Contact Angles And Bubble Motions in the Aluminum Reduction Electrochemical Cell.

[NNadir]

The paper I'll discuss in this post is this one: Effects of Contact Angle on Single and Multiscale Bubble Motions in the Aluminum Reduction Cell (Seyed Mohammad Taghavi et al Ind. Eng. Chem. Res. 2019, 58, 37, 17568-17582)

One of my peculiarities is to spend a lot of time thinking about anodes, since any serious effort to address climate change - no such serious efforts are underway - will be very much involved in electrochemistry, and to the extent that electrode chemistry involves cokes obtained from dangerous fossil fuels, which must be banned, it is supremely necessary that they be considered. (Another important reason to consider anodes is in the anodic dissolution of used nuclear fuels, which in my view, is the best of all potential processes for dissolving them.)

I have written about anodes in the electrochemical reduction aluminum elsewhere on this website: Can Biocoke Address the Anode CO2 Problem (Owing to Petroleum Coke) for Aluminum Production?

It turns out that a consideration in the behavior of anodes is the behavior of bubbles, the physics of which are rather complex. In addition, the physics of bubbles also play key roles in many other processes of extreme environmental importance, notably heat transfer, with particular respect to nucleate and film boiling. It turns out that the only viable path to removing the carbon dioxide we have dumped and continue to dump on future generations in our contempt for them while we all wait for the grand renewable energy nirvana that did not come, is not here, and will not come, will involve issues in heat transfer at extraordinarily high temperatures, and the physics of bubbles will be very much involved in the processes that our children, grandchildren and great grandchildren will need to clean up from the wild party of our sybaritic consumer excesses.

Thus this complex and rather long paper caught my eye in my general reading.

From the introduction:

Bubble nucleation, growth, coalescence, and detachment play important roles in many engineering applications such as the gas–liquid separation, chemical reaction, boiling, bubble column motion, and cavitations. Several researchers have studied bubble movements(1−5) on the upward-facing and vertical surfaces. However, in some applications, such as in the aluminum electrolysis process, bubble behaviors beneath downward-facing surfaces are not fully understood. In the aluminum electrolysis process, microdispersed bubbles are formed under the anode when the electrochemical reaction happens. Then, the bubbles move along the anode bottom as they grow, coalesce, and detach from the surface. Bubble motion is a part of the magneto-hydrodynamics in the cell and not only affects the electrical resistance but also changes the current efficiency. However, it is hard to measure the bubble motion directly under the harsh operating environment and high temperatures in the industrial aluminum reduction cell. In the previous studies, some researchers(6−17) have considered the bubble motion via experimental models. Many factors, such as the current densities,(6) the anode surface shapes,(7−9) the liquid properties,(10,11) the gas–liquid surface tensions,(12,13) the anode types(14,15) and the wettability,(16,17) have been explored to reveal the bubble dynamics beneath downward-facing surfaces.

To understand the bubble dynamics, the contact angle is an essential factor, which quantifies the wettability of the anode surface and affects the bubble motion. The contact angle is calculated with the Young–Dupre equation considering the function of the solid–gas, liquid–solid, and liquid–gas surface tensions(37,38) (as seen in Figure 1)



for which the parameters are presented in the caption of Figure 1...

Figure 1:



The caption:

Figure 1. Schematic diagram of a single bubble (black line) beneath the anode (orange block) in the liquid with the contact angle θw determined by the liquid–solid surface tension σLS, solid–gas surface tension σSG, and liquid–gas surface tension σLG. The green dash line represents the bubble length L, H is the bubble thickness, and the yellow point is the intersection point of gas–liquid–solid phases.

...Based on our brief review of the literature, it is clear that there is a lack of deep understating of the effects of the contact angle on the bubble dynamics in the aluminum reduction cells, which is the subject of our numerical study. The outline of the paper includes the followings: “Model Description,” “Numerical Details”, and “Results and Discussion”. In the Section 2, a three-dimensional (3D) transient mathematical model is employed to study the effect of the contact angle on the single bubble flow using the VOF method (Section 2.1). Then, a 3D transient model coupled with the discrete phase model (DPM)-VOF method is applied for predicting the multiscale bubble motion with various contact angles. A transition model from dispersed bubbles to continuous gas is used to bridge the conversion of bubbles in the Eulerian and Lagrangian frames (Section 2.2), which is achieved by a user-defined function (UDF) in the Fluent software. The Section 3 introduces the boundary conditions, flow regimes, and some material properties. The Section 4 presents the model validation and bubble behaviors with various contact angles. Finally, the Section 5 summarizes the main findings...

It follows from this portion of the introduction that this is a very long and elegant paper, and cannot be covered in too much depth in a brief blog post, and the post is merely a teaser for an interested party to look into the original.

Here though, is some flavor of the paper which, no, does not involve, um, Beto:

2.1.2. Collision and Coalescence Model

In the Fluent software, the collision and coalescence models are calculated by O’rourke’s algorithm,(30) which is a stochastic estimate of collisions and it also assumes that two bubbles collide in the same continuous-phase cell. The collisions among three or more bubbles are not explored within this method. If a smaller bubble moves in a flat circle around a larger bubble of the area π r1 + r2)2, a collision takes place. The collision volume Vcol for the 3D model can be written as the smaller bubble traveling distance in a given time step



where r1, r2, u⃗rel, and Δt are the small bubble radius, the large bubble radius, the relative velocity of the two bubbles, and the time step, respectively.

If the bubble has a uniform probability being anywhere in the cell, the probability of the two bubbles’ collision can be defined as the ratio of the collision volume and the cell volume Vcell(31)



The actual probability distribution of the number of collisions Nc based on the Poisson distribution is calculated by the expected collision number N̅



where N1 is the number of smaller bubbles.
To calculate the collision and the coalescence between the bubbles, O’rourke’s algorithm(30) selects two random numbers, x and y, in the range of [0, 1]. If x > P(0), the collision happens between the two bubbles. After the collision, the second random number y is adopted to determine if there a two-bubble coalescence or a grazing collision...

...and so on...

A few pictures from the paper:



The caption:

Figure 2. Schematic diagram of multiscale bubbles regarding the mesh at the anode bottom. (a) Macrobubble surface, (b) macro–microbubbles, and (c) microdispersed bubbles.

The caption:

Figure 4. Schematic our 3D model (symmetric with respect to x and y) for a single bubble motion. Gas is injected into the bath from the inlet surface (red surface) at the anode bottom and escapes from the outer surface.

The caption:

Figure 5. Force analysis of a single bubble (black line) beneath the anode (orange block) with static contact angles θw of (a) 0 < θw ≤ 90° and (b) 90° < θw ≤ 180°. The forces are the pressure gradient force F⃗p (red vectors), the surface tension force F⃗s (blue vectors), and the buoyancy force F⃗b (green vectors). F⃗sx and F⃗sy are the components of surface tension force along x and y directions, respectively. F⃗px and F⃗py are the components of pressure gradient force along x and y directions, respectively.

The caption:

Figure 8. Evolution of a single bubble shape in the plane of y = 0, with the contact angles of (a) 45°, (b) 60°, (c) 75°, (d) 90°, (e) 105°, and (f) 120° with the mass flow rate of 0.0000735 g·s–1 at (black short dash-dotted line) t = 1.0 s, (red dashed lines) t = 2.0 s, (blue dotted line) t = 3.0 s, (pink dash-dotted line) t = 4.0 s, (green dash-dotted-dotted line) t = 5.0 s, and (blue short dash line) t = 6.0 s. The operating parameters are listed in Table 2.

The caption:

Figure 9. Bubble shapes beneath the horizontal downward-facing surface in the plane of y = 0, with the contact angles of (black short dash-dotted line) 45°, (red dash line) 60°, (blue dotted line) 75°, (pink dash-dotted line) 90°, (green dash-dotted-dotted line) 105°, and (blue short dash line) 120° at 2.0 s with the mass flow rate of 0.0000735 g·s–1. The operating parameters are listed in Table 2.

The caption:

igure 10. Velocities at 6 s in the plane of y = 0, with the contact angles of (a) 45°, (b) 60°, (c) 75°, (d) 90°, (e) 105°, and (f) 120° with the mass flow rate of 0.0000735 g·s–1. The red line represents the bubble surface. The operating parameters are listed in Table 2.

The caption:

Figure 14. Evolution of the (a) gas coverage and (b) bubble thickness with a contact angle of 90° at a current density of 9000 A·m–2. The operating parameters are listed in Table 3.

The caption:

Figure 15. Minimum gas coverages (■ points 1–4) in the first cycle after bubble detaching from the anode bottom at a current density of 9000 A·m–2 with the contact angles of (red dashed line) 75°, (green dash-dotted line) 90°, (blue short dashed line) 105°, and (pink dash-dotted-dotted line) 120°. The operating parameters are listed in Table 3.

The caption:

Figure 16. Multiscale bubble distribution at 2 s with the contact angles of 75, 90, 105, and 120° (columns from top to bottom) in the current densities of 5000, 7000, and 9000 A·m–2 (rows from left to right). (a) θw = 75°, J = 5000 A · m–2, (b) θw = 90°, J = 5000 A · m–2, (c) θw = 150°, J = 5000 A · m–2, (d) θw = 120°, J = 5000 A · m–2, (e) θw = 75°, J = 7000 A · m–2, (f) θw = 90°, J = 7000 A · m–2, (g)θw = 105°, J = 7000 A · m–2, (h) θw = 120°, J = 7000 A · m–2, (i) θw = 75°, J = 9000 A · m–2, (j) θw = 90°, J = 9000 A · m–2, (k) θw = 105°, J = 9000 A · m–2, (l) θw = 120°, J = 9000 A · m–2. The operating parameters are listed in Table 3.

...and so on...

I do not know these authors nor am I familiar with their work, but it has to be a joyous exercise to contemplate these things, to think about them.

Hell, it would be a wonderful thing to just have the time to thoroughly read and understand the paper, because things like this, more than many things on which we spend our time are important to humanity and to the future, whether we recognize it as such or not.

Have a wonderful work week.

[gibraltar72]

1. Huh?

[defacto7]

2. The opening paragraphs are key even if you don't understand the science.

[defacto7]

3. Most people try to simplify complicated forms to understand them.

It amazes me to see the simplest forms reduced to the most complex explanations and yet find there an even purer simplicity. It's art.

[NNadir]

4. Yes, it is a kind of art, isn't it. The mathematical physics of bubbles turns out...

...to have many important applications.

I started to focus on them in consideration of a very different case, specifically the solubility and outgassing of liquid metal systems, particularly fission gases in liquid actinides and their effect on an important nuclear parameter, the reactivity, as well as the ultimate distribution of elements among fission products.

I had little idea that a very simple question would involve such wonderful physics. I have now, a whole monograph on bubbles in my library:

Acoustic Cavitation and Bubble Dynamics

Last week in connection with some issues in heat transfer, I came across an interesting application involving cavitation, and I hope I can find some time to actually read a little more in this book.

I've written about bubbles before in this space, Rayleigh's paper: I just stumbled into a very old paper by "Lord Rayleigh" contemplating water boiling in a pot.

It turns out that Rayleigh's musing on bubbles in a boiling proved to be quite important, the Rayleigh-Plesset equation is an important equation in the study of bubbles. I didn't know that when I wrote that post.

From the text just referenced (pg. 41):

This equation gives the relationship between the the radius of a bubble, the first and second derivatives of the change in its radius with respect to time, pressure of the vapor inside the bubble, instantaneous accoustic pressure, pressure of non-condensable gas inside the bubble, ambient pressure, the viscosity in which the liquid forms.

It's a marvelous equation and one is in awe of it's creation and the people who built it.

Life is exquisite and then you die.