Gravity In Non-Newtonian Bubbles

Bubbles are often observed in fluids of industrial interest. For instance, bubbles are important in the water treatment process and design of reactors. In addition, the dynamic behaviour of bubbles in fluids, and more specifically viscoelastic and non-Newtonian fluids, is of great importance in different fields such as polymer sciences, composites, boiling, plastic foam processing and bubble absorption . Pharmaceutical, petro-chemical and food industries also encounter issues with rising bubbles in non-Newtonian fluids such as detergents, paints and foods (ketchup, yoghurt etc.) As a result, a better understanding of bubble motion in non-Newtonian fluids can be helpful in many scientific and industrial applications. Non
Newtonian fluids are in general

For example, the discontinuity in the rising velocity of a gas bubble in CMC (Carboxymethyl Cellulose) solution has been confirmed in one research article while other works reported no discontinuity
Discontinuity takes place at a certain critical bubble volume, the critical volume. It has been shown that the critical volume and the terminal velocity of the bubble decreases with increasing fluid concentration and elasticity. However, the size of the fluid container seems to have no effect on the critical volume.
It has been observed in some research that if a solution does not have any surfactant no jump discontinuity occurs . The addition of some surfactants to a solution has resulted in the jump appearing. However, it has been concluded in another study that the jump discontinuity is not caused by surfactant
The relaxation time of the polymer seems to be important to the existence of a critical volume regardless of the polymer properties. A fast relaxation can delay or eliminate the discontinuity while a slow relaxation (relaxation time) may create an upward force causing a discontinuity
When the bubble’s shape becomes cusped, a vortex appears close to the trailing end of

For example, for a CMC solution the cusped shape was observed but the plot of the velocity with respect to the bubble volume did not have any discontinuity while other other studied have shown, for the same solution, that a cusp and discontinuity occurred
It has been observed that the cusped shape of the bubble may not be symmetric. In fact, the bubble’s trailing edge can been seen to be sharp or broad depending on the point of observation. It is a cusped shape from one view point while in an orthogonal direction the shape is spade edged. In more detail, the broad edge can be like a spade, an axe, an arrow or a guillotine blade. When the bubble has a larger volume, from one view point the cusp shape appears while in the perpendicular direction the axe shape is viewed. Therefore, for a small enough horizontal angle view the broad edge of the cusp is always parallel to the container wall and the cusp shaped forms in all sizes and shapes of the container but the broad edge is related to the side