Number Eo Research Articles

Lattice Boltzmann simulation of the rise and dissolution of two-dimensional immiscible droplets

We used a coupled multiphase lattice Boltzmann (LB) model to simulate the dissolution of immiscible liquid droplets in another liquid during the rising process resulting from buoyancy. It was found that there existed a terminal rise velocity for each droplet, and there was a power law relationship between the Eötvös (Eo) number and the terminal Reynolds (Re) number. Our simulation results were in agreement with the empirical correlation derived for predicting bubble rise. When more than two identical droplets rose simultaneously in a close proximity, the average terminal rise velocity was lower than that of a single droplet with the same size because of the mutual resistant interactions. The droplet trajectories at the noncentral positions were not straight because of the nonzero net horizontal forces acting on the droplets. The Damkohler (Da) and Peclet (Pe) numbers were varied to investigate the coupling between droplet size, flow field, dissolution at the interface, and solute transport. For a given Pe, increasing Da led to a higher dissolution rate. For a given Da, increasing Pe led to a higher dissolution rate. For a large Da and a small Pe, the process near the interface was diffusion limited, and the advective flow relative to the droplet resulting from droplet rise was unable to move the accumulated solute away from the interface quickly. In this case, it was favorable to split the single droplet into as many small ones as possible in order to increase the interface area per unit mass and consequently enhance the whole dissolution process. For a small Da and a large Pe, the process was dissolution limited near the interface. The mass of accumulated solute near the interface was little, so the advective flow at the top side of the droplet was able to clean the solute quickly. In this case it was favorable to keep the droplet as a single one in order to obtain a high rise velocity and consequently enhance the whole dissolution process. By studying the coupling between Da and Pe, we qualitatively proposed to construct a Da-Pe phase plane and found the interface dividing the plane into regions 1 and 2. Region 1 was the collection of points where it was favorable to break down the droplet into as many small ones as possible in order to accelerate dissolution, while region 2 was the collection of points where it was favorable to keep the droplet in a single one for the same purpose. Based on our LB simulations, we found that the interface was an increasing function of Pe. Region 1 was the portion above the interface, while region 2 was the portion below it. In real applications, if both Pe and Da are obtained, it will be easy to judge whether it is favorable to break down the droplet or not in order to accelerate dissolution by checking whether (Pe, Da) falls in region 1 or 2.

Effect of nonionic surfactant molecular structure on cloud point extraction of phenol from wastewater

Above a temperature known as the cloud point, aqueous solutions of nonionic ethoxylated surfactants separate into two phases: a coacervate phase concentrated in surfactant and a dilute phase with low surfactant concentration. The coacervate phase contains surfactant aggregates which are micelles or micelle-like and will solubilize any organic solutes originally present in the water, resulting in a liquid–liquid extraction known as a cloud point extraction (CPE). Removal of pollutants from water is an important potential application of CPE and we use phenol as a model organic pollutant in this work. In this study, we investigate the effect of surfactant structure on important equilibrium CPE parameters like cloud point, fractional coacervate volume, and phenol and surfactant partition ratios for alcohol ethoxylates (AEs), a major class of nonionic surfactants. Pure, homogeneous surfactants with linear hydrophobes are studied as well as commercial heterogeneous AEs with both linear and branched hydrophobes. The effects of degree of polymerization in the polyethoxylate group (EO number) as well as hydrophobe size (alkyl carbon number) are systematically investigated as well as the effect of hydrophobe branching. The solubilization equilibrium constant is shown to increase linearly with EO number and is unaffected by alkyl carbon number or hydrophobe branching from which we deduce that the phenol is solubilized with the benzene ring at the surface of the micelle core and the hydroxyl group having attractive interactions with the polyethoxylate chains in the palisade layer of the micelle. The effects of surfactant structural features on net intermicellar attractive forces, micellar excluded volume, and solubilization capacity are discussed. A model is developed which can predict the phenol partition ratio at a given temperature for any AE surfactant dependent on only one simple measured parameter: fractional coacervate volume. This universal model is somewhat unique to phenolics or short chain alcohols because of their solubilization loci in the micelle and mechanism of solubilization. Guidelines for surfactant selection for CPE of phenol or similar solutes are outlined.

Physiochemical Properties of Hydroxy Mixed Ether HMEnSurfactants and their Interaction with Sodium Dodecyl Sulfate SDS

AbstractThis paper is focused on the phase behavior, interaction with anionic surfactant sodium dodecyl sulfate SDS, adsorption and wetting investigations of new hydroxy mixed ether nonionic surfactants HMEn. The phase diagrams of (0.1–100) %wt of HMEn(n-value is the ethoxylation number EO) at the temperature range 20–100°C have shown that the increasing of n-value raises the cloud boundary toward higher temperature. Remarkable result was obtained from the interaction between SDS and HMEB, at which the mixed system exhibits a unique homogeneity and a liquid crystal phase formation. Macroscopically, the liquid crystal region was found when the SDS concentration range between 8 and 24 mM mixed with 10% wt HMEB. The interaction between HMEnand mica was also investigated using atomic force microscopy AFM and a pronounced adsorption of HMEnon mica was observed. Moreover, contact angle results reveal that glass substrate shows strong wettability of HMEnsurfactant solutions compared with polyethylene PE and polymethylmethaacrylate PMMA substrates. This wettability however also decreases with EO number.

New hydrophilic interaction/reversed-phase mixed-mode stationary phase and its application for analysis of nonionic ethoxylated surfactants

We have developed a new stationary phase that combines both hydrophilic interaction and reversed-phase characteristics. The new phase is based on high-purity, porous and spherical silica gel functionalized with a silyl ligand consisting of both hydrophilic and hydrophobic functionalities. This phase can be operated in both HILIC mode (high organic solvent) and RPLC mode (low organic solvent). An optimal balance of hydrophilic and hydrophobic moieties on the silica surface provides unique chromatographic properties that make it useful for determination of alkyl chain distribution and degree of ethoxylation (EO number) of nonionic ethoxylated surfactants.

Correction of the penetration theory based on mass-transfer data from bubble columns operated in the homogeneous regime under high pressure

A new correction term was developed which allows the classical penetration theory to be applied successfully to k L a data obtained from oblate ellipsoidal bubbles formed in bubble columns operated in the homogeneous regime at various pressures ( 0.1 – 4.0 MPa ) . The correction factor is a function of both the Eötvös number Eo and dimensionless gas density ratio. The new correlation was compared with literature k L a data in 18 pure organic liquids, 14 adjusted liquid mixtures and tap water. In some of the liquids (tetralin, xylene and ethanol) not only air but also other gases (nitrogen, helium and hydrogen) were used. In total, 263 experimental k L a points are fitted with an average relative error of 10.4%. In the theoretical approach for the k L a prediction, the gas–liquid contact time (used in the penetration theory) is defined as the ratio of bubble surface to the rate of surface formation. All further calculations are based on the geometrical characteristics (bubble length and height) of an oblate ellipsoidal bubble. It was found that the new correction factor f c gradually reduces with the increase of both superficial gas velocity u G and gas density ρ G (operating pressure P ).

Eosinophilic Esophagitis Disease in Children from West Virginia: A Review of the Last Decade (1995?2004)

Eosinophilic esophagitis (EoE) is a newly established disease in adults and children. The incidence and prevalence of the disease among children from the United States are largely unknown. We examined the endoscopy reports of children who attended our gastroenterology clinic in the last 10 yr. MATERIALS A AND METHODS: retrospective review of all diagnostic upper endoscopy procedures was executed between 1995-2004, of which a quarter (25%) per each year was randomly selected for pathological reevaluation of the number of Eos. The diagnosis of EoE was established when higher than 15 Es/hpf was detected in the esophageal biopsy; and the prevalence of EoE was calculated. The clinical symptoms, endoscopic presentation, and treatment of the patients with EoE disease were also reviewed. A total of 1,424 procedures were reviewed, of which 355 esophageal samples were reevaluated. During the study period, 44 patients were diagnosed with EoE. The prevalence rate of EoE disease was 0.73/10,000 children during the study period. Similar results were found when the number of Eos was established at >20 Es/hpf. Abdominal pain (55%), vomiting (43%), and heartburn (39%) were the most common symptoms, and characteristic mucosal appearance was found in only 11% of the patients. The rate of EoE in our pediatric patient population is low. Prospective studies are needed to establish the incident and prevalence of EoE disease in children living in the United States.

Shapes of Single Drops Rising Through Stagnant Liquids

Shapes of single drops rising through infinite stagnant liquids under terminal conditions were measured using a high-speed camera for a wide range of fluid properties. Aspect ratios E and distortion factors γ of drops were evaluated from drop images. Effects of initial shape deformation, surfactants and viscosity ratio κ on E and γ were investigated. As a result, the following conclusions were obtained. (1) Initial shape deformation does not affect E and γ of single drops. (2) Addition of surfactants decreases E and breaks the fore-and-aft symmetry of a drop shape especially in systems of low Morton numbers M. (3) The Tadaki number Ta is the best dimensionless number among the Eotvos number Eo, the Weber number We and Ta for correlating E of drops, and an empirical correlation of E in terms of Ta was proposed for clean drops under the conditions of -11.6 ≤ log M ≤ -0.9, 1.5 × 10-2 ≤ Re ≤ 8.5 × 102, 1.7 × 10-2 ≤ Eo ≤ 9.3, 7.4 × 10-3 ≤ Ta ≤ 3.6 and 0.1 ≤ κ ≤ 100. (4) The viscosity ratio κ does not affect E so much but influences γ. For κ > 1, γ decreases with increasing the drop diameter, that is, the front part of a drop is flatter than the rear part. On the contrary, the rear part is flatter than the front part when κ < 1. The fore-and-aft symmetry always holds for drops with κ ∼ 1.0. (5) Various drop shapes were presented as a database utilized for verification of numerical methods such as an interface tracking method and a boundary element method.

Effect of C 12EO n mixed surfactant systems on the formation of viscoelastic worm-like micellar solutions in sucrose alkanoate– and CTAB–water systems

With successive addition of mixed polyoxyethylene dodecylether (C 12EO n ) surfactant with an average EO number of 3 to the aqueous solution of hexadecyltrimethylammonium bromide (CTAB) and sucrose monohexadecanoate (P1695), one-dimensional micellar growth occurs and the viscosity increases sharply leading to the formation of viscoelastic solutions of worm-like micelles. Steady and oscillatory shear rheological measurements show that in the aqueous CTAB system, the extent of micellar growth decreases with increasing the dispersion in EO chain in the mixture in following order C 12EO 3 > C 12EO 2 + C 12EO 4 > C 12EO 0 + C 12EO 4 > C 12EO 1 + C 12EO 5. With C 12EO 0 + C 12EO 6 no micellar growth occurs but a phase separation is observed. In P1695 system, the viscoelastic solution is formed at relatively lower concentration of mixed C 12EO n and the extent of micellar growth decreases in the following order: C 12EO 3 ≈ C 12EO 2 + C 12EO 4 > C 12EO 1 + C 12EO 5 > C 12EO 0 + C 12EO 6. The effect of the dispersion of EO chain length on the micellar growth is also discussed.

Effect of Headgroup Size on Permeability of Newton Black Films

Gas permeability and thin-film interferometry are used as a tool to elucidate the orientation of polymeric headgroups in free-standing foam films. Nonionic polyoxyethylene (EO) surfactants were used to stabilize the foam films, keeping the size of the hydrophobic part constant (C12) and varying the size of the hydrophilic (EO numbers) part. The effect of headgroup size on the gas permeability of Newton black foam films was studied. Thickness, contact angle, and surface tension were measured to understand the permeation mechanism. Increase of film thickness and surface tension was observed while increasing the headgroup size, but the contact angle remains small and constant. Upon increasing the headgroup size, the permeability decreases showing that the headgroups provide a resistance to permeation. For smaller headgroups, the permeability follows a linear dependence on the film thickness, whereas for larger headgroups, the permeability essentially deviates from linearity. We use the conventional "coil model" of the EO chains to explain the observed results providing a detailed picture of the orientation of this important molecule in a confined volume of foam films.

Effects of interleukin-18 on asthmatic airway inflammation: experimental study of guinea pig asthmatic model

To investigate the effects of Interleukin-18 (IL-18) on asthmatic airway inflammation. Thirty healthy adult male guinea pigs were randomly divided into 3 equal groups: asthmatic model group (Group A, undergoing intraperitoneally injection of ovalbumin (OVA) once and spraying of OVA aerosol once a day for 5 days; control group (Group B), undergoing intraperitoneally injection of OVA once and spraying of normal saline aerosol once a day for 5 days; and interleukin (IL)-18 intervention group (Group C, undergoing intraperitoneally injection of OVA once and intraperitoneal injection of IL-18 on the days 1, 3, 8. 10. 15, 17, and 19. Twenty-four hours after the final spraying or IL-18 injection the bronchalveolar lavage fluid (BALF) of the left lungs were obtained. HE staining was conducted to the sediment to examine the numbers of eosinophils, neutrophils, and monocytes. ELISA was used to detect the Th1/Th2 cytokines in the BALF. The left lungs underwent pathological examination. The number of EOS in BALF of Groups A was (98 +/- 58) x 10(6)/L, significantly higher than those of Group B, (12 +/- 10) x 10(6)/L, and Group C, (29 +/- 10) x 10(6)/L (P < 0.01 and P < 0.05). The numbers of neutrophils in the BALF of Group A was (24 +/- 16) x 10(6)/L, significantly higher than those of Group B and C [(9 +/- 7) x 10(6)/L and (10 +/- 5) x 10(6)/L respectively, both P < 0.05]. The concentration of IFN-gamma and IL-2 in group A were both significantly lower than those of Group B and Group C (P < 0.05 and P < 0.01). The concentration of IL-4 in Group A was significantly higher than those of Groups B and C (both P < 0.05). The concentration of IL-5 of Group A was significantly higher than those of Group Bs and C (both P < 0.01). IL-18 effectively inhibits asthmatic airway inflammation by regulating the Th1/Th2 balance.

Adsorption of Nonylphenol Ethoxylates in the Presence of Competing Natural Organic Matter

Three NPEO mixtures containing NPEO compounds having attached EO numbers in the ranges of 1–6, 2–12 and 4–19 were subjected to batch activated carbon adsorption experiments in solutions with and without the presence of competing natural organic matter (NOM) existent extensively in drinking water sources. The liquid phase composition of the NPEO mixtures, described in the ratios (C i /C T ) of the equilibrium concentrations of individual compounds (C i ) to the total mixture (C T ), did not change after adsorption at varied carbon dosages, no matter if NOM was present or not. However, their adsorption capacity was significantly reduced with the adsorption of NOM due to site competition and pore blockage. The adversary impact was found to be greatly dependent upon the initial presence levels of NPEO and NOM as well as the NOM sources.

Aggregation Behaviors and Interfacial Properties of Oxyethylated Nonionic Surfactants

Four nonionic surfactants C16En with varying EO number were synthesized. The characteristics of this series of nonionic surfactants, including surface tension, critical micelle concentration (CMC), interfacial activity, and surface pressure, were presented. The surface tension data indicated that γCMC increased with hydrophilic PEO chain length while CMC decreased. The area per surfactant molecule at the air/water interface increased as PEO chain length increased. The probe, pyrene, was employed to investigate nonionic micelles of varying EO number in steady‐state fluorescence. The CMC, obtained from the I3/I1 ratio, agreed well with the results of the surface tension experiment. The interfacial properties were studied by using a heptane‐toluene/water model system. We found that interfacial activities increased with the degree of ethoxylation because of their hydrophile‐lipophile balance. From the π–A isotherm, it can be deduced that C16En nonionic surfactants had excellent molecular flexibility. The surface pressure data also showed that this kind of surfactant with longer PEO chains occupied a larger area per molecule at the interface.

Optimizing the Polyethylene Oxide and Polypropylene Oxide Contents in Diethylenetriamine-Based Surfactants for Destabilization of a Water-in-Oil Emulsion

In this work, we used polyoxyalkylenated diethylenetriamine (DETA) demulsifier with various polyethylene oxide (PEO) and polypropylene oxide (PPO) contents to destabilize a stable water-in-oil emulsion. The demulsifiers were characterized by the relative solubility number (RSN). The efficiency of emulsion destabilization was measured by the degree of separation of the oil and water phases. It was found that the destabilization of an emulsion is closely correlated with the PO and EO numbers. When the PO number in a molecule is much greater than the EO number, the surfactant gives a very low oil resolution rate, requires high dosages, and produces a stable middle phase. When a surfactant contains more EO than PO, it gives a high oil resolution rate at a low dosage, but it is easily overdosed, and some surfactants of this type (high molecular weight) also produce a stable middle emulsion phase. When the PO and EO numbers in the surfactant are close to equal, the surfactant breaks the emulsion rapidly at a ve...

Microemulsions Containing Polyethylene Glycol

AbstractIt is well known that some water/oil/surfactant systems can be optimised to give three phases. The middle phase is a thermodynamically stable microemulsion. Three-phase systems can also form when most of the water is replaced by polyethylene glycol (PEG). The phase behaviour of such PEG-based systems with undecyl and oleyl ethoxylates as surfactants has been studied. The PEG reduces the temperature sensitivity and shifts the optimum to higher EO numbers, i. e. higher HLB values. In single phase O/W microemulsions the polyethylene glycol also reduces temperature sensitivity, though the effect seems to be less than for three-phase systems. It also promotes the solubilisation of higher molecular weight oils, such as triglycerides.

Thermodynamics of Aqueous Poly(ethylene oxide)−Poly(propylene oxide)−Poly(ethylene oxide)/Surfactant Mixtures. Effect of the Copolymer Molecular Weight and the Surfactant Alkyl Chain Length

A calorimetric study was performed to focus attention on the interactions between copolymers and anionic surfactants in aqueous solutions. Three aspects were analyzed: (1) the hydrophobicity of the surfactant, (2) the change of the copolymer molecular weight, and (3) the nature of the hydrophilicity of the copolymer. To this purpose, the family of sodium alkanoates (sodium octanoate through sodium dodecanoate) and the tri-block copolymers EO76PO29EO76 (F68), EO103PO39EO103 and EO132PO50EO132 were investigated. Comparing F68 and EO13PO30EO13 (L64), previously studied by us, provided information on the effect of the copolymer hydrophilicity. The experimental data were analyzed by means of a thermodynamic model which assumes that in the surfactant dilute region monomers of surfactant interact with unimeric copolymer leading to the formation of surfactant-copolymer aggregation complexes; when micelles do form, they can solubilize the copolymer, and then, the copolymer−micelle aggregates formation takes place. Data modeling provided useful parameters which allowed us to discriminate the various effects contributing to the formation of such aggregates. The thermodynamic properties for the formation of both the surfactant−copolymer aggregation complexes and copolymer−micelle aggregates were not consistent with the expectation; despite the more hydrophilic sites available in F68, the enthalpy and entropy for F68 were larger and the free energy more negative than those of L64. Moreover, the role of the copolymer molecular weight was important although the ratio between the number of the hydrophilic and the hydrophobic sites of binding is constant. An effort was done to verify whether these findings are representative of the physical interactions between copolymer and surfactant or reflect the large difference in the molecular masses. Therefore, the thermodynamic properties were normalized for the number of EO and PO units. They straightforwardly showed that L64 has a larger hydrophobic character than F68 and the copolymer molecular weight plays a small role.

Breaking Water‐in‐Bitumen Emulsions using Polyoxyalkylated DETA Demulsifier

AbstractAdding demulsifier is currently the most widely used method for breaking water‐in‐oil emulsions. Experimental demulsifiers based on DETA with various PO and EO contents were synthesized and their RSN values were determined. The dehydration efficiency of these demulsifiers was measured in diluted bitumen using both gravitational settling and centrifugation tests. The results indicate that some of the DETA products could perform potentially at least as well or better than the demulsifier currently used in a commercial plant. RSN values are correlated very well with EO and PO numbers. Optimal dehydration efficiency is in the RSN range of 18 to 22, which corresponds to a PO‐to‐EO ratio in the range of 1 to 1.8.

Characterization and quantitation of mixtures of alkyl ether sulfates and carboxylic acids by capillary electrophoresis with indirect photometric detection.

The separation, characterization, and determination of mixtures of alkyl ether sulfates (AES) and fatty acids (C10-C16) in background electrolytes (BGEs) containing acetonitrile (ACN)-water mixtures is addressed. Due to inhibition of the ionization of the carboxylate groups, the migration time and the resolution between the fatty acids decreased when the water content of the BGE was reduced, but efficiency and resolution between the AES oligomers improved. The migration times increased and resolution improved by substituting 5% ACN by an equivalent amount of dioxane. A complete separation of the two surfactant classes, up to the AES oligomers with 8 ethylene oxide units (EOs) with respect to C10, with excellent resolution between the AES oligomers, while preserving a satisfactory resolution between the fatty acids, was achieved with a BGE containing 5 mM trimethoxybenzoic acid, 7 mM dipentylamine, 85% ACN, 5% dioxane, and 10% water. The two surfactant classes were increasingly resolved by further reducing the water content of the BGE. Thus, C2 (acetate) was resolved from the AES oligomers up to 7 EOs using 90% ACN and 5% dioxane, but the resolution between the heavier fatty acids was poor with this BGE. Identification of the AES oligomers was eased by the excellent regularity of the successive migration times; thus, within each AES subclass or series of oligomers with the same number of carbon atoms in the alkyl chain, the migration times decreased following a mild curve as the number of EOs increased. The way how the data obtained by indirect photometry (corrected peak areas that are proportional to the molar concentrations) should be managed to avoid systematic error when the calibration curve is constructed using an AES standard with an oligomer distribution different from that of the samples is discussed and equations are given. Decyl sulfate was successfully used as internal standard. The detection limits (S/N = 3) were of ca. 2 microM for individual AES oligomers.

Effects of Ethylene Oxide Spacer Length on Solution Properties of Water‐Soluble Fluorocarbon‐Containing Hydrophobically Associating Poly (Acrylic Acid‐co‐Rf‐PEG Macromonomer)

AbstractPoly (acrylic acid)s (PAAs) modified with a series of fluorocarbon group (Rf) end‐capped Poly(ethylene glycol) (PEG) macromonomers (number of ethylene oxide unit: 1, 9, 23, 45) and corresponding copolymers without fluorocarbon end groups were synthesized. It was found that the effect of the hydrophobic association of fluorocarbon groups on the solution viscosity prevailed over that of the hydrogen bond between grafted PEG and the backbone. Rheological measurement on the aqueous solutions of these poly (acrylic add‐co‐RrPEG macromonomer)s demonstrated that the best thickening performance was shown when the number of ethylene oxide unit (EO number) was 23.

Chronic psychological stress induces intestinal sensitization to luminal antigens in the rat

Background: The prevalence of food allergies associated with gastrointestinal hypersensinvity is rising. The etiology of such conditions is not fully understood. Recent evidence suggests a relationship between stress and gastrointestinal disorders including food allergy, IBS and IBD. Our previous studies revealed that chronic psychological stress increases intestinal epithelial permeability allowing uptake of macromolecular antigens from the lumen. The aim of this study was to examine the role of stress in sensitization o[ rat intestinal tissues to luminal antigens. Methods: WKY rats were subjected to water avoid stress (WAS, rat on platform surrounded by water) 1 h daily for 10 consecutive days, whereas control rats were exposed to sham stress (SS, no water). Horseradish peroxidase (HRP, a model antigen) was delivered by garage (1 mg/rat) on day 5, along with appropriate adjuvants. To determine the role of corticotropin-releasing hormone (CRH) in the stress induced effects, additional rats were injected ip with the CRH antagonist, a-helical-CRH (aCRH, 25 rag), 30 rain before each WAS session. Following the final session, blood was obtained and jejunal tissues were removed for histology and Ussing chamber studies. Sensitization was indicated by specific IgE (by passive cutaneous anaphylaxas), inflammatory cells in jejunal mucosa (mast cells, MC; eosinophils, EOS; mononuclear cells, MNC), and the intestinal response to HRP antigen added to the chambers: increase in short-circuit current (lse) and permeability (HRP flux). Results: All rats subjected to WAS became sensitized as indicated by: anti-HRP IgE titer; significant increases in numbers of MC, EOS and MNC in intestinal mucosa; and responses to HRP challenge in Ussing chambers. None of the SS or aCRH treated WAS rats developed any positive indications of sensitization. Conclusion: The present study demonstrates that the concurrence of chronic psychological stress and antigen presence in the gastrointestinal tract can initiate intestinal sensitization that can be prevented by antagonism of peripheral CRH receptors.

Lateral Force Acting on a Deformed Single Bubble due to the Presence of Wall

Lateral migration of a deformed single bubble rising in the vicinity of a vertical flat plate was measured to evaluate a wall force acting on the bubble. Experimental results indicated that a wall force coefficient CW is a function of the bubble Reynolds number Re and Morton number M under the condition of low bubble Reynolds number, whereas it is a function of the Eotvos number EO for high bubble Reynolds number condition. Empirical correlations of CW were deduced from the experimental results. It was confirmed that the wall force model proposed by one, of the authors and the proposed correlations of CW are applicable for the bubbles under the condition of -6.0&le;log10M&le;-2.5, 2.0&le;EO&le;10.0 and 0.4&le;Re&le;65, and have a potential for the application to a bubble in an air-water system, provided that the bubble does not collide with the wall.