Investigation of the phenomena occurring near the liquid–vapor interface during evaporation of water at low pressures

The evaporation of water in a rectangular microchannel at low pressures was studied experimentally and numerically to demonstrate the interplay between the heat transfer and fluid dynamics during evaporation of the liquid at low pressures. The three-dimensional flow below the interface was quantified using scanning particle image velocimetry. Temperatures in the fluids on the centerline in both phases as well as the liquid temperatures along the interface were measured with a fine thermocouple. A numerical simulation, which accounted for the transport of mass, momentum, and energy in the fluids as well as those at the interface, was developed and validated with the measured experimental data. Once good agreement between the model and the experimentally obtained parameters was achieved, the model was used to examine some aspects of the evaporation phenomenon which could not be understood from the experiments alone. An important result from this work has shown that a buoyancy driven flow in the liquid water competes with a thermocapillary flow at the interface and does not allow the thermocapillary flow to spread over the interface. This is suggested to be a possible answer to the the question of why a thermocapillary flow in water, in contrast to many other liquids, does not always exist.

Figure 1

The vacuum chamber and other components used in evaporation experiments. The cuvette and copper block are magnified to enhance small details.

Figure 2

The configuration of the thermocouple used in the temperature measurements. Due to the concave interface, a small portion of the vapor above the interface which appears as a dark region was not visible. The lower edge of the dark region shows the interface at the center plane, and the upper edge indicates the interface in contact with the front wall. The junction and a portion of the fine wires could not be seen as the thermocouple measured the interfacial temperatures in the vapor.

Figure 3

Representation of the simplified experimental setup that was studied numerically. Only half of the domain was simulated due to symmetry. The thermocouple was not included in the simulation. The cuvette and copper block are magnified to enhance small details.

Figure 4

3C3D experimental velocity vectors below the evaporating meniscus for a typical pressure of 190 Pa. The arrow size and color scale to the local velocity magnitude. Only every 150th arrow from 1 650 000 available data points is illustrated to avoid cluttering the image. The dimensions are shown in millimeters. The front wall is named according to the position of the camera.

Figure 5

Comparison of the simulated and experimental velocity magnitudes in the liquid at three pressures. The top row compares the experimental and simulated velocities assuming in the model that the liquid slipped freely along the interface [Eq. (14)]. The second row compares the experimental and simulated velocities assuming in the model that the liquid did not slip along the interface. Only one quarter of the liquid is shown. The experimental velocities within a fraction of the liquid volume below the interface could not be measured due to the high reflection of light emitted from accumulated PIV particles at the interface. The third row compares the experimental and simulated x-component of the velocity at the center plane $\left(xz\right)$ and 3 mm away from the centerline $\left(x=3\mathrm{mm}\right)$. Only every third experimental data point is shown. When the tangential velocity at the interface was set to zero in the simulation, excellent agreement between the simulation and the PIV results was achieved.

Figure 6

(a) Simulated temperature distribution on a horizontal plane below the interface. Colors represent the temperatures. The solid curves on the plane show the contours of density of the liquid. A clear outline of the liquid–vapor interface is illustrated above the horizontal plane. The liquid near the solid walls is warmer and denser. (b) Simulated velocity magnitude and direction at $P^V=300$ Pa. Only one quarter of the liquid close to the interface is shown to display the details in the center. Buoyancy forces induce the large vortex that flows outward near the interface. Thermocapillary forces produce the small flow near the contact lines which flows inward.

Figure 7

Experimental and simulated temperature profiles in the liquid and vapor along the centerline at five pressures. The position zero denotes the interface. The temperature profile in the liquid at 190 Pa was not measured to avoid freezing of the liquid.

Figure 8

Interfacial temperatures in the liquid during evaporation at 382 Pa. (a) The distribution of the liquid temperature at the interface obtained from the numerical simulation and indication of the location of points ABCD (b) The experimentally measured temperatures at A, B, C, and D and comparison with the simulated temperatures along the curve ABCD.

Figure 9

Experimental and simulated evaporation fluxes as a function of pressure in the vacuum chamber. The black and open diamonds were measured in this study. Each data point shows the average of three measurements. The error bars show the maximum and minimum values and are covered by the data points. The red circles show the measured fluxes in a similar cuvette which are extracted from Ref. [42]. The solid curve indicates the results of the simulation for the case in which the tangential velocity was allowed at the interface. The simulated curve of the evaporation flux by assuming a zero tangential velocity at the interface is not shown as it overlaps the solid curve. The dashed curve shows the results of the simulation for the case when an estimated value of radiative heat flux was added to Eq. (17).

Figure 10

(a) The position of the interface vs. time for a typical experiment at 380 Pa. (b) The three images show the recession of the interface and the subsequent stretch of the liquid films. The parameter $H$ shows the distance from the center of the interface to the bottom of the cuvette. (c) A 50-$\mu \mathrm{m}$-thin film with a constant cross section but a variable length of up to 4.2 mm was considered in the simulation to study the contribution of the thin films to the total evaporation rate. The mesh size used in the thin film region was $10\mu \mathrm{m}$. Further refinement of the mesh in this region did not change the velocity and temperature fields or the total evaporation flux from the interface.