Transport Processes In Biologi... - Modeling Of Mass

) because the path is obstructed by cells and extracellular matrix (ECM). Movement driven by fluid velocity ( ), like blood flow or interstitial fluid. Nconv=vCbold cap N sub c o n v end-sub equals bold v cap C 3. Key Applications Oxygen Delivery: Modeling how O2cap O sub 2 moves from capillaries into deep tissue. Since O2cap O sub 2 is consumed by mitochondria, is negative and usually follows Michaelis-Menten kinetics :

𝜕C𝜕t+∇⋅N=Rthe fraction with numerator partial cap C and denominator partial t end-fraction plus nabla center dot bold cap N equals cap R : Concentration of the species. Nbold cap N : Mass flux (movement).

Predicting how a drug spreads through a solid tumor. High interstitial fluid pressure in tumors often opposes inward convection, making diffusion the primary (and often slow) delivery method. Modeling of Mass Transport Processes in Biologi...

Modeling how solutes cross the lipid bilayer via passive diffusion or protein channels (Kedem-Katchalsky equations). 4. Dimensionless Numbers (The "Reality Check") To understand which process dominates, engineers use: Péclet Number ( ): Ratio of convection to diffusion ( , flow dominates (like in large arteries). , diffusion dominates (like in the brain parenchyma).

The core of these models is the , which ensures mass conservation: ) because the path is obstructed by cells

Movement driven by concentration gradients.

(Diffusion Coefficient): In tissues, we use an Effective Diffusivity ( Deffcap D sub e f f end-sub Key Applications Oxygen Delivery: Modeling how O2cap O

: Net rate of production or consumption (e.g., metabolic reaction). 2. The Mechanisms of Flux ( Nbold cap N