"Suction" force of an aspiration catheter with varying cross sectional area Assume there are two catheters:
Catheter A has a constant inner diameter D1, whereas catheter B has an inner diameter D1 at the very tip (distal), but a larger inner diameter D2 in the proximal section

Question: When a vacuum pump generates the same pressure difference across the catheters and "sucks" a blood clot from the distal tip, let's imagine that the blood clot is connected to a load cell. Would the load cell perceive a greater magnitude of force from catheter B? Or would it be the same as catheter A?
According to a published research (https://jnis.bmj.com/content/11/2/190), maximum suction force increased due to a larger proximal inner section. But I do not understand how that is achieved?
According to Bernoulli's principle, the pressure should be the same at the distal and proximal ends when there exists no fluid flow. I would imagine that the "suction" force (or the push force from within the blood vessel) can only be increased by increasing the pressure difference applied, or by increasing the tip's cross-sectional area. How does changing the proximal area affect the force applied at the tip? Much thanks!
 A: The system can be approximated with Poiseuille's equation:
\begin{equation}
\Delta P=\frac{8\mu LQ}{\pi R^4}
\end{equation}
where $Q$ is the volumetric flow rate through a catheter.
So, for catheters $A$ and $B$ of equal lengths with the same pressure difference ($\Delta P$) between their endpoints,
\begin{equation}
\Delta P = \frac{8\mu (L_1+L_2)Q_A}{\pi R_2^4}=\frac{8\mu L_1 Q_B}{\pi R_1^4}+\frac{8\mu L_2 Q_B}{\pi R_2^4}
\end{equation}
where $R_2$ is the smaller radius, and $R_1$ the larger one. Rearranging, one finds:
\begin{equation}
Q_A=Q_B\left( \frac{L_1}{(L_1+L_2)}\frac{R_2^4}{R_1^4}+\frac{L_2}{L_1+L_2} \right)
\end{equation}
You can check that the quantity inside the brackets is less than 1 (it becomes 1 in the limit $R_2\to R_1$). This implies that $Q_B>Q_A$, i.e. the flow rate of blood through catheter $B$ is greater than that through catheter $A$. This is possible because the pressure gradient along their lengths are different, despite the total pressure difference being equal in both cases.
Intuitively, this also makes sense since a larger cross-sectional area means that there is more "room" for blood to flow. As an analogue, think of e.g. 1 traffic lane opening up into 2 lanes vs only having 1 lane for the entire length of the road.
