## 4 Spatial Resolution of the Measurements
### 2D Diffusion Influence
As the first criterion, we will consider that a variation of the wall temperature (dry side) of 1 \({}^{\circ}\)C is enough to detect a bubble attached to the wall. In order to consider bubble timescales to be measurable, a second criterion was set. The detachment of the bubble will induce a slightly higher temperature variation so that a second step corresponding to a variation of 2 \({}^{\circ}\)C of the wall temperature is considered. Moreover, conventional detectors for high-speed, high-performance cameras have pixel sizes in the range of 10 to 25 \(\upmu\)m. The bubble detection criterion for the size of the influence area \(d\) is, therefore, set at 2 pixels or 50 \(\upmu\)m.  
As an example, Figure 20 shows (for a bubble size corresponding to 120 \(\upmu\)m for a pressure of \(P=50\) bar and a temperature variation of 5 \({}^{\circ}\)C under the nucleation site) the limit thickness selection, with the red-dashed curve named the 1 \({}^{\circ}\)C limit for the detected first criterion and the blue-dashed curve named the 2 \({}^{\circ}\)C limit for the measurement of the second criterion. Figure 19: Influence area during a bubble growth on a nucleation site. This area can be characterized by the size \(d\) and the amplitude of the thermal disturbance \(A\) for the dry side of the plate. The determination of the thickness is done in two steps:  
* The first step consists of identifying the thickness corresponding to the camera-readable amplitude of the dry-side temperature variation (example Figure 20; criteria 1 gives a 170 \(\upmu\)m of thickness, criteria 2 gives 110 \(\upmu\)m of thickness. ),
* The second step determines the dry-side influence area considering the two temperature criteria (see Figure 21; criteria 1's thickness is valid (\(d_{1}\) = 60 \(\upmu\)m), but criteria 2 correlates with 100 \(\upmu\)m of thickness (\(d_{2}\) = 60 \(\upmu\)m)). Table 1 summarizes (for the pressure and bubble size) the thickness corresponding to the first and second sets of criteria defined above. These values were identified after the two steps of checking the amplitude and area of influence explained before. Figure 21: Example of the verification of the zone of influence of the temperature variation according to criteria 1 and 2. Here, for a pressure of 20 bar, for a thickness of 170 \(\upmu\)m (**left**), criterion 1 is respected, the zone of influence is 60 \(\upmu\)m; for the second criterion (**right**), it is necessary to reach 100 \(\upmu\)m of thickness to detect the influence area on the dry side. This problem–solution was solved with the following values: \(N_{x}=50\), \(N_{y}=200\), \(n=50\), \(t_{g}=0.005\) s, \(t_{w}=0.01\) s, \(\Delta t=0.00031\) s, \(P=1\) bar, \(I=400\) A, \(\Delta\)T = 5 \({}^{\circ}\)C, \(C_{P}=502\) J/K-kg, \(\lambda=15\) W/m\(\cdot\)K, \(\rho=7960\) kg/m\({}^{3}\). Figure 20: Example of the determination of the limit thickness at \(y=y_{0}\) for 20 bar pressure, a 120 \(\upmu\)m bubble diameter was imposed. This problem–solution was solved with the following values: \(N_{x}=50\), \(N_{y}=200\), \(n=50\), \(t_{g}=0.005\) s, \(t_{w}=0.01\) s, \(\Delta t=0.00031\) s, \(P=1\) bar, \(I=400\) A, \(\Delta\)T = 5 \({}^{\circ}\)C, \(C_{P}=502\) J/K\(\cdot\)kg, \(\lambda=15\) W/m\(\cdot\)K, \(\rho=7960\) kg/m\({}^{3}\). This result shows that a 50 um thickness is a good compromise to be able to detect bubbles over the plate, to measure the timescales of the bubble growth and to maintain a sufficient thickness to ensure the representativeness of the surface. For higher pressure values, the bubble size calculated with the Unal correlation [3] decreases, and the temperature variation under this bubble could be more complicated to capture.