Intercambio de partículas y calor

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ID:(1630, 0)



CO2 diffusion

Description

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The absorption of CO2 by the oceans helps mitigate the effects of this gas in the atmosphere and therefore delays climate change. However, the processes involved are more complex and include:

- Gas exchange with the atmosphere: The ocean and the atmosphere are in constant exchange of CO2 through gas diffusion. Atmospheric CO2 dissolves in the surface of the ocean and forms carbonic acid (H2CO3), which then dissociates into hydrogen ions (H+) and bicarbonate ions (HCO3-). This process helps balance the CO2 levels between the ocean and the atmosphere.

- Photosynthesis and respiration: Marine organisms, such as phytoplankton and algae, perform photosynthesis and take up CO2 from the water to produce organic matter and release oxygen. This process, known as carbon fixation, helps extract CO2 from the ocean. On the other hand, marine organisms also respire, which means they release CO2 into the water during the decomposition of organic matter.

- Ocean circulation: The ocean is characterized by its global circulation, in which currents transport CO2-rich water from the surface to the depths and vice versa. This contributes to the distribution and mixing of CO2 throughout the ocean, allowing deep waters to store large amounts of dissolved CO2.

- Sedimentation and burial: Part of the organic matter produced by marine organisms, including CO2 captured through photosynthesis, can sink to the ocean floor. As sediments accumulate over geological time, the organic carbon can become buried and stored in the seafloor for long periods.

Ocean-Atmosphere Interactions of Gases and Particles, Peter S. Liss Martin T. Johnson (Editors), Springer, 2014

ID:(12297, 0)



Diffusive flux with the transfer velocity

Equation

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Since the diffusive flux $F$ can be modeled using Fick\'s law:

$ F = - D \displaystyle\frac{d C }{d t }$



We can establish a relationship between the transfer velocity $k$ and the concentration difference $\Delta C$ as follows:

$ F = k \Delta C$

$F$
Densidad de flujo de gases atmósfera océano
$1/m^2s$
$\Delta C$
Diferencia de concentración
$1/m^3$
$k_w$
Velocidad de transferencia agua aire de CO2
$m/s$

The diffusive flux $F$ is described by Fick\'s law:

$ F = - D \displaystyle\frac{d C }{d t }$



where $D$ is the diffusion constant and $dC/dx$ is the concentration gradient. By defining a transfer velocity as:

$ k_a = \displaystyle\frac{ D }{ \delta }$



we can establish a flow equation of the form:

$ F = k \Delta C$

ID:(12226, 0)



Transfer speed

Equation

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If we consider Fick\'s law:

$ k_a = \displaystyle\frac{ D }{ \delta }$



we recognize that the term

$\displaystyle\frac{D}{dx}$



corresponds to a transfer velocity. Therefore, we have:

$ k_a = \displaystyle\frac{ D }{ \delta }$

$D$
Constante de difusión en masa acuosa
$m^2/s$
$\delta_c$
Grosor de la capa superficial
$m$
$k_u$
Velocidad de transferencia aire a agua de CO2
$m/s$

ID:(12227, 0)



Transport of a quantity

Equation

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The transfer velocity of a quantity $k$ is defined as the flux $F$ divided by the concentration difference between the two media, represented by

$C_0-C_b$



Therefore, it can be expressed as:

$ k =\displaystyle\frac{ F }{ C_0 - C_b }$

$C_b$
Concentración de gas en el agua
$1/m^3$
$C_0$
Concentración de gas en el aire
$1/m^3$
$F$
Densidad de flujo de gases atmósfera océano
$1/m^2s$
$k$
Velocidad de transferencia
$m/s$

ID:(12213, 0)



CO2 exchange

Equation

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The transfer rate of CO2 from the atmosphere to water can be modeled using an equation similar to the general rule

$ k =\displaystyle\frac{ F }{ C_0 - C_b }$



In this model, the concentration difference is replaced by the difference in partial pressure of the gas and its solubility $\alpha$. The equation can be expressed as:

$ k_w =\displaystyle\frac{ F }{ \alpha \, \Delta p_{CO2} }$

$\alpha$
Coeficiente flujo CO2 agua a aire
$1/J$
$F$
Densidad de flujo de gases atmósfera océano
$1/m^2s$
$\Delta p_{CO2}$
Diferencia de presión de CO2 entre agua y aire
$Pa$
$k_w$
Velocidad de transferencia agua aire de CO2
$m/s$

If we consider the gas flux as $F$ and the transport velocity as $k$, according to the general relationship:

$ k =\displaystyle\frac{ F }{ C_0 - C_b }$



By replacing the concentration difference $C_0 - C_b$ with the difference in partial pressure of the gas using the solubility $\alpha$, we have:

$C_0 - C_b = \alpha \Delta p_{CO2}$



we can obtain:

$ k_w =\displaystyle\frac{ F }{ \alpha \, \Delta p_{CO2} }$

ID:(12214, 0)



Velocidad de transferencia en el modelo de penetración

Equation

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El modelo de difusión y el de renovación de la superficie por torbellinos tienen falencias por lo que se ha creado un tercer modelo que asume que el gas penetra y con ello cambia la situación para la transferencia de los gases.

En ese caso con se asume

$ \displaystyle\frac{1}{ k_w } = \displaystyle\frac{ h }{ D } + \displaystyle\frac{ 1 }{ 1.13 }\sqrt{\displaystyle\frac{ \tau }{ D }}$

ID:(12231, 0)



CO2 exchange, speed from water

Equation

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The transport velocity of the gas, denoted as kw, can be modeled based on measured data. Firstly, it depends on the rate at which the system removes carbon from the air-water interface, making the transport velocity proportional to the relative velocity between the two mediums.

Secondly, there is an effect of ion mobility, which can be described by the Schmidt number, representing the ratio of momentum diffusion to particle diffusion. However, this dependence is non-linear and influenced by a factor n ranging between -1/2 and -2/3, depending on the surface roughness.

Lastly, the transport velocity also depends on a constant that, in turn, is determined by the level of surface roughness.

Taken together, the gas transport velocity kw can be described as follows:

$ k_w = u_* \beta Sc ^ n $

$n$
Exponente de Schmidt
$-$
$\beta$
Factor beta del transporte aire a agua de CO2
$-$
$Sc$
Numero de Schmidt
$-$
$k_u$
Velocidad de transferencia aire a agua de CO2
$m/s$
$u_a$
Velocidad del aire
$m/s$

ID:(12215, 0)



Schmidt\'s number Sc

Equation

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The Schmidt number establishes a relationship between viscous diffusion

$ D_p \equiv \displaystyle\frac{ \eta }{ \rho }$



and particle diffusion

$ D_N \equiv \mu k_B T $

.

The former is equal to viscosity divided by density, while the latter corresponds to the diffusion constant. Therefore, it is defined as follows:

$ Sc =\displaystyle\frac{ \eta }{ \rho D }$

$D$
Constante de difusión en masa acuosa
$m^2/s$
$\rho$
Densidad en capa de masa acuosa
$kg/m^3$
$Sc$
Numero de Schmidt
$-$
$\eta$
Viscosidad en masa acuosa
$Pa s$

ID:(12216, 0)



Transfer rate and relative speed

Description

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In a first approximation, the dependence of the transfer velocity $k$ on the relative velocity $u_*$ is linear.

ID:(12298, 0)



Transfer rate and Schmidt number

Description

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The relationship between the transfer velocity is inversely proportional to the Schmidt number raised to a fractional power.

The value of the fractional power depends on the roughness of the water surface, ranging from 1/2 for rough surfaces to 2/3 for smooth surfaces.

ID:(12299, 0)



Solubility as a function of Schmidt number

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The solubility of the gas $\alpha$ is a function of the mobility of molecules, which is described by the Schmidt number. This relationship is directly observed in the representation of measured values.

Ocean-Atmosphere Interactions of Gases and Particles, Peter S. Liss, Martin T. Johnson (eds.), Springer-Verlag Berlin Heidelberg

ID:(12245, 0)



Grosor superficie y capa viscosa

Equation

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El grosor de la superficie y de la capa viscosas son proposicionales siendo la constante una función de la constante difusión, viscosidad y densidad.

Por ello con es

$ \delta_c = \sqrt{\displaystyle\frac{ \rho D }{ \eta }} \delta_{\eta}$

ID:(12229, 0)



Disipación de energía en capa superficial

Equation

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La energía disipada se puede estimar de la viscosidad, densidad y grosor de la capa.

Por ello con es

$ \epsilon = \displaystyle\frac{ \eta ^3 }{ \rho ^3 \delta_{\eta} ^4 }$

ID:(12230, 0)



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