1. submerged in polymer solution was studied from the

Bubble motions in different yield-stress fluids

Rising behavior of bubbles is the main
bubble motion studied previously. This is based on knowing how bubbles form or
deform in yield stress fluid and the factors that can affect the stability in
the system. These behaviors have been studied from various aspect such as the
effect of yield stress, surface tension, the way to produce bubbles, bubble
size, etc. The related researches are divided into three parts: bubble motions
in polymer solution; bubble motions in polymer gel; bubble motions in
concentrated surfactant solution.

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1.1   Bubble motions in polymer solutions

solutions are the most widely studied yield stress fluids on discussing bubble
motions. Commonly used polymer solutions include different types of Carbopol
and xanthan gum.

Bubble formation
at a nozzle submerged in polymer solution was studied from the aspect of rheological
properties of the fluid, gas flow rate, gas chamber volume, etc (Terasaka & Tsuge,
2001) . It was found that at the same gas flow rate, larger bubble can
form under larger liquid shear stress. Bubble size also increased when the
volume of gas chamber became larger at the same gas flow rate. The growth rate
of bubble formation in steady growth region increased as the gas flow rate

In pure water,
bubbles trapped inside the liquid can rise to the surface and disappear by
simply shake the vessel. It is not always true when bubbles are trapped in yield
stress material since its viscosity can entrap bubbles inside. The critical ratio
of yield stress to buoyancy which decides a bubble can move or not was studied both
numerically and experimentally(Dubash & Frigaard,
2004),(Dubash & Frigaard,

The experiment-based
study on rising bubbles investigated the terminal velocity(Dubash & Frigaard,
2007). The radius of bubbles (bubble size) comparing to the radius of column
filled with Carbopol solution, R/Rc is the main factor influences
terminal velocity.

Another study was
done discussing terminal velocity as well as bubbles shape(Lopez, Naccache &
de Souza Mendes, Paulo R, 2018) . In a higher concentration, bubbles exhibited
a cusped shape and had a tail, while in lower concentration, bubble shape is slender.
Bubble shape also changed obviously when the effective radius of the bubble increased
in the lower concentrated Carbopol solution.


1.2   Bubble motions in polymer gels

In polymer gels,
bubble formation and propagation are largely affected by internal stress(Mougin, Magnin &
Piau, 2012). Polydispersity of microgels and their stack compactness



2.3   Bubble motions in concentrated surfactant

One type of yield-stress fluids in
which bubble motions are widely studied is concentrated surfactant solution. In
most studies, oil-in-water emulsions stabilized by surfactants are used as the
fluid while a few studies focus on water-in-oil emulsion.

Emulsions are consistent of
dispersed phase and continuous phase. Using oil-in-water emulsions as the
experimental yield stress fluids involves two required condition: 1) the volume
fraction of oil droplet is high enough to enable the presence of yield stress;
2) diameter of gas bubble (bubble size) is much larger than that of oil droplet
so that bubbles in the system consider the emulsions as a yield stress fluid. Producing
bubbles in this type of yield-stress fluids has been studied based on
T-junction geometry(Laborie et al., 2015)

Factors that influence the
stability of bubble in emulsion/gas system have been researched. It is found
that buoyancy is a factor that causes the destabilizing of bubbles (Dutta et al., 2004).
In this study, buoyancy was found to cause both a vertical spatial
heterogeneity of gas volume fraction and bubble size distribution with time.
Besides buoyancy, in the condition that average bubble size is rather small, Ostwald
ripening contribute to the destabilizing of bubbles as well. Evaporation of
foam solution becomes significant to the system at relatively high temperature(Turner, Dlugogorski
& Palmer, 1999).

Experiments on
bubble rising in this category are carefully performed with fluids of low yield
stress(Stein & Buggisch,
2000) . This enables the convenience of obversation. Experiment setup
is shown in Figure, where the bubble is injected by a syringe. This study focused
on the bubble rising velocity affected by applied pulsation amplitudes, hence
air saturated fluid is guaranteed for a constant bubble size.