Ueber das Zeitgesetz des kapillaren Aufstiegs von Flüssigkeiten

Lucas, Richard

doi:10.1007/bf01461107

Cited by 1,115 publications

(732 citation statements)

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“…However, we can now state that it takes about 8 times that time for the flow to become independent of inertial effects. and the Lucas-Washburn equation [1,2] reads…”

Section: Resultsmentioning

confidence: 99%

“…For the intermediate flow period Lucas [1] and Washburn [2] neglect the influence of inertia and the influence of gravity. They find…”

Section: Purely Viscous Time Stagementioning

confidence: 99%

“…Finally one can calculate the equilibrium height (where capillary pressure equals hydrostatic pressure) to be [1] h eq = α β = 2σ cos θ ρgR .…”

Section: Viscous and Gravitational Time Stagementioning

confidence: 99%

“…These assumptions are mostly the neglect of certain forces. This, however, limits the validity of the derived equations to certain time intervals where these forces can actually be neglected [1][2][3][4]. Stange et al [5,6] separate the individual time stages by means of dimensionless numbers.…”

Section: Introductionmentioning

confidence: 99%

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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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“…However, we can now state that it takes about 8 times that time for the flow to become independent of inertial effects. and the Lucas-Washburn equation [1,2] reads…”

Section: Resultsmentioning

confidence: 99%

“…For the intermediate flow period Lucas [1] and Washburn [2] neglect the influence of inertia and the influence of gravity. They find…”

Section: Purely Viscous Time Stagementioning

confidence: 99%

“…Finally one can calculate the equilibrium height (where capillary pressure equals hydrostatic pressure) to be [1] h eq = α β = 2σ cos θ ρgR .…”

Section: Viscous and Gravitational Time Stagementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The transition from inertial to viscous flow in capillary rise

Fries

Dreyer

2008

Journal of Colloid and Interface Science

186

142

View full text Add to dashboard Cite

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“…Integration of Eqn 3 for water rise in the direction of gravity leads to Eqn 4 for the rate of liquid movement (Lucas, 1918) : In the case of water ascent against gravity, a final height is reached where the capillary force balances the gravity term : …”

Section: Impervious Capillariesmentioning

confidence: 99%

Water rise kinetics in refilling xylem after desiccation in a resurrection plant

et al. 2000

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The acropetal water refilling kinetics of the dry xylem of branches (up to 80 cm tall) of the resurrection plant Myrothamnus flabellifolia were determined with high temporal resolution by observation of light refraction at the advancing water front and the associated recurving of the folded leaves. To study the effect of gravity on water rise, data were acquired for cut upright, horizontal and inverted branches. Water rise kinetics were also determined with hydrostatic and osmotic pressure as well as at elevated temperatures (up to 100mC) under laboratory conditions and compared with those obtained with intact (rooted) and cut branches under field conditions. Experiments in which water climbed under its capillary pressure alone, showed that the axial flow occurred only in a very few conducting elements at a much higher rate than in many of the other ones. The onset of transpiration of the unfolded and green leaves did not affect the rise kinetics in the ' prominent ' conducting elements. Application of pressure apparently increased the number of elements making a major contribution to axial xylem flow. Analysis of these data in terms of capillary-pressure-driven water ascent in leaky capillaries demonstrated that root pressure, not capillary pressure, is the dominant force for rehydration of rooted, dry plants. The main reasons for the failure of capillary forces in xylem refilling were the small, rate-limiting effective radii of the conducting elements for axial water ascent (c. 1 µm compared with radii of the vessels and tracheids of c. 18 µm and 3 µm, respectively) and the very poor wetting of the dry walls. The contact (wetting) angles were of the order of 80m and decreased on root or externally applied hydrostatic pressure. This supported our previous assumption that the inner walls of the dry conducting elements are covered with a lipid layer that is removed or disintegrates upon wetting. Consistent with this, potassium chloride and, particularly, sugars exerted an osmotic pressure effect on axial water climbing (reflection coefficients zero, but small). Although the osmotically active solutes apparently suppressed radial water spread through the tissue to the leaf cells, they reduced the axial water ascent rather than accelerating it as predicted by the theory of capillary-driven water rise in leaky capillaries. Killing cells by heat treatment and removal of the bark, phelloderm, cortex and phloem also resulted in a reduction of the axial rise rate and final height. These observations demonstrated that radial water movement driven by the developing osmotic and turgor pressure in the living cells was important for the removal of the lipid layer from the walls of those conducting elements that were primarily not involved in water rise. There is some evidence from field measurements of the axial temperature gradients along rooted branches that interfacial (Marangoni) streaming facilitated lipid removal (under formation of vesicle-like structures and lipid bodies) upon wetting.

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Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

March

Doster

Geiger

2016

Water Resources Research

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Spontaneous countercurrent imbibition into a finite porous medium is an important physical mechanism for many applications, included but not limited to irrigation, CO 2 storage, and oil recovery. Symmetry considerations that are often valid in fractured porous media allow us to study the process in a onedimensional domain. In 1-D, for incompressible fluids and homogeneous rocks, the onset of imbibition can be captured by self-similar solutions and the imbibed volume scales with ffiffi t p . At later times, the imbibition rate decreases and the finite size of the medium has to be taken into account. This requires numerical solutions. Here we present a new approach to approximate the whole imbibition process semianalytically. The onset is captured by a semianalytical solution. We also provide an a priori estimate of the time until which the imbibed volume scales with ffiffi t p . This time is significantly longer than the time it takes until the imbibition front reaches the model boundary. The remainder of the imbibition process is obtained from a selfsimilarity solution. We test our approach against numerical solutions that employ parametrizations relevant for oil recovery and CO 2 sequestration. We show that this concept improves common first-order approaches that heavily underestimate early-time behavior and note that it can be readily included into dual-porosity models. Key Points: New physically based model for spontaneous imbibition Model captures transition from earlytime to late-time imbibition Model validated for different applications Correspondence to: R. March, rafael.march@pet.hw.ac.uk Citation: March, R., F. Doster, and S. Geiger (2016), Accurate early-time and latetime modeling of countercurrent spontaneous imbibition, Water Resour.

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Ueber das Zeitgesetz des kapillaren Aufstiegs von Flüssigkeiten

Cited by 1,115 publications

References 0 publications

The transition from inertial to viscous flow in capillary rise

The transition from inertial to viscous flow in capillary rise

Water rise kinetics in refilling xylem after desiccation in a resurrection plant

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

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