# What is the spatial profile of fluid infiltration within an anisotropic medium?

+ 0 like - 0 dislike
90 views

Starting at time $t = 0$, a unit of compressible fluid of volume $v$ and density $\rho_f$ is pumped into a medium at some location $\mathbf{r}_0$. Initially, the density $\rho_m(0)$ and pressure $P_m(0)$ of the medium are constant everywhere; furthermore, $\rho_f = a\rho_m (0)$ and $P_f = bP_m(0)$ where $a >>1$ and $b << 1$. The medium is anisotropic, such that the fluid is $x$ times more likely to diffuse along $\hat{\mathbf{z}}$ than along all other directions. The time rate of fluid delivery decreases with the amount of stress exerted by fluid already delivered into the surrounding medium. [1]. After how much time does fluid delivery end? [2]. Over what total volume $V$ has the fluid diffused? [3]. What is the shape of $V$?

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:$\varnothing\hbar$ysicsOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.