 So we're going to talk about another type of reaction in 1D column, which is option-disoption. And actually, it's very similar to surface complexation, but it's much easier chemical or simple chemical system that I can write these expressions for retardation factor or things like that. So it's really to illustrate the general principles. But if you want to look at how surface complexation, if you want to think about how surface complexation will be behaving these different systems, essentially it will be like here I'm talking about one equation, but in a surface complexation system you will be talking multiple equations with different species. So it's different, but it's also similar in its principles. So I'm going to use this example again that have 1D column again. You'll notice sometimes I draw vertically. Sometimes I draw horizontally. When I draw horizontally, usually, I kind of indicate this as those things that the conceptual figure in my mind is that's what happened in the groundwater system. Typically, you have horizontal flow or ladder flow. So let's say we have a sobbing chemical going through the system, which is different from the non-reacting chosen before. So this is maybe an organic material. It's called that OR. OK, so it goes through a system. It's going to attach to some of the solid phase in the past media. So when you think about the processes that it goes through, again, it will have advection process, which is not surprising, and then dispersion and advection or diffusion. But again, there's this sobbing reaction happening. So let's say we have a solid phase, not really solid. It's like this sobbing organic matter is in exchange with the species in the water phase. So now usually, we think about absorption, desorption, or like surface interactions. These reactions tend to occur very fast or semi-dynamic control. So it's different from mineral desorption precipitation. We talk about these reaction rates, reaction rate loss. Here, because they happen very fast, we consider they have algebraic relationship between the solid phase condition and aqueous phase condition. So the expression between how it governs, how it's different from previous one is here, you have essentially algebraic relationship. Instead of rate law, m equals to kd concentration. So this c is aqueous condition. This is a solid condition. This is a condition on solid. How much it's sobbed on the solid phase. And it could be in the units of, for example, mass of this chemical species per mass of solid phase or per volume of solid phase are different units of that. So as long as they are consistent. So the kd, what we call, this is a linear isosome. So it's simplest sobbing isosome you can get. There's no non-linearity here. So there's kd. This kd is called sobbing coefficient. You can imagine if you have large values of kd, this chemical species tend to sob on solid phase a lot. If it's small, it doesn't sob on solid phase much. So again, here we only have one species, which is much simpler than the multiple species we talked about in other units for the mineral distribution or complexations. Now, so how is this different from the non-reactive tracer? So here you have a species that actually sobbing on solid phase. So in the previous one, when we talked about AD equations that involve non-reactive tracer, the solid phase does not have that chemical species. It does not sob on solid phase. So actually, we can derive the equation of sobbing species based on the non-reacting one and this relationship. But I'm not going to go so detailed with that. I'm going to just give you the expression of that, which is going to be, actually, everything also will be the same. All these terms that we talked about before. But there will be one more extra term in front of this, which is 1 plus 1 minus phi over phi. And then you have rho, which is the density of a solid phase. You have kd. So you're imagining that all these E for each term, the units need to be consistent. So this is dimensionless. These should be the units of these should cancel out. And depends on how this isosome coefficient are defined, you will have different type of units. But eventually, they should cancel out. So this term domain dimensionless. But essentially, what this tells you is, for example, if you think about this, if this is a constant, if given a particular post-media, you would have the same porosity, how much space you have. You would have the same density of solid phase. And this is a property of the absorbing material. So if you have the same absorbing species, you should have the same vessels. This is a constant that we call epsilon, which is retardation factor. Because it's constant, and it does not change with time x, t, and x, which means we can potentially divide each term by this. So you would actually have an equivalent equation would be this. But you would have minus u and then divided by epsilon, partial c, partial x, plus d. Again, here are the same. And then again, divided by this epsilon. I essentially move this to the other term. Now, what are the effects of that is, again, let's think about a pulse of injection of some chemicals or a riso. Let's say it's a very sharp injection, which is, so you would imagine, let's say you are injecting this organic material, but also at the same time you are injecting a non-reactive tracer to compare it with as a reference. So how would these two different chemicals behave when you think about, OK, they inject at the same time. One is sobbing, the other is not sobbing. And also, actually, based on this equation, what can they tell you? So I'm just going to draw something. So this is the concentration infection of time. So we are really looking at here. And we're correcting samples, water sample, and measure the concentration. We correct sample at different time and measure the concentration at different time. So you can think about how, which, like, I already put this, right, there's a pulse of chemical goes in. So there should be another pulse coming out. And they should be coming out at different time. And which one should coming out first? And which one should coming out later? Is that the non-reacting one going to come out first? So is sobbing material going to come out first, right? So while you are thinking I'm drawing this, we talk of it with a pulse you have at some point when it comes out of it looking kind of like that, if it's a homogeneous medium, right? And there's another one. They're supposed to have the same way of saying I'm probably not drawing this. But anyway, if you think about that, compare the two species, right? So one that should come out first is a non-reacting one. If you think about non-sobbing, this will be the non-sobbing species. Because it's not going to go on the solid phase, take its time, come out again. But for the sobbing species, once they get into the pulse medium in contact with the solid phase, it's going to go into a solid phase first, right? And then it will be kind of in equilibrium at some point, then it will become out again. So sobbing species will spend some time to interact with a solid phase so that delays the whole process of freshening out. So if we think about this, we call that T sobbing species. And this is T just the chaser. So it's non-sobbing. So let's just call it sobbing. If we are doing this experiment measuring these and joining these figures, you actually can calculate this optional value or the tradition factor. It's equals to this time of the sobbing species, the peak of sobbing species versus the time of non-sobbing. And this is actually how people measure the retardation factor in lab systems. So essentially, what the sobbing species does is to delay the process of coming out of the system. And actually, more or less, you can expect this, right? Because the sobbing, the u or the velocity appears as if it's slower, because this retardation factor is almost always larger than. If it's equal to 1, then it's essentially as the non-acting chaser. So it really should be larger than 1. And so it's going to be slower than the sobbing, than the non-sobbing one, than the chaser. OK, so that's the effect of the retardation factor, sobbing, and everything. If you think about complexation, soficial conversation, it's essentially very similar behavior, except that you would need to deal with body component system. And users as peer-dependent and the solid phase tend to have hydrogen on these sobbing sides that are peer-dependent. So I'm not going into these complexity and details. You can look at some of the material online.