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Traction force due to aqueous foam flow rising in a vertical pipe
V. S. Álvarez Salazar1, A. Pérez Terrazo1, J. R. Aguilar Sánchez2, I. Carvajal Mariscal1, F. Sánchez Silva1, A. Medina2
1ESIME Zacatenco, Instituto Politécnico Nacional, Av. Instituto Politécnico Nacional s/n, Unidad Profesional "Adolfo López Mateos", Col. Lindavista, 07738, Gustavo A. Madero, México, D.F. México. 2ESIMEAzcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas No. 682, Col. Sta. Catarina, 02250, Azcapotzalco, México D.F. México. 2
Abstract This paper discusses experimentally the traction force exerted by the flow of aqueous foam through the annular space between a central rod and the inner walls of the pipe. These studies were made to prove if foam behaves as a granular material or as apower-law fluid. Experiments allow concluding that the flow of dry foam is a type of slipping flow where the traction does not depend on the radius of the pipe or on the radius of the rod.
1 Introduction

In this work we are interested in to characterize the overall frictional force (traction), against the surrounding walls, when a foam flow occurs inside a vertical cylindrical pipe. This probleminvolves the stability of foam in relation to film rupture due to its strong interaction with the solid boundary of the pipe. Thus, in this case a purely mechanical analysis is tackled and the chemistry of the foaming solutions is left aside.
To our knowledge, the quantification of traction has been absent from studies of the generic foam properties (Weaire & Hutzler, 1999). Like as agranular medium, foam is a disordered system made of a punctuated collection of unit cells, initially growing by gas injection into a quiet liquid. In order to have a monodisperse cell population with an average bubble diameter, d, it is necessary to inject the gas, at a constant rate, and the gas flow rate will be low or medium. Conversely, at high gas flow rates the bubble population will be verydisperse, and the cells have in a wide range of sizes (Longuet-Higgins 1991; Corchero et al. 2006, Higuera and Medina (2006); Higuera 2005; López-Villa et al. 2011)
Once foam was formed it obeys a set of dynamic phenomena, for example, foam drainage, driven by gravity, through the films or faces of each cell and through the Plateau borders; among each cell there is gas diffusion or coarsening, drivenby pressure differences; and occurs film rupture or coalescence, driven by film instabilities (Isenberg 1992).
In real fluids, we often observe a bubble rising to the surface, and then floating on the surface. Multiple bubbles interact. If they do not burst, they will stack, forming foam. The water between those stacked bubbles will drain, leaving a micrometer-thin film of liquid betweenbubbles. The resulting structure is called dry foam.
Our goal in this work is characterizing the overall friction force originated by the simple rise of aqueous foam in a vertical pipe when air is injected. In our experiments we uses common detergent foams because they are remarkably stable against film rupture, and are ideal for the study of many properties.

2 The elements of foam structure
Foamis a two-phase system in which gas cells are enclosed by liquid. Simulation of bubbles in wet or dry foam is very challenging since foam can have a complicated liquid/gas interface. Each bubble is surrounded by several faces of thin films, which may meet at junctions, where liquid is clustered. These junctions may move, merge and split. In addition, bubbles or liquid drops can merge and split.Thus, the topology of the interface changes often. This behavior causes difficulties for simulations based on the Lagrangian and Eulerian methods. See Fig. 1.

Fig. 1: Three-dimensional foam consists of cells whose faces are thin films, meeting in Plateau borders (Weaire & Hutzler 1999).
In this work we will study the formation of foam in a pipe through measurements of the bulk property named...