Foam invasion through a single pore

Aline Delbos and Olivier Pitois

Phys. Rev. E 84, 011404 – Published 27 July 2011

Abstract

We investigate experimentally the behavior of liquid foams pumped at a given flow rate through a single pore, in the situation where the pore diameter is smaller than the bubble diameter. Results reveal that foam invasion can be observed only within a restricted range of values for the dimensionless flow rate and the foam liquid fraction. Within this foam invasion regime, the liquid content of invading foams is measured to be three times higher than the initial liquid content. Outside this regime, both gas alone and liquid alone invasion regimes can be observed. The gas invasion regime results from the rupture of foam films during local T1, during bubble rearrangements events induced by foam flow, whereas the liquid invasion regime is allowed by the formation of a stable cluster of jammed bubbles at the pore's opening.

Received 24 February 2011

DOI:https://doi.org/10.1103/PhysRevE.84.011404

Authors & Affiliations

Aline Delbos^* and Olivier Pitois

Université Paris-Est, Laboratoire de Physique des Matériaux Divisés et des Interfaces, CNRS FRE 3300, 5 boulevard Descartes, F-77454 Marne la Vallée Cedex 2, France

^*Present address: University of Massachusetts Amherst, Department of Polymer Science and Engineering, 120 Governors Drive, Amherst, Massachusetts 01003, USA; adelbos@polysci.umass.edu

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Vol. 84, Iss. 1 — July 2011

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Images

Figure 1
Experimental setup. The column containing the foam is wetted from the top in order to control liquid drainage and foam liquid fraction. Fluids are forced to invade the pore (capillary) by imposing an infusion flow rate through the pore. Generally, foam invades the pore, but as explained in this paper, there exist conditions for which invading fluid is liquid only, or instead gas only.Reuse & Permissions
Figure 2
Liquid volume fraction of fluids invading the pore as a function of infusion flow rate, for two foam liquid fractions ( $ɛ_{\infty}$ ). The foam bubbles and the pore are, respectively, 1 mm and 0.5 mm in radius. For the largest foam liquid fraction, a marked transition is observed for a given value $q^{*}$ of the infusion flow rate. For $q < q^{*}$ , a stable bubble cluster is formed at the pore's opening and prevents foam bubbles from invading the pore (see the image showing three symmetrically organized bubbles). This invasion regime is referred to as the liquid invasion regime.Reuse & Permissions
Figure 3
Diagram showing the liquid volume fraction of fluids invading the pore as a function of foam liquid fraction, for several values of bubble radius ( $R$ ) and pore aperture ( $r_{t}$ ). The dotted line shows the relation $ɛ_{t} = 3 ɛ_{\infty}$ ; the solid line shows the relation $ɛ_{t} = 3 ɛ_{\infty} + b ɛ_{t}^{+}$ (see text for more details). Arrows indicate transitions for the foam invasion regime towards the liquid invasion regime (controlled by the infusion flow rate) and the gas invasion regime (controlled by the foam liquid fraction).Reuse & Permissions
Figure 4
The diagram shows observed transition behavior of foam when forced to invade a pore, as a function of foam liquid fraction (ε) and bubble radius ( $R$ ). Foam is found to invade the pore for liquid fractions above ∼0.001, whatever the bubble size. For lower liquid fractions, only the gas phase invades the pore.Reuse & Permissions
Figure 5
Illustration of the bubble fractionation mechanism during foam invasion. The pore's opening cannot be distinguished and it as been marked with a solid black circle; the dotted circle shows the external side of the pore (5-mm diam). Numbers are used to mark bubbles around the pore's opening. (a) Bubble 1 is invading the pore (note that the bubble-pore connection is covered by two small bubbles). (b) Bubble 2 invades the pore before bubble 1 has completely invaded the pore, thus highlighting the bubble fractionation mechanism. A topological rearrangement occurred between (b) and (c), so that bubble 3 is now connected to the pore. (d) Bubble 4 is connected to the pore and experiences a new topological rearrangement between (d) and (e). None of the bubbles was allowed to invade the pore without fractionation.Reuse & Permissions
Figure 6
Comparison of measured values for the infusion flow rate corresponding to the transition between the foam invasion regime and the liquid invasion regime, with theoretical values given by Eq. (7), using $a$ $=$ 2.26. The sketch shows the curvatures of three contacting bubbles (radius $R$ ) jammed at the pore's opening (aperture radius $r_{t}$ ). As the local liquid fraction is decreased in front of the pore's opening, contacting areas (foam films) increase, and the smallest radius of curvature of the bubbles decreases. When this radius is decreased to $r$ $^{*}$ , one of the three bubbles can invade the pore in passing through the gap between the pore wall and the two other contacting bubbles.Reuse & Permissions

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