Explain and label the axes and any variables

Reference no: EM13195539

For a microfluidic device, two Newtonian fluids (A and B) are flowing in a unidirectional flow inside a thin horizontal rectangular slit of thickness d due to an applied pressure gradient along the length L of the channel. The fluid flow rates have to be adjusted such that the slit is half filled with A and half fillled with B and the two remain in laminar flow to minimize mixing. Assume that Density of B < Density of A and that R = viscosity of B/ viscosity of A is the ratio of the viscosities of the two liquids. The liquids can be assumed to be immiscible.

(a) Draw a schematic of the flow. Clearly define and label the axes and any variables to be used. Indicate on the schematic the
fluid on top and bottom of the slit.

(b) Find the expression for the volumetric flow rates of the two fluids as a function R by applying equation of continuity and the Navier-Stokes equations. Clearly state assumptions for simplification of the N-S equations, the boundary conditions applied, and the solution of the differential equations. Then plot the ratio of volumetric flow rates of the two fluids as a function of R ranging from 0.1 to 10.

(c) If one of the fluids is water and the other fluid is 1,2-Dichlorobenzene and the Reynold's number of 2100 indicates the transition from laminar flow, what is the maximum pressure gradient (SI units) that can be applied along the length of a slit with width 5 cm? Also find the average velocity of the two fluids at this maximum pressure drop.

Reference no: EM13195539

Questions Cloud

How rapidly is the area enclosed by the ripple : How rapidly is the area enclosed by the ripple increasing when the radius is 5 feet?

What are the length and width of the rectangle : The dimensions of a rectangle are such that its length is 3 in. more than its width. If the length were doubled and if the width were decreased by 1 in., the area would be increased by 234 in.^2. What are the length and width of the rectangle?

Find the amount of all 4 pizzas tyrone sold during dinner : tyrone is selling 4 pizzas by the slice to help raise money for the marching band. After lunch, he has 2 1/2 pizas remaining. During dinner he sells 1/4 remaining pizza. Write an expression can be used to find the amount of all 4 pizzas Tyrone sol..

Humidity as outlined in the procedure for the experiment : The atmospheric pressure was measured to be0.9337 atm, the room temperature was 20.00oC. At this temperature, the vapor pressure of water is 17.50 torr -- but assume a 50% relative humidity as outlined in the procedure for this experiment.

Explain and label the axes and any variables : Draw a schematic of the flow. Clearly define and label the axes and any variables to be used. Indicate on the schematic the fluid on top and bottom of the slit.

What is the range of national ecological footprints : What components go into the footprint calculation for a nation? Per capita, what is the range of national ecological footprints from the largest to the smallest country?

State what is the ph of the final solution : What is the pH of the final solution? Answer IS 7.58 Q 3.) What additional volume of 10.0 M HCl would be needed to exhaust the remaining capacity of the buffer after the reaction described in Part B?

What are the expected ratios among progeny : What are the expected ratios among progeny that result from these matings and How many Punnett squares will you have (including crosses between homozygotes)

Protein disulfide isomerase : If you were to remove the ER retrieval signal (KDEL) from protein disulfide isomerase (PDI), which is normally a soluble resident of the ER lumen, where would you expect the modified PDI to be located? Why?

User Account

All Pages