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ID:(1032, 0)

Limite estacioanrio Membrana Basal sin Hatch

Beschreibung

En el caso estacionario sin hatch no existe difusión perimetral y los flujos radiales totales tanto en la membrana basal como en la intermedia deben ser cero. Por ello se tiene que

$J_{e,k}-J_{e,k}=0$

y

$J_{a,k}-J_{n,k}=0$

Como

$J_{e,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_l\Delta s}{\pi R_l^2}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{e,k}}{d_e}\right)$

$J_{a,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_{e,k}}{d_e}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{a,k}}{d_a}\right)$

$J_{n,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{3o}}{c_{3o}}\displaystyle\frac{N_{a,k}}{d_a}-\displaystyle\frac{j_{3i}}{c_{3i}}\displaystyle\frac{N_n}{d_n}\right)$

se tiene que el número de moleculas de glucosa en un largo $\Delta z$ es

$N_{e,k}=\displaystyle\frac{N_nR_l^2c_{1i}c_{1o}c_{3o}d_ej_{1i}j_{3i}\pi+\Delta sN_lc_{1i}^2c_{3i}d_ed_nj_{1o}j_{3o}+\Delta sN_lc_{1i}c_{3i}c_{3o}d_ed_nj_{1i}j_{1o}}{j_{3o}(R_l^2c_{1i}^2c_{3i}d_nj_{1o}\pi+R_l^2c_{1i}c_{1o}c_{3i}d_nj_{1i}\pi)+R_l^2c_{1o}c_{3i}c_{3o}d_nj_{1i}^2\pi)}$

ID:(8548, 0)

Limite estacionario Membrana Intermedia sin Hatch

Beschreibung

$J_{e,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_l\Delta s}{\pi R_l^2}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{e,k}}{d_e}\right)$

$J_{a,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_{e,k}}{d_e}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{a,k}}{d_a}\right)$

$J_{n,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{3o}}{c_{3o}}\displaystyle\frac{N_{a,k}}{d_a}-\displaystyle\frac{j_{3i}}{c_{3i}}\displaystyle\frac{N_n}{d_n}\right)$

se tiene que el número de moleculas de glucosa en un largo $\Delta z$ en la membrana intermedia es

$N_{e,k}=\displaystyle\frac{(j_{3i}(N_nR_l^2c_{1i}^2c_{1o}c_{3o}d_aj_{1o}\pi+N_nR_l^2c_{1i}c_{1o}^2c_{3o}d_aj_{1i}\pi)+\Delta sN_lc_{1i}^2c_{3i}c_{3o}d_ad_nj_{1o}^2}{j_{3o}(R_l^2c_{1i}^2c_{1o}c_{3i}d_nj_{1o}\pi+R_l^2c_{1i}c_{1o}^2c_{3i}d_nj_{1i}\pi)+R_l^2c_{1o}^2c_{3i}c_{3o}d_nj_{1i}^2\pi)}$

ID:(8549, 0)

Algoritmo

Modell

Variablen

Symbol

Text

Variable

Wert

Einheiten

Berechnen

MKS-Wert

MKS-Einheiten

$c_o$

c_o

Concentración Externo

1/m^3

$c_i$

c_i

Concentración Interno

1/m^3

$c_{so}$

c_so

Concentración Saturada Externa

1/m^3

$c_{si}$

c_si

Concentración Saturada Interna

1/m^3

$j_{so}$

j_so

Flujo Saturado por Largo Externo

$j_{si}$

j_si

Flujo Saturado por Largo Interno

$J_V$

J_V

Fluss

m^3/s

$\Delta z$

Largo de Capilar

Berechnungen

Gleichung

Zahl

Zuerst die Gleichung auswählen:

, dann die Variable auswählen:

Symbol

Gleichung

Gelöst

Übersetzt

Berechnungen

Symbol

Gleichung

Gelöst

Übersetzt

Variable

Gegeben

Berechnen

Ziel :

Gleichung

Zu verwenden

Gleichungen

$J_{k+1,k}=-D\Delta z\,d\displaystyle\frac{(c_{k+1}-c_k)}{\Delta s}$

(ID 8468)

$N_k=c_k\Delta z \Delta s\,d$

(ID 8469)

$N_k(t+\Delta t) = N_k(t)+(J_{k,k-1}-J_{k+1,k})\Delta t$

(ID 8470)

$N_k(t+\Delta t) = N_k(t)+D\displaystyle\frac{(N_{k+1}+N_{k-1}-2N_k)}{\Delta s^2}\Delta t$

(ID 8471)

$J=\left(j_{si}\displaystyle\frac{c_i}{c_{si}}-j_{so}\displaystyle\frac{c_o}{c_{so}}\right)\Delta z$

(ID 8472)

$J_{e,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_l\Delta s}{\pi R_l^2}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{e,k}}{d_e}\right)$

(ID 8473)

$J_{a,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_{e,k}}{d_e}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{a,k}}{d_a}\right)$

(ID 8474)

$J_{n,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{3o}}{c_{3o}}\displaystyle\frac{N_{a,k}}{d_a}-\displaystyle\frac{j_{3i}}{c_{3i}}\displaystyle\frac{N_n}{d_n}\right)$

(ID 8475)

$N_{e,k}(t+\Delta t) = N_{e,k}(t)+(D\displaystyle\frac{(N_{e,k+1}+N_{e,k-1}-2N_{e,k})}{\Delta s^2} + J_{ek} - J_{ak})\Delta t$

(ID 8476)

$N_{a,k}(t+\Delta t) = N_{a,k}(t)+(D\displaystyle\frac{(N_{a,k+1}+N_{a,k-1}-2N_{a,k})}{\Delta s^2} + J_{ak} - J_{nk})\Delta t$

(ID 8477)

$J_h=D\displaystyle\frac{s_h}{d_h\Delta s}\left(\displaystyle\frac{N_{e,0}}{d_e}-\displaystyle\frac{N_{a,0}}{d_a}\right)$

(ID 8478)

Beispiele

Limite estacioanrio Membrana Basal sin Hatch

En el caso estacionario sin hatch no existe difusi n perimetral y los flujos radiales totales tanto en la membrana basal como en la intermedia deben ser cero. Por ello se tiene que

$J_{e,k}-J_{e,k}=0$

y

$J_{a,k}-J_{n,k}=0$

Como

$J_{e,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_l\Delta s}{\pi R_l^2}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{e,k}}{d_e}\right)$

$J_{a,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_{e,k}}{d_e}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{a,k}}{d_a}\right)$

$J_{n,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{3o}}{c_{3o}}\displaystyle\frac{N_{a,k}}{d_a}-\displaystyle\frac{j_{3i}}{c_{3i}}\displaystyle\frac{N_n}{d_n}\right)$

se tiene que el n mero de moleculas de glucosa en un largo $\Delta z$ es

(ID 8548)

Limite estacionario Membrana Intermedia sin Hatch

$J_{e,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_l\Delta s}{\pi R_l^2}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{e,k}}{d_e}\right)$

$J_{a,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{1o}}{c_{1o}}\displaystyle\frac{N_{e,k}}{d_e}-\displaystyle\frac{j_{1i}}{c_{1i}}\displaystyle\frac{N_{a,k}}{d_a}\right)$

$J_{n,k}=\displaystyle\frac{1}{\Delta s}\left(\displaystyle\frac{j_{3o}}{c_{3o}}\displaystyle\frac{N_{a,k}}{d_a}-\displaystyle\frac{j_{3i}}{c_{3i}}\displaystyle\frac{N_n}{d_n}\right)$

se tiene que el n mero de moleculas de glucosa en un largo $\Delta z$ en la membrana intermedia es

(ID 8549)

ID:(1032, 0)