PROCESO DE ELABORACIÓN DEL QUESO

In order to characterise the 3!RT response to fluid flow, a simple single channel microfluidic device was designed. The channel was 20 mmlong and had a 125µm_⇥125µmsquare cross- section. A 3!RT was integrated into the base of the channel, such that it was directly exposed to fluid in the channel. To fabricate the device, a channel mould was machined using the CNC milling process described previously in Section 6.2.1. Negative replica moulding was used to produce the channel in PDMS. The RT was pre-fabricated on the microscope slide using lift-o↵ patterning, as described in Chapter 3. The microscope slide, RT, and microfluidic channel were then manually aligned and permanently bonded with oxygen plasma. Three RT designs were tested, linear (perpendicular to flow), linear (parallel to flow), and serpentine (perpendicular to flow). These di↵erent designs were tested to establish the e↵ect of the RT geometry on the 3! response to fluid flow. These three designs are shown in Figure 6.5. The linear RT designs are identical to a standard 3! method RT.

Calibrated fluid flow between 0 and 400µl/min was generated in the channel via a syringe pump (Harvard Apparatus, PHD 2000) and external flow sensor (Elveflow). The process for acquiring the 3! frequency response followed the same procedure as the “classical” 3! method measurements. As such, the recorded 3! voltage can be directly transformed into a temperature [6] via,

T(2!) = 2X3!

I!Re0↵

(6.1) whereT(2!) is the temperature response at 2!,X3! the in-phase third harmonic voltage,I!

the fundamental heating current, Re0 the zero current resistance of the RT element, and ↵ the temperature coefficient of resistance. In order to relate the temperature response of the RT to the fluid velocity, a control measurement with the fluid stationary was recorded. This was intended to capture all thermal transport mechanisms not related to fluid motion. A measurement with the fluid in motion would then produce a signal change from the control that is a function of fluid velocity, and thermal wavelength via the thermal frequency. For the purposes of this work, it is proposed that the temperature response due to the fluid motion (convection) can be found by,

Tf low( ) =Tf luid motion( ) Tf luid stationary( ) (6.2)

where is the thermal wavelength of an AC thermal wave,Tf low( ) the temperature response

due to fluid motion as a function of thermal wavelength, Tf luid motion( ) the temperature

response of the substrate and moving fluid, andTf luid stationary( ) is the temperature response

due to the substrate and stationary fluid. This linear subtraction of control and sample response is similar to that of the di↵erential 3! method, and forms a starting hypothesis for the purposes of this work. It assumes that phonon conduction in the fluid is independent of fluid motion, and that the convection and conduction response are linearly separable. This assumption is supported through literature in the form of the Nusselt number, a dimensionless number expressing the ratio of convective and conductive thermal transport in a fluid. In the calculation of the Nusselt number, the conductive coefficient is a constant property of the material [179]. This supports the assumption that the stationary fluid measurement will sufficiently control for the conductive transport in the system.

In the “classical” 3!method, the slope of the in-phase response withln(2!), or the magnitude of the out-of-phase response, are both proportional to the thermal conductivity of the material surrounding the RT [6]. In a quasi-static fluid velocity field then, the 3!temperature response should be related to the fluid velocity at a distance from the RT related to the thermal wavelength ( ). The exact solution to this problem is complicated, and is outside the scope of this thesis. As such, an interim model is proposed purely for this work. This model essentially proposes that, based on the “classical” 3! method, that the velocity at some distance from the RT will be related to the second derivative of the in-phase response, or the first derivative of the out-of-phase response with respect to thermal wavelength. Formally,

c_/ 2_X T2! 2 and c/ YT2! (6.3)

where c is fluid velocity, XT2! is the in-phase temperature response, and YT2! is the out-

of-phase temperature response. The fluid velocity inside a microfluidic channel is generally considered to be parabolic [180]. It is stationary at the walls and is at its maximum in the centre of the channel. This can be represented by a piecewise parabola, shifted by the channel dimensions. This is,

⌫(r) = 8 > > > < > > > : 0 x <0 A·(r R₂)2 _{2RA 0< r <2R} 0 x >2R (6.4)

Where ⌫(r) is the velocity as a function of distance r, R the half-width of the channel, and

A the peak velocity in the channel. Following Equation 6.3 and 6.2, the expected response will have the a polynomial form of the order x4 _{and x}3 _{for the in-phase and out-of-phase} temperature response, respectively.