The rate of capillary penetration and the applicability of the washburn equation

Szekely, J.; Neumann, A. W.; Chuang, Yu-Lin

doi:10.1016/0021-9797(71)90120-2

Cited by 290 publications

(199 citation statements)

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“…which results from the combination of the expression for the Laplace pressure and the Hagen-Poiseuille equation for steady flow conditions (Szekely et al 1971;Grundke et al 1991;Tröger et al 1998), where r, the liquid surface tension; h, the solid/liquid contact angle; A, the cross-sectional area; r, the radius of the capillary; g, the liquid viscosity; q, the liquid density; m, the weight of the liquid that penetrates into the capillary, and t, the penetration time.…”

Section: Wetting Measurementsmentioning

confidence: 99%

Analysis of the effects of catalytic bleaching on cotton

et al. 2007

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Hydrogen peroxide can be catalyzed to bleach cotton fibers at temperatures as low as 308C by incorporating dinuclear tri-l-oxo bridged manganese(IV) complex of the ligand 1,4,7-trimethyl-1,4,7-triazacyclononane (MnTACN) as the catalyst in the bleaching solution. The catalytic system was found to be more selective under the conditions applied than the non-catalytic H 2 O 2 system, showing better bleaching performance while causing slightly lower decrease in degree of polymerization (DP) of cellulose. In order to gain fundamental knowledge of the bleach effect on cotton fibers and cellulose as its main component, especially after catalytic bleaching, X-ray Photoelectron Spectroscopy (XPS) was used to study surface chemical effects. The Washburn method was applied to investigate wetting properties, and liquid porosity was used to obtain pore volume distribution (PVD) plots. Parallel analyzes performed on model cotton fabric, i.e. ''clean'' cotton fabric stained with morin -a pigment regularly found in native cotton fiber, helped to differentiate between pigment oxidation and other bleaching effects produced on the (regular) industrially scoured cotton fabric. Bleaching was not limited to the chemical action but also affected cotton fiber capillary parameters most likely due to the removal of non-cellulosic materials as well as chain-shortened cellulose.

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Section: Wetting Measurementsmentioning

confidence: 99%

Analysis of the effects of catalytic bleaching on cotton

et al. 2007

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“…Stange et al [5,6] separate the individual time stages by means of dimensionless numbers. There are also approaches to solve the full momentum balance numerically as done in [7,8]. Ichikawa and Satoda [9] compare several previous works, present experimental results and conduct a dimensional analysis.…”

Section: Introductionmentioning

confidence: 99%

The transition from inertial to viscous flow in capillary rise

Fries

Dreyer

2008

Journal of Colloid and Interface Science

186

142

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We investigate the initial moments of capillary rise of liquids in a tube. In this period both inertia and viscous flow losses balance the pressure generated by the meniscus curvature (capillary pressure). It is known that the very first stage is purely dominated by inertial forces, where subsequently the influence of viscosity increases (visco-inertial flow). Finally the effect of inertia vanishes and the flow becomes purely viscous. In this study we derive the times and meniscus heights at which the transition between the time periods occur. This is done in an attempt to provide a method to determine a priori which terms of the momentum balance are relevant for a given problem. Analytic solutions known from previous literature are discussed and the time intervals of their validity compared. The predicted transition times and the calculated heights show good agreement with experimental results from literature. The results are also discussed in dimensionless form and the limitations of the calculations are pointed out.

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“…Thus there are many publications dealing with this problem, its mathematical description and its physical explanation [1][2][3][4][5][6][7]. To obtain a better understanding of a problem its dimensionless consideration is always of interest.…”

Section: Introductionmentioning

confidence: 99%

Dimensionless scaling methods for capillary rise

Fries

Dreyer

2009

Journal of Colloid and Interface Science

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In this article the different dimensionless scaling methods for capillary rise of liquids in a tube or a porous medium are discussed. A systematic approach is taken, and the possible options are derived by means of the Buckingham π theorem. It is found that three forces (inertial, viscous and hydrostatic forces) can be used to obtain three different scaling sets, each consisting of two dimensionless variables and one dimensionless basic parameter. From a general point of view the three scaling options are all equivalent and valid for describing the problem of capillary rise. Contrary to this we find that for certain cases (depending on the time scale and the dominant forces) one of the options can be favorable. Individually the different scalings have been discussed and used in literature previously, however, we intend to discuss the three different sets systematically in a single paper and try to evaluate when which scaling is most useful. Furthermore we investigate previous analytic solutions and determine their ranges of applicability when compared to numerical solutions of the differential equation of motion (momentum balance).

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The rate of capillary penetration and the applicability of the washburn equation

Cited by 290 publications

References 1 publication

Analysis of the effects of catalytic bleaching on cotton

Analysis of the effects of catalytic bleaching on cotton

The transition from inertial to viscous flow in capillary rise

Dimensionless scaling methods for capillary rise

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