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Capillaries

Capillaries are extremely narrow tubes.

 

V Hydrophobic confinement
V Hydrophilic confinement
V Capillary rise

V Cavity filling
V Venturi effect

V Capillary flow cause of ring stains

Capillary effects

 

Capillary effects

Capillary rise

The movement of water (and other liquids) up or down capillary (narrow bore) tubes and confined spaces is due to the Laplace pressure at curved surfaces. a Thus, if the water curves towards the surface (hydrophilic surfaces, left in Figure right; the meniscus is the curved liquid-gas surface b) then water enters the capillary until the pressure of the water above the liquid surface, = weight per unit volume (ρ ˣ g; density ˣ acceleration due to gravity) ˣ height (h) counteracts the reduced pressure = 2 ˣ surface tension (γ) ˣ cos(θ)/radius (r).

Thus,

hρg = 2γcos(θ)       

 

where θ is the contact angle (cos(θ) = 1 at zero contact angle, see below left).

 

The contact angle

 

The contact angle

Young's equation describes the forces acting along the contact line between the water, gas and solid (see left).

 

γSG = γSL + γLG ˣ cos(θ)

 

The interfacial free energies between the solid and gas, solid and liquid and liquid and gas are γSG, γSL, and γLG respectively. γSG and γSL are generally difficult to determine.

 

Capillary rise with capillary radius

Capillary rise with capillary radius

Thus, water will rise (a maximum) 1.47 cm within a glass capillary 1 mm in diameter at 25 °C (see left).

 

An opposite effect occurs in hydrophobic capillaries (far right). It is the presence of the extensive gas-liquid interfaces and many capillary bridges that are responsible for the characteristic of wet sand that allows it to be easily molded into sand castles [1537].

 

Capillary rise with capillary radius and contact angle

Capillary rise with capillary radius and contact angle

 

 

 

 

 

 

If the meniscus does not meet the capillary wall at zero angle (θ = 0) then the contact angle (θ) is related to the radius of curvature R of the meniscus (cos(θ) = r/R) and the Laplace pressure is

 

2γcos(θ)/r       (0 < cos(θ) < 1)

 

rather than               2γ/r

 

Allowance for the volume within the meniscus is easily made by using the value for the height (h) that gives the actual volume of fluid involved [1448]. In reality, the meniscus will not be spherical in shape [1448]. The equations will not necessarily hold in very small capillaries (nm) or when the length of the capillary is shorter than required by the relationships.

 

There are confounding factors when very fine capillaries are considered. The surface will not be uniform but involve a number of molecularly organized environments. Also, strongly bound water will reduce the effective capillary diameter, so increasing any water movement. Although the capillary rise phenomenon does hold for very small diameter capillaries, it is not clear that it can scale down to nanometer or molecularly sized capillaries [1449].

 

Capillary flow (wicking) may also occur between closely spaced surfaces, such as within fine brushes and fine dry powders such as in thin layer chromatography. Also, it causes flow in dry porous materials such as paper, soil, and bricks. Water is usually static next to hydrophilic surfaces but slips at hydrophobic surfaces, with the slip length varying with surface hydrophobicity, surface roughness, and shear rate. This may be due, at least partially, to the surface nano-bubbles often present on hydrophobic surfaces. Slip lengths are usually a few hundred Ångström but may be as much as a micron.

 

Soil consists of a wide range of capillaries, important for water retention, heat and water transport as well as the behavior of frozen soils. Ice forms over a wide range of temperatures (from −50 °C to 0 °C) with liquid water remaining. Solutes, capillarity, and adsorption control the freezing process of pore water. The relationship between temperature and unfrozen water content in frozen soils is defined as the unfrozen water characteristics curve (UWCC). The UWCC is an important soil property for calculating the frozen behavior of the soils. Several UWCC modes have been developed including a recent one that differentiates the freezing processes of capillary and adsorbed water [3374].

Cavity filling

Liquid water on rough surfaces, containing cracks, hollows, pits or pores, may or may not fill these spaces. The ability to penetrate and fill depends on a number of factors [3391];

  1. The contact angle, θ. This depends on the surface hydrophilicity.
  2. The concentration of the dissolved gas. High dissolved gas may give rise to surface nanobubble production filling some spaces, whereas water absent of dissolved gas may help dissolve some of the gas from the gas-filled spaces.
  3. Water already present on the indented surfaces or as droplets within the cracks, hollows, pits or pores. These affect the rate of capillary condensation inside the cavities.
  4. Any surfactants/impurities present. These lower the surface tension,.
  5. Cavity geometry, particularly at the edges to the surface. Dead-end pores fill much less rapidly than double-ended pores.

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Venturi effect

The Venturi effect occurs with all fluids. Here we discuss it in terms of water. It is the reduction in the pressure of the water when water flows through a constriction (narrowing). As water volume varies little with pressure (< 0.5 % over 0.1 - 10 MPa) at the lower pressures encountered, the velocity of the water must increase within the constriction. The change in the pressure is given by:

The effect of tube narrowing on fluid pressure

 

The effect of tube narrowing on fluid pressure

 

              Pressure lowering= (density/2)x(difference in the squared flow rates)

where P, ρ, v and r represent the pressure (Pa), density (997 kg ˣ m-3 at 25 °C), water velocity (m ˣ s-1) and pipe radius (m) and the subscripts 1 and 2 represent the values at wide and narrow pipe respectively. If r2 < r1 (as shown), v2 > v1 and P2 < P1. As an example, if r1, r2, v1, and P1 are 10 cm, 1 cm, 1 m ˣ s-1 and 10 MPa respectively, v2 and P2 are 100 m ˣ s-1 and 5 MPa respectively, [Back to Top to top of page]

Instant coffee stain

instant coffee stain
Capillary flow cause of ring stains

If you spill a suspension of dispersed solids, such as coffee, on a flat solid surface and allow it to dry, a stain forms as a ring along the spill's perimeter. This is due to capillary flow towards the perimeter as the drop dries. The contact line of the drying spill is static (pinned) such that any liquid that evaporates from its edge must be replenished by liquid carrying the suspension and flowing from the spill's interior. Such ringed deposits have importance in printing, washing and coating processes [3043].

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Footnotes

a The rise can also be attributed to the energy of binding of the water at the capillary wall being available to do the work needed to lift the liquid column against gravity. [Back]

A 20.00 ml reading;

from PRHaney

 

a 20.00 ml reading; from PRHaney

 

 

b A meniscus is the catenary-like curved liquid-gas surface, caused by surface tension. When a volume is determined using a burette (see right), the bottom of the meniscus is taken; thus the volume right is read at eye level as 20.00. The shape and volume of the meniscus has been described [3287]. [Back]

 

 

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This page was established in 2015 and last updated by Martin Chaplin on 20 August, 2018


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