The simulation of fluid flow, diffusion and convective, and electric conductivity in biochip microfludic vortex chamber performed using COMSOL Multiphysics in order to investigate the fluid flow in both the main channel and the vortex chamber, calculate the change in ion concentration with time and calculate the measured vortex chamber fluid electrical resistance and hence conductance.
In this report, we presented results made possible by use of fluid dynamics, convective and diffusion, electromagnetic modules of COMSOL Multiphysics. These modules deal with movement of fluid in biochip microfluidic vortex chamber, the diffusion and concentration with time of fluid also the electric conductivity between electrodes in chamber. Also, illustrate how the fluid flow in the media channel and move in chamber.
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Biotechnology is a new technology in order to produce or modify molecules, to develop new and useful products, processes, or services. However, It is important in biotechnology, to assess and understand how reactions occur in the cells in order to change the physical and chemical environment of it to develop a product or production of a new product using biochip microfluidic.
Microfluidic biochips revolutionized the clinical diagnosis and DNA Sequence, and other procedures involving molecular biology. Development in microfluidic technology has given the possibility in the analysis of enzymatic and DNA analysis, which included the analysis of proteins and protein peptides, immune, drug delivery implant devices, environmental monitoring toxicity. Also carrying out further tests on the biological biochip at the same time, integration and complexity of the design system is expected to rise dramatically.
However, in this paper we have vortex chambers in which are circular is nature with an opening onto a main outlet channel and a narrow control channel opposite the opening. Cells can be directed into and out of the chamber by a number of means. The simplest method for directing cells into the chamber is to restrict the fluid flow through the outlet channel and direct all flow through the control channel. Once cells are within the chamber, closing the control channel allows cells to be held within the containment chamber. Allowing a fluid to flow along the media channel, past the entrance to the vortex chamber, causes the fluid within the vortex chamber to move and circulate. While a small portion of the fluid within the chamber will flow into the media channel, this is balanced by fresh media entering from the media channel into the vortex chamber. At the same time, chemical species in the circulating fluid within the vortex chamber diffuse into the fluid stream within the media channel and vice versa. Cells within the vortex chamber are carried by the fluid flow and circulate around the chamber so keeping the cells in suspension. There is little diffusive movement of cells from the containment chamber to the media channel due to their low diffusion rate. Figure 1 shows a schematic diagram of the vortex chamber including a series of optional microelectrodes which can be fabricated on either or both of the upper and lower surfaces of the containment chamber. The electrodes can be used to sense changes within the chamber fluid composition.
However, the model geometry for a vortex chamber is as shown in figure . Assume that at the start of the modelling the vortex chamber contains a sodium chloride solution with a concentration of 150mM. The fluid in the main channel is water (sodium chloride concentration 0mM) and a voltage of 1V is applied to alternate electrodes with all other electrodes connected to 0V. As the fluid in the main chamber flows, sodium and chloride ions will diffuse into the main channel. We will use COMSOL Multiphysics to find how the fluid flow in both the main channel and the vortex chamber, calculate the change in ion concentration with time and calculate the measured vortex chamber fluid electrical resistance and hence conductance.
In this section we will present physical equations which we can use it when we deal with fluid flow in the vortex chambers.
The flow of fluids is describe using the Navier-Stokes equation which can used to most phenomena observed in fluid mechanics. However, fluid flow can be turbulent or laminar . Reynolds number (Re) used to divide fluid flow to laminar or turbulent .
If Re < 1,400 the flow is laminar so if Re < 2,100 the flow is turbulent. Generally, fluid is incompressible under this condition
Which means that the density of fluid is constant . However, Navier-stokes equation in this case is:
2 u +(u.)u +
Where is the rate of change in momentum or net acceleration, is convection force, n2 u is viscous force, is pressure force and F is the external body force.
The velocity of laminar flow between parallel plate various from zero at the walls to a maximum along the centerline of the vessel as shown in figure
However, the diffusion in laminar flow is need to be folded rather than stirred because the laminar flow is hard to mix the molecular diffusion is just transport process between layers. The general diffusion equation as follow:
Where c is the concentration, D diffusion coefficient and R is the reaction rate.
On the other hand, the conductivity of water is depend on concentration of dissolved salts. Electric conductivity of water sample is used to calculate how salt-free , ion-free or impurity-free the sample is. therefore, pure water has low conductivity. We can get the electric conductivity from this equation:
Where is the current density and E is the electric field . Also, we can get the conductivity from the mobility as this equation state:
Where n is the number density , e is electron charge and is the mobility.
In order to calculate the measured vortex chamber fluid electrical resistance and hence conductance ,also to find out how long does it take for the vortex fluid conductance to reach that of the fluid in the media channel for media channel peak fluid velocities from 10ÎÂ¼m/s to 100ÎÂ¼m/s. we will deal with the model geometry in three stages:
fluid flow was simulated using incompressible form(steady-state analysis) of Navier-Stokes equation in 3D from model Navigator in COMSOL Multiphysics . we used option in COMSOL and chose content and we created table with these values :
H2O- diff = o.2272e-8
where (h2o- diff ) water diffusion coefficient , rho is density, eta is viscosity , v0 is velocity.
Then, subdomain settings was selected from the physics menu. We defined the physical properties of the fluid, in this case viscosity and density according to the values above. The Naver ââ‚¬”stokes equation for the subdomain was:
This subdomain for both main channel and the vortex chamber .
After that, boundary expression selected from expression in option menu to add the expression for laminar flow which equal:
Then, boundary setting selected from physics menu and the inlet wasdefine with laminar expression where the equation for the boundary condition velocity inlet was:
We did that because the flow was laminar . Also, the boundary condition for outlet defined as pressure as following:
This was to set the outlet pressure to 0 Pa gauge.
The boundary condition equation for outlet was:
Where n is viscous stress. Then, we kept other boundary type as wall where the boundary condition for it ( no slip).
Diffusion and convection
We stayed with the same model geometry . Diffusion of fluid was simulated using model navigator , selected COMSOL Mulitphysics and chose convection and diffusion.
Subdomain setting was selected from the physics menu. The equation for subdomian was:
ts c2 concentration
Where ts =1 time- scaling coefficient, D (isotropic)= 2.032e-6 m2/s diffusion coefficient for Chlorine. We put diffusion for chlorine because it was the same result when we put Sodium diffusion coefficient. This subdomain for both main channel and chamber. We put the concentration of main channel zero and the chamber 150 Mm.
Then, boundary condition selected from physics menu , the inlet was define as concentration and the equation for boundary condition inlet in this case was:
Where we put:
C20=0 mo/m3 concentration because there is no concentration in inlet.
R=0 mo/(m3*s) reaction rate.
u=u m/s x-velocity
v=v m/s y-velocity
w=w m/s z-velocity
and we put the time for concentration 300.then we moved to outlet to boundary condition for outlet. We defined outlet as convective flux because the flux happened in outlet and the equation here was:
Other boundary condition type for main channel and chamber has this equation for boundary condition :
u*N=O , N=-D
In order to calculate the measured vortex chamber fluid electrical resistance and hence conductance. We stayed with the same model geometry which we did the fluid flow and diffusion for it.
Then, we simulated conductivity using model navigator , selected COMSOL Multiphysics . conductive media was selected from electromagnetic.
Subdomain setting was selected from physics menu. The equation for subdomian was:
Where Je =0 A/m2 External current density.
is the conductivity and it is equal 1.89e-3*C s/m electric conductivity.
We calculated the conductivity from this relation:
is the mobility . However, the mobility for Na=0.582 and for Cl=1.0382. The diffusion for Na=1.334e-9and for Cl= 2.032e-9.
This subdomian setting for both main channel and chamber. Then, we moved to boundary setting . Avoltage of 1V is applied to alternate electrodes with all other electrodes connected to 0V. The boundary condition of inlet was formulated as ground , the equation v=o. However, the boundary condition for outlet formulated as electric insulation and the equation was: n*J=0. The boundary condition for the electrode which has 0Vwas v0 =0 electric potential , the equation was V =V0 but the boundary condition for the electrode which has 1V was V0 =1 electric potential, the equation was V =V0 . other boundary condition set as electric insulation and the equation was n*j =0.
Result and discussion
As we mentioned in method section we deal with model geometry in three stages. However, we presented the result according to these steps:
The result from the simulation of fluid flow was as shown in figure . The model shows that the water flowed from the inlet towards the outlet with the control channel away from the containment chamber. The figure shows the fluid flow with the cells in
a viable condition for extended periods of time.on the entrance side which seems larger than the control channel side of the chamber. It is clear that the velocity various in main channel from zero at the wall to the maximum in the center of the media channel and this confirm what we mentioned previously in the Theoretical section. The maximum velocity for laminar flow was 2.246e-5 in the centre of main channel but the minimum velocity was 0 in the walls of the main channel.
The figure shows also the circulatory nature of the fluid flow within the chamber. However, The fluid flow shows higher velocity in the chamber entrance compared to the other places of the chamber.
Diffusion and convection
This figure shows the simulation of diffusion and convection in fluid. The concentration focused in the containment chamber, it contained a sodium chloride solution with a concentration of 150mM. The maximum value for the concentration in the chamber was 6.304e-3 where the minimum value for the concentration was zero in the main channel at inlet this confirm what we mentioned before in theoretical section that the laminar flow it is hard to mix the molecular diffusion is just transport process between layers . The change in the concentration in the chamber occurred as a result of forced convection and diffusion processes between the chamber fluid and the main channel fluid. The figure shows that the Changing in the concentration within the chamber is occurred by changing the composition of the fluid flowing along the main channel with time.
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The result from the simulation of conductivity with time shows how the conductivity change in the chamber with time depend on the change of chemical composition of the fluid in chamber. As we set the electrodes respectively from 1V and 0V in the chamber the conductivity focused between electrodes where it was start reduce conductivity in the entrance of chamber because it is linked with the Main channel which had zero concentration . therefore, the conductivity in the main channel reduced to zero. The maximum conductivity was 1.102 e-5 in the chamber where the electrodes set there and the minimum conductivity was zero in the main channel .
This paper aimed to simulate the flow, diffusion and convective and electric conductivity for the fluid in the vortex chambers which can be used to assess physiochemical changes in biological cells by applying electrokinetic processes which can keep cells in a viable condition for extended periods of time.
The result showed that the fluid flow in the vortex chamber acted as laminar flow in the media channel , the maximum velocity in center of media channel and it was reduce to be zero at walls.
However as we know that chamber contained sodium chloride solution with a concentration of 150mM, the diffusion and electric conductivity were simulated and the maximum concentration and the electric conductivity focussed in the chamber and reduced to be zero in media channel which had zero concentration . The composition fluid in the chamber changing according to the forced convection and diffusion processes between the chamber fluid and the media channel fluid which means that concentration and conductivity changed in chamber with time.
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