V04_Flow Profile of Pressure-Driven Flow in a Microchannel

17 Questions

What type of flow profile is observed in a microchannel with laminar and pressure-driven flow?

Parabolic

In the context of fluid flow, what does the term 'Shear stress' represent?

Force per unit area in the direction parallel to flow velocity gradient

What is the flow profile like in Stokes flow?

Linear

Which type of flow exhibits a velocity profile described by the Poiseuille equation?

Parabolic flow

What is the relationship between shear stress and the rate of change of velocity with respect to distance in a fluid?

Directly proportional

What is the relationship between the decrease of the radius (r0) by a factor of 10 and the increase of fluid resistance (Rfl) in a cylindrical channel, according to the text?

Rfl increases by a factor of 100

In the context of fluid resistance, if the radius (r0) of a cylindrical channel is quadrupled, how does it affect the fluid resistance (Rfl)?

Rfl decreases by 16 times

How does the Hagen-Poiseuille equation relate to Ohm's Law analogy in the context of fluid dynamics?

It emphasizes the similarities in how fluid resistance and electrical resistance are calculated

What is the specialized term used to describe the resistance to flow in a fluid when it flows through a rectangular channel?

Hydraulic resistance

Which geometry for a channel results in the highest fluid resistance as per the text?

Slit-type channel with width much greater than height

In a cylindrical channel, if the length (L) is doubled while keeping other parameters constant, how does it affect the fluid resistance (Rfl)?

Rfl doubles

In a pressure-driven flow through a microchannel, what is the shape of the velocity profile?

Parabolic

What is the relationship between shear stress and velocity gradient in a Newtonian fluid?

Shear stress is proportional to the velocity gradient

What is the characteristic length used in the calculation of the Reynolds number for a microchannel flow?

The diameter of the microchannel

In Stokes flow, what is the relationship between the pressure gradient and the velocity profile?

The pressure gradient is linearly proportional to the velocity

What is the characteristic feature of Poiseuille flow?

The velocity profile is parabolic with a maximum at the center

In a pressure-driven flow through a microchannel, what is the relationship between the volume flow rate and the pressure difference?

The volume flow rate is directly proportional to the pressure difference

Study Notes

Flow Profile of Pressure-Driven Flow in a Microchannel

Water flow in a microchannel with a diameter of 100 µm, velocity of 0.2 m/s, and Reynolds number of 300 µm has a parabolic flow profile.
Entrance length (Le) is the distance needed to establish a parabolic flow profile, which is 0.06 times the Reynolds number times the channel diameter.

Hagen-Poiseuille Equation

The Hagen-Poiseuille equation describes the flow of incompressible fluids in cylindrical tubes and is applicable to laminar flow.
The equation states that the pressure difference (Δp) is proportional to the volume flow rate (Q), the dynamic viscosity (η), and the length of the tube (L), and inversely proportional to the radius (r0) of the tube.

Flow Characteristics

In a microchannel, the flow profile for laminar and pressure-driven flow is parabolic.
Shear stress (τ) is proportional to the derivative of velocity (dv/dy) and is maximum at the channel walls.
The maximum velocity (vmax) occurs at the center of the channel.

Fluid Resistance

Fluid resistance (Rfl) is analogous to electrical resistance in Ohm's Law.
Rfl is proportional to the dynamic viscosity (η), the length of the tube (L), and inversely proportional to the radius (r0) of the tube.
Decreasing the radius (r0) by a factor of 10 increases Rfl by a factor of 10^4.

Other Channel Types

For rectangular channels with w ≈ h, the fluid resistance equation is modified to include the width (w) and height (h) of the channel.
For slit-type channels (w >> h or w << h), the fluid resistance equation is modified accordingly.

This quiz covers the flow profile of pressure-driven flow in a microchannel with specific parameters like water as the fluid, channel diameter of 100 µm, flow velocity of 0.2 m/s, and the concept of entrance length for establishing a parabolic flow profile.

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