Microfluidic cell under consideration has two input flow channels, mixing micro chamber and one output (Fig.1). Input channels cross-section is 50 × 50 µm, which are leading to a 50 × 100 µm output.
Fig. 1. Microfluidic cell general view (left), cell drawing (right).
The cell prototype is manufactured over a glass substrate by laser lithography and two pieces are assembled by ultrasound glass ablation. Therefore, glass material properties and channel wall roughness are used in the CFD modeling for wall friction estimation. Modeling is performed via Comsol software.
CFD Model and Governing Equations
A 3D model of the proposed microfluidic cell was created in order to study the, velocity and pressure distributions inside the cell channels. On Fig.2 is shown drawing of created model and its sizes. Fluid-structure interaction is carried out combining fluid-flow and structural mechanics in to calculate the equivalent velocity and pressure values. The cell channel fluid flow is calculated by Navier–Stokes equations [11]
, (1)
where ρ is fluid density, v is fluid velocity vector, I is indentity tensor, p is the pressure and K is kinematic viscosity term, μ is dynamic viscosity coefficient,
, (2)
Fluid domain is considered as incompressible,
. (3)
For inlets a velocity boundary condition is set to 0.02 m/s.
The level set method is used to track the fluid interface of two phase fluid solution, normalized as ϕ=ϕ1+ϕ2=1, it uses the following equation
, (4)
where ε is the interface thickness controlling parameter around the interface boundary, set to 1/2 from the maximum element size in the domain. Model mesh statistics is shown in Table II.
The density is a function of the level set function. Let ρ1 and ρ2 be the densities of two mixing fluids. Here, the first fluid corresponds to the domain where ϕ1<0.5, and second fluid corresponds to the domain where ϕ2>0.5. When density averaging is set to volume average, the density is defined as
. (5)
Similarly, the dynamic viscosity can be defined by setting viscosity average μ to volume average
, (6)
where μ1 and μ2 are the dynamic viscosities of mixing fluids, material properties are presented in Table I.
Glass architecture is manufactured by laser lithography, channel wall roughness is dependent from optical power and speed of glass melting. Channel wall roughness, used for wall friction drag force F in equation (1) estimation, is set to 0.2 µm.
Modeling and Measurement Results
Calculated results velocity field stream lines in the mixing chamber domain are presented in Fig.2.
Micro-convective effects are observed in the modeled results, which are related with channel cross-section changes. Pressure drop is observed, which is dependent from achieved channel fluid velocity. Calculated pressure in the microfluidic cell mixing chamber cross-section is presented in Fig.2.
Fig. 2. Transient pressure distribution of moving oil droplet insertion in the mixing chamber domain filled with water. Simulation end time is 0.1 s.
Material properties used for CFD two phase modeling are presented in Table I. Base fluid is water with density and dynamic viscosity as shown. Oil like fluid is injected in upper cell channel into the water. Transient pressure distribution of moving oil droplet insertion in the mixing chamber domain filled with water is shown in Fig.3.
Table I Material properties.
Fig. 3. Calculated velocity field stream lines in the mixing chamber domain.
Modeling results for CFD problem solving are confirmed by single cell acoustic spectrum measurements. Measuring ceramic microphone is directly located over the cell mixing chamber with frequency bandwidth of 44 kHz. Fluids are pumped with precise Cytosurge FluidFM MFCS v2 fluid controlled with single 0.2 Pa pulses during testing.
Calculated velocity field stream lines in the mixing chamber domain, after oil droplet insertion are shown in Fig.4. They are covering 200 ms time range. A main fluid vortex around low density droplet is visible in all frames of the simulation. Time dependent fluid pressure variations are considered as a sound source with same frequency content determined by pressure transients. These pressure variations are transmitted to microfluidic cell surface and acquired by mounted microphone crystal.