Convection AND diffusion
Вставка
- Опубліковано 27 лип 2024
- 0:00 Intro
0:23 Convective VS diffusive
0:59 Convective AND diffusive
1:48 Moving coordinate system
3:31 Adding them together
3:53 Getting rid of velocity
5:03 Two special cases
Explains how to deal with a situation where we have simultaneous convection and diffusion and how
that relates to your feeling of standing still as you hurdle through the cosmos. Towards the end two special cases are introduced:
* Equimolar counter diffusion and
* Diffusion in stagnant component
These videos deserves 100x more viewers and followers, exellent class, exeellent explanation.
those lectures are pure gold!! Thank you very much!
These lectures are awesome. I wish my professor would spend office hours making these vids.
Thanks, glad you like them. Don't be too harsh on your professor though, making videos this way (adding text and illustration afterwards) has taken me a rather substantial amount of office hours (and some out-of-office hours for the Blender animations). I myself have a few more videos (in Swedish, on membrane filtration) planned but have difficulties finding enough time to do them. That there aren't plenty more videos out there is partly a political question regarding how education is financed.
@@PLE_LU we love you sir, you did a lot❤️
Nice explanation sir
Sir, you explained it so well..!!
Thanks for clearing my doubts.
You're welcome, glad it helped you
Thank you very much for your time. İ have checked all other videos relates to Mass transfer . İt is short and excellence interpretation.
You're welcome, glad you find them appropritate
Hello sir , sir I have a doubt
, we have seen here that even when there is no forced convection there can be convected transport due to the bulk ( molar average velocity) , what if the fluid has a forced velocity V, then in CaV , what is V? forced velocity ? and this transport is in direction of fluid flow only? or is there any transport in other direction too? what about them are they convected or diffusive?
Please only write your comment in the apropriate video. I have removed your duplicate comment from the Swedish video on using the mailings command in Microsoft Word.
Now to your question: Convection is per definition the average movement of molecules, thus v is _always_ the average velocity of all molecules.
In each case, you must look at your system and try to find a mathematical description that seems appropriate (e.g. two-film theory, penetration theory, boundary-layer theory or something else) If you need to, you may even add one more hierarchial level in your equation and talk not only about diffusion and convection, but also about eddie diffusion (which behaves mathematically like diffusion, but has a "diffusivity" that is different from the diffusivity that I talk about in my videos)
You do not need to have a fan or a pump to get convection, there is also natural convection. A simple example of natural convection is the air movement on the outside of a radiator. So, if you have an average movement of molecules, in any direction, that is nonzero that is your convection, regardless of the cause of that movement (pump/fan/density gradient/…)
More advanced answer: You might need to consider more than one direction… In the boundary layer theory video ua-cam.com/video/FDfWyeqkKkU/v-deo.html we are interested in the mass transfer (or heat transfer or transfer of momentum) in the direction orthogonal to the main direction of flow. You can think of this as diffusion through a stagnant compoment, although that would be to simplify a bit. The film next to the surface (laminar closest to the initial edge, turbulent further away) is moving.
The molecules (or the universe for that matter) do not care what equations we use. Our convention to divide the movement of molecules in to convection (average movement of all molecules) and diffusion (movement through random walk relative to this average movement) is just a handy mathematical abstraction that helps us making the mathematics easier to handle.
Hi Professor. Those equations applies for liquid liquid diffusion+convection?
If you're thinking "applies" as in "is exactly correct for", then some of the equation only apply to ideal gases and very special liquids. The problem with liquids is that different molecules take up a different amount of volume and if you mix different molecules, strange things often happen with the volume (if you add 1 liter of ethanol to 1 liter of water, you get less than 2 liters of solution). Thus, in liquids the situation might not be exactly that simple that you can say that Ntot=Ctot*v
On the other hand, many of the equations might be _good enough_ for liquids in many situations. Furthermore, these equations gives you an idea of what _approximately_ happens in liquids.
Note
1. This video is one in a series on mass transfer ua-cam.com/video/EG4ZoVTSA5I/v-deo.html
2. The BIG elephant in the room here is that we're talking about binary mixtures and only one spatial dimension, and in how many cases can you say that your system is one-dimensional and only has two components? However, we are (in this series of videos) building up to mass transfer in three dimensions (although still only "two" components, or systems which you may treat as consisting of two components, e.g. like moist air). The course that this video is a part of doesn't go into models for multi-component diffusion, but I think it is safe to say that it is a lot easier to understand multi-component system if you first get a grasp of binary systems.
3. In many real world situations, the use of diffusivities breaks down due to complex geometry and we have to settle for using mass transfer coefficients. However, understanding how these ideal model works and how mass transfer coefficients are connected to diffusivity can tell you a great deal regarding how the value of mass transfer coefficients are expected to change if you change operating conditions. More on that in later videos in this series
Sir, is your explaination of a moving camera and stagnant camera same as Lagrangian and Eulerian description of flow? because that will settle my confusion on the difference between both
I haven't gone so far down the Lagrangian/Eulerian rabbit hole, but I think essentially, yes. I'm not an expert in that field, however, so I wouldn't be surprised if there are subtelties in the Langragian and Eulerian perspectives that go beyond my simple explanations in this video.
Thankyou for the videos. I learnt a lot
Dear professor,
As I know, this equation is used for molecular diffusion where NA = Fick's law + the bulk motion contribution.
If I compare it to what u wrote ==> bulk motion contribution = convection. But in your first video you said that convection is on larger scale ==> we dont speak on convection when we solve molecular diffusion as in this case. is it only a pronunciation difference? I do not know, the tittle convection vs diffusion is confusing for me, this equation is for molecular diffusion only taking into consideration the motion of the binary system and not an applied velocity.
I'm not sure I fully understand your question, i.e. what it is that you misunderstand.
First attempt to answer: Are you thinking of the difference between advection and convection? The term advection seems to be used differently by different people, some meaning that advection is a synonym for convection, others (like me) that advection is a convection that is caused by a pump or a fan or something similar. The latter implies that advection = forced convection but leaves the question somewhat open wether or not natural convection should be considered as advection or not (think air close to a heat source moving due to temperature-induced differences in density)
Second attempt: Note that the phrase "large scale" here means "larger than a group of only a few molecules". With large scale we here thus imply a large enough package that we can start talking about an _average velocity_ (with a certain direction) of the molecules.
Third attempt: Note that in some situations no pump or fan is needed to create a situation where there is an average velocity of the molecules. If you look at the video ua-cam.com/video/VXIwAkjYMLM/v-deo.html you see that if you have a glass of water slowly evaporating, there is convection out of the glass (simply because 1 mol water vapour occupies more volume than 1 mole of water as liquid)
So, what this video is about is when you combine the effect of convection (average movement of packages of liquid) with diffusion.
I guess the second and the third attempts are quite satisfying. Thank you so much for your clear 'answers'.
1- Does it mean that if we have a homogeneous medium (@ equilibrium) pumped in a tube, we still can write NA = CA.V? i.e. no need to have a difference in concentration.
2- What is the difference between NA = CA.V and NA = K.DeltaCA used in convective applications
Yes, kind of:
If you have a difference in concentration you can't use the equation. Situations where you have a difference in concentration includes the situation describe by Reynolds analogy and Chilton Colburn analogy, see ua-cam.com/video/7YlQ_4jL_gs/v-deo.html
So the equation is only valid if there is no difference in concentration, like when you pump a salt solution with constant concentration through along a tube.
I would hesitate to use the term homogenous here, as that term can imply that there is only one _phase_ (e.g. liquid) rather than that the concentration is constant. So if you pump a _heterogenous_ system, i.e. sea water with some sand, through a pipe (like what they do in some countries including Denmark to attempt to keep the sea from eating away at their shore lines) you can still use the equation since the salt concentration is constant.
Sir, while taking N total = NA+NB , if N total taken as total convective flux how can u add NA and NB to get N total?
NA and NB normally include diffusion flux and convective flux right ,so how can you add then these both to get total convective flux Ntotal?
I think you misunderstand what convective flux is. By definition, convective flux IS the net transport of molecules, thus in a system with only two components, the convective flux is the total flux (summed over both species), i.e. Ntot=NA+NB=Nconvective.
Thus, in Stefan diffusion (which you get if a liquid in a narrow tube evaporates and diffuses out into the surrounding) the fact that the volume increases when a liqud evaporates and forms a gas, together with the concentration gradient that causes diffusion, you have both diffusive transport and convective transport in the tube.
I think it might help you if you watch the entire playlist on mass transfer
ua-cam.com/video/XsujCJ_ko3k/v-deo.html
dear professor
fisrt, i'm not goot at english.... sorry....
sir i have some doubt
you wrote the convective transport NA =vCA (i think NA is total molar flux so where is diffusion??)
but later (totalflux)NA=diffusion + convection
what is the difference between above two??
Because we talk about convection only in those cases:
At 0:24 we repeat what we have learnt in a previous video, where we only had convective transport, i.e. we have N_A=0+v*C_A=v*C_A
At 0:44 "if we have _diffusive transport_" Here we start thinking about a situation where we have diffusive transport also
At 2:09 to 3:04 I still show the equation N_A=v*C_A I mean this more as a reminder of how you calculate convective transport, not that N_A=v*C_A if you also have diffusive transport. There are only so many characters in our alphabet and while we do use J_A for denote diffusive transport, we don't have a symbol commonly used to denote the convective _part_ of the total transport.
At 4:20 we state Ntot=Ctot*v If you have no problems believing this, stop reading here!
OK, you continue to read at the risk of becoming a bit confused, because now we dig a bit deeper: If there is no diffusion then Ntot=Ctot*v must be true, right? But what if we have diffusive transport also? Well, actually, for a binary system that must be true even if there is diffusion
N_A=-D dCA/dz + vC_A
N_B=-D dCB/dz + vC_B
Note that D for how A moves in B must be identical with D for how B moves in A in each point in space. We sum the two together:
N_tot=N_A+N_B = -D (dCA/dz+dCB/dz) + v(C_A+C_B)
But we have a binary system, so the concentration gradient of A must have the same value but opposite sign as the concentratration gradient of B, i.e. dCA/dz=-dCB/dz and we get
N_tot = -D*0 + v(C_A+C_B) or N_tot=v*Ctot
i have noticed that u have not mentioned anywhere about chemical potential being the true driving force of diffusion. pls can u make a video on it as iam unable to understand it from nowhere. also, can u explain about "N" and "J" in detail and there difference.
I don't think I used the term "chemical potential" anywhere, I rather usually say "difference in concentration" or "concentration gradient". Diffusion is due to random movement (e.g. due to Brownian motion). You can compare this with carefully putting black marbles on top of white marbles (the white and black marbles having the exact same size and density) in a glass jar and then shaking the glass jar. The result is white and black marbles mixed, simply because there are vastly more configurations where the black and white marbles are mixed than configurations where all black marbles are separated from the white.
I use N to denote molar transport in general. J I reserve for molar transport due to diffusive transport.
But in many books it is written that Chemical potential is the true driving force of diffusion. I get what u said completely. But what about the true driving force.
@@ritviksharma5949 I don't teach that and in many cases the difference between concentration and activity, pressure and fugacity doesn't matter much compared to the large uncertainties involved anyway. I would recommend you to look for people dealing with physical chemistry for good explanations of chemical potential and how that is related to diffusion.
Thank u sir
These notations are confusing.
If Ntot is total mass transfer then what is NA?
The notation predates the change in the SI-unit system where N_A nowadays should always be Avogadro's number. Here N_A is the total mass transfer OF SUBSTANCE A, i.e. the sum of convective and diffusive transport. As most introductory texts/books/videos on mass transfer it is assumed that we have binary systems, i.e. only two components (A and B). When you introduce a third or more components it gets a bit more complicated.
Conductive mass transfer or diffusion is same or different
There is no such thing as "conductive mass transfer". I think you are confusing mass transfer with heat transfer. Conductive heat transfer is the same thing as diffusive heat transfer. In a gas, conductive heat transfer is both due to diffusive transfer of mass (e.g. a molecule with higher velocity than the average moving from left to right) and due to transfer of velocity (and thus momentum) from one molecule to another when molecules collide with each other. In solids, diffusive heat transfer is due to transfer of velocity due to interaction between molecules. (In an ideal gas, the transfer mechanisms for heat transfer, mass transfer and transfer of momentum is so similar that the mass diffusivity equals the heat diffusivity which equals the diffusivity of momentum, if all are measured in m2/s.)
It might help you to watch other videos in the mass transfer playlist.
ua-cam.com/video/XsujCJ_ko3k/v-deo.html
@@PLE_LU Thank you sir