot fluid is mainly depends upon the mass flow rate of the working fluid. The heat transfer area per unit volume of tube is more. So, it increases the temperature of the cold fluid. Here, the hot and cold fluids are moving in the alternate tubes of heat exchanger in the counter flow direction. The small amounts of pressure drop are occurred but which is less compared to existing model. Flow disturbances are rectified in the MHE through the modifications made. Since, silicon carbide material is used as a polishing material to avoid the deposit of carbon at the inner side of the flow passage and this waste heat energy is used for heating passenger cabin during winter season. The wood is used as an insulating material to avoid the heat flow from fluid to atmosphere. Keywords-Heat transfer rate, Matrix heat exchanger, Working fluid, Polishing material.

Effect of the pressure on pre-column sample dispersion theory, experiments, and practical consequences

The effect of the pressure on the dispersion of a low molecular weight compound along 0.508 and 1.016mm i.d. × 50cm long open circular tubes was investigated theoretically and experimentally. The theoretical predictions were based on the early models of dispersion derived by Aris and Taylor (1953) and on the approximate model of Alizadeh for the time moments (1980). Experimentally, the system pressure was increased at constant flow rate (0.15mL/min) from less than 20 to nearly 1000bar by using a series of capillary tubes (25μm i.d. PEEKSIL tubes) of increasing flow resistances placed upstream the detection cell of a commercial very high pressure liquid chromatograph (vHPLC) but downstream the 50cm long tube. Theoretical and experimental results agree that the peak variance increases linearly with increasing pressure in the tube volume. The relative increase of the peak variance is 7% above that measured at low pressure (<20bar) for each 100bar increment in the tube volume. This result confirms that accurate measurements of the column efficiency corrected for extra-column contribution cannot be made by replacing the column with a zero dead volume union connector, because the pressures applied in the pre-column volume are significantly different in these two cases. This work shows also that increasing the pressure in the pre-column volume by increasing the flow rate affects the apparent column efficiency that is measured, independently of the direct effect of the flow rate. For a 2.1 × 50mm column packed with 1.3μm core–shell particles run with a classic Acquity system, the associated relative decreases of the column efficiency are expected to be −30%, −20%, and −5% for retention factors of 1, 3, and 10, respectively. The column HETP is no longer independent of its length.