<figure><img src="image_118.png" /><figcaption>FIGURE 3. Four drops of blood: (a) sample from a 27-year-old woman in good health, (b) person with anaemia, (c) sample from a 31-year-old man in good health and (d) person with hyperlipidaemia.</figcaption></figure>

(iv) Stage 4 (from 70 to 85 %): the central part of the drop desiccates producing much smaller plaques. Desiccation of the corona finishes and circular drying spots are observed around the corona.

(v) Stage 5 (from 85 to 100 %): the large plaques of the corona move slightly as soon as they are totally desiccated. This concludes the desiccation of the drop and no further changes are observed.

All patterns observed with dried drops of blood present similar characteristics: the central part of the drop, the wide mobile plaques of the corona with wide white cracks, and the fine periphery (figure 2). Whereas the central part of the drop and the fine periphery stick onto the glass plate due to the absence of RBCs, the corona is where mobile deposits form and these do not adhere to the substrate. The explanation of this wetting phenomenon lies in the proteins which exist on the RBCs (glycoproteins). The function of these proteins is to avoid wettability with a wall and, in particular, the internal wall of organs, veins.

At the beginning of drop evaporation, the fluid is homogeneous in colloids, this is why a thin periphery can dry on the glass plate. However, since Marangoni convection is occurring, the RBCs (and other heavy colloids) accumulate at the drop triple line, which is receding. The RBCs accumulate by Marangoni convection to form a solid deposit which will be called hereafter ‘the corona’. The remaining fluid, which consists mainly of serum without heavy colloids, leads to typical small-sized patterns adhering to the glass substrate after its evaporation.

## 3.2. Repeatability and reliability about whole blood experiments

The pattern formation observed in drying drops of blood is totally different for individuals in good health and for those who have a disease. However, for healthy people, the patterns observed are quite similar and are presented in figure 3. They are as follows.
(i) Cases (a) and (c): case (a) is a 27-year-old woman and case (c) is a 31-year-old man, neither smokes or consumes alcohol on a regular basis. The results of drying drops of blood for these two cases reveal the same patterns which will be detailed in §4.

(ii) Case (b): the person is anaemic. The external part of the drop corona is very light-coloured compared to the central part; furthermore, the formation of dark lines is observed in this area and then the appearance of white lines in a central torus which corresponds to a non-wetting situation of the blood on the glass substrate. There are small-sized plaques on the central part of the drop.

(iii) Case (d): the person is hyperlipidaemic. The external part of the drop corona is thick and 'greasy'. This external zone is followed by the formation of intermediate plaques with white lines which also demonstrate a non-wetting situation on the glass substrate. There are small-sized plaques on the central part of the drop.

# 4. Discussion

## 4.1. *Physical mechanisms involved*

Based on the biological and physical properties of blood obtained in the previous section, we can estimate the dominating forces. RBC speed can be measured using flow visualization and is determined to be ~8 µm s⁻¹. With the blood viscosity and density, we obtain a Reynolds number for the internal drop flow of $Re = ρUD/μ ≈ 3 × 10^{-3}$, where ρ is the whole blood density, U is the average speed estimated using a RBC displacement, D is the drop radius and μ is the blood viscosity. The capillary number which compares the viscous and the capillary forces is: $Ca = Uμ/σ ≈ 1.1 × 10^{-6}$, where σ is the blood surface tension. The Rouse number which compares the sedimentation fall velocity and the shear velocity is: $Ro = U_s/(k * \sqrt{τ/ρ}) ≈ 8.2 × 10^{-5}$, where U_s is the sedimentation fall velocity (1 mm h⁻¹ during the first hour) and k is the Von Kármán constant. Consequently, the flow inside the blood drop is driven only by Marangoni convection.

To confirm the different mechanisms involved in the drying process, we compared the evaporation mass flux of three drops: blood, serum and pure water on a glass substrate. The stages of the drops evaporation are all reported in figure 4, where it appears that the drying process is mainly driven by the Marangoni flow, since the blood and serum curves are in agreement with the pure water curve. The colloidal suspension curves (blood and serum) are corrected by dividing the evaporation mass flux by the real fluid mass concentration (which is 76.1 % for blood and 88.1 % for serum, water fluid mass concentration is 100 %, since we use pure distilled ultra-filtered water). Since the evaporation process is related to the fluid phase transition to vapour phase, the solid phase of the suspension is not of concern. One notices that when the blood drop is deposited on the glass substrate, the evaporation mass flux is slightly more important compared with the pure water case. Then this enhancement tends to disappear with time while the colloid concentration changes.

At the beginning of the experiment, the blood drop is deposited and its shape is hemispherical. The RBCs are homogeneously dispersed inside the drop which is about 0.5 mm in thickness and 6 mm in diameter. Marangoni flow is acting (see the supplementary movie), the RBCs movement from the inner of the drop to the periphery is clearly observed. The blood drop desiccates since the water contained in it is evaporating. At the same time due to Marangoni flow, the RBCs are accumulating at the drop periphery creating a layer of biological deposit (cellular components). From 50 % of evaporation time, the drop shape is no more classical with a central
<figure><img src="image_119.png" /><figcaption>FIGURE 4. Evolution of the evaporation mass flux per drop perimeter: a correction for the solid mass fraction (C) is applied for blood and serum taking into account the real fluid mass under evaporation (room temperature, 29°C; microscope glass substrate).</figcaption></figure>

flat area. Marangoni flow is no longer possible and the remaining RBCs are trapped into the central area of the drop, while most of the cellular components have been deposited in the drop corona area. At 70% of the total evaporation time, the central area of the drop starts to completely desiccate and evidences small-sized pattern formation. This last stage of the process is characterized by a sharp decrease of the evaporation mass flux, since the remaining water is that which is inside the RBCs. Finally, after 85% of the total evaporation time, the RBCs which are just shells containing the haemoglobin, crack and free the remaining liquid which can evaporate. This leads to a typical cross-section deposit which can also be called a 'donut' shape.

The drying process behaviour based on the evaporation mass flow rate is not modified by the drop diameter as presented in figure 5. After this, the evaporation mass flux sharply decreases. This second dynamic is clearly related to the absence of convection, since the drop is now mainly a solid with a small amount of liquid remaining inside the red blood cells. The last stage of the drop evaporation consists of the red blood cells shell cracking, which releases the haemoglobin. This last stage of evaporation takes more time since the fluid has to migrate through the solid deposit, which does not wet the glass microscope plate.

As evidenced in figures 4 and 5, the evaporation dynamics can be scaled assuming that the blood is a colloidal suspension composed of pure water and 23.9% by mass RBCs 8 µm in diameter and the serum as a colloidal suspension of pure water
<figure><img src="image_120.png" /><figcaption>FIGURE 5. Evolution of the evaporation mass flux per drop perimeter for five blood drops. The blood comes from the same tube, thus the initial colloid concentration for each drop is identical (room temperature, 29°C; microscope glass substrate; colloid mass concentration, C = 23.9 %).</figcaption></figure>

and 11.9% by mass proteins 1 µm in diameter. For several drop diameters of blood investigated, the same evaporation dynamics is observed like for pure water. Thus, the total evaporation time can be predicted based on the blood haematologic composition by comparison with pure water.

## 4.2. Axisymmetric pattern formation

Depending on the diameter, cracks can be observed as shown in figure 6, where we present drops with different diameters formed simultaneously from the same blood with the same experimental conditions. The drop with a diameter of 3.8 mm shows no wide axisymmetric cracks, whereas the drop which is 5.4 mm in diameter clearly shows periodic cracks around the corona. This cracking phenomenon is only observed above a critical diameter which for this case is 4.2 mm. The mechanical stresses inside the solid deposit desiccating can be advanced as the origin of this cracking. The formation of wide cracks is similar to the desiccation of drops of nanoparticles on glass plates studied by Pauchard, Abou & Sekimoto (2009) to which the RBCs in the present case may easily be compared. Pauchard *et al.* (2009) observed cracking which depended on the initial concentration and deformability of nanoparticles. In our study, the concentration and shape of RBCs can lead to the same consequences on the final patterns observed. The corona of the drop is mainly composed of RBCs which have been deposited by internal drop convection. Thus, the central part of the remaining blood is less and less rich in RBCs. After stage 4, the liquid remaining in the central area of the drop contains mainly proteins, white blood cells, blood platelets and a few amount of RBCs. All these elements present hydrophilic behaviour with glass and wet the substrate.

For small drops below a critical value, drop evaporation which is related to the volume to be dried, is much faster. For large drops with a diameter of more than 4.2 mm, evaporation takes place over 30 min and Marangoni convection observed
<figure><img src="image_121.png" /><figcaption>FIGURE 6. Dependency of the number of cracks in the corona on the external diameter of the drop (blood coming from the same tube taken from a healthy subject; microscope glass substrate; room temperature, 22°C; humidity, 47%).</figcaption></figure>

through RBC motion is noticeable. RBCs accumulate at the edge of the drop. When the desiccation phenomenon occurs on the glass substrate, a decrease in volume is observed due to the large amount of water required. During the desiccation process, stress inside the solid deposit of desiccated blood built up and induced surface cracks periodically releasing the stress. Furthermore, the RBCs present at their surface proteins induce a hydrophobic behaviour with all materials. This is observed with glass. The dried RBCs at this position in the drop do not wet the substrate and reveal an hydrophobic behaviour. This enables a cracking phenomenon linked with the diameter of the drop, and consequently with the perimeter of the corona. For small drop perimeters, the stress inside the RBCs solid deposit is small compared with large drop diameters.

**5. Concluding remarks**

Observations of the Marangoni flow motion inside a drop of blood using a digital camera at a good resolution (about 2.3 µm) enable us to show that the motion of RBCs at the edge of the drop is the main mechanism of blood drop evaporation and deposition. The mechanisms involved in the blood drop evaporation are confirmed through the evaporation mass flux which is measured to be in agreement with a pure water drop evaporation. Other biological elements (white blood cells, proteins) are transported to the edge of the drop with the RBCs and contribute to the pattern formation through the deposit wettability with the substrate and mechanical properties. The blood evaporation dynamic can be predicted by a comparison with the pure fluid evaporation case corrected by the mass concentration in colloids. Totally different patterns are formed according to whether the person is healthy or suffers from anaemia or hyperlipidaemia. This is leading our research to correlate the pattern formation with blood diseases. An analysis of the corona of the drop reveals the presence of large solid plaques measuring several hundred micrometres which are
clearly visible for a normal individual, but are absent for someone with a disease. This simple, reliable and inexpensive indicator could be used for the diagnosis of blood diseases. The fluid mechanics involved in this real colloid suspension include convection of the main colloids (cellular components), but also evidences hydrophobic behaviour between the RBCs and the substrate, which modify the pattern observed after the drop has desiccated. An explanation for nonlinear evolution of the number of cracks with increasing diameter is currently being prepared, in conjunction with elements of solid mechanics.

The authors gratefully acknowledge the help with blood viscosity measurements and the fruitful discussions raised with F. Boyer.

Supplementary movies are available at journals.cambridge.org/flm.

## REFERENCES

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* DEEGAN, R. D., BAKAJIN, O., DUPONT, T. F., HUBER, G., NAGEL, S. R. & WITTEN, T. A. 1997 Capillary flow as the cause of ring stains from dried liquid drops. *Nature* **389**, 827–829.

* MARTUSEVICH, A. K., ZIMIN, Y. & BOCHKAREVA, A. 2007 Morphology of dried blood serum specimens of viral hepatitis. *Hepatitis Mon.* **7**, 207–210.

* PAUCHARD, L., ABOU, B. & SEKIMOTO, K. 2009 Influence of mechanical properties of nanoparticles on macrocrack formation. *Langmuir* **25**, 6672–6677.

* PAUCHARD, L., PARISSE, F. & ALAIN, C. 1999 Influence of salt content on crack patterns formed through colloidal suspension desiccation. *Phys. Rev.* E **59**, 3737–3740.

* POPOV, Y. O. 2005 Evaporative deposition patterns: spatial dimensions of the deposit. *Phys. Rev.* E **71**, 036313.

* POZRIKIDIS, C. 2006 Flipping of an adherent blood platelet over a substrate. *J. Fluid Mech.* **568**, 161–172.

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* THIERET, M. 2008 *Biology and Mechanics of Blood Flows – Part II: Mechanics and Medical Aspects*. Springer.

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* ZHUANG, H., COULEPIS, A. G., LOCARNINI, S. A. & GUST, I. D. 1982 Detection of markers of hepatitis B infection in serum dried on to filter-paper: an application to field studies. *Bull. World Health Organ.* **60**, 783–787.
# Annexe F

Structural and evaporative evolutions in
desiccating sessile drops of blood

Benjamin Sobac & David Brutin

*Physical Review E* **84**, 011603 (2011).
Structural and evaporative evolutions in desiccating sessile drops of blood

B. Sobac* and D. Brutin

IUSTI, Aix-Marseille Université, UMR 6595 CNRS, Technopôle de Château-Gombert, 5 rue Enrico Fermi, 13453 Marseille, France

(Received 9 February 2011; revised manuscript received 23 May 2011; published 6 July 2011)

We report an experimental investigation of the drying of a deposited drop of whole blood. Flow motion, adhesion, gelation, and fracturation all occur during the evaporation of this complex matter, leading to a final typical pattern. Two distinct regimes of evaporation are highlighted: the first is driven by convection, diffusion, and gelation in a liquid phase, whereas the second, with a much slower rate of evaporation, is characterized by the mass transport of the liquid left over in the gellified biocomponent matter. A diffusion model of the drying process allows a prediction of the transition between these two regimes of evaporation. Moreover, the formation of cracks and other events occurring during the drying are examined and shown to be driven by critical solid mass concentrations.

DOI: 10.1103/PhysRevE.84.011603

PACS number(s): 68.03.–g, 82.70.Dd, 64.70.fm, 82.70.Gg

I. INTRODUCTION

The evaporation of a colloidal suspension is a very
interesting system, allowing the formation of patterns. Early
investigations conducted by Deegan et al. [1] revealed the
formation of a ringlike pattern of the deposit along the triple
line. They pointed out that an outward flow induced by
the evaporation of the solvent transports the solute to the
self-pinned edge, creating the so-called “coffee stain.” Since
this work, several studies [2–5] have investigated fundamental
mechanisms influencing deposition phenomena, such as the
kinetics of evaporation, internal flow motions, or the triple line
dynamic, in order to find a means to control the final pattern.
For industrial applications, this is of capital importance in
evaporative self-assembly techniques [6,7] or in printing and
coating technologies [8,9].

However, when the concentration of solute near the surface reaches a critical value, a skin is formed which is considered a gel phase [10,11]. A sol-gel transition then occurs during the desiccation. This process, also called gelation, is characterized by a change of the rheological behavior with the appearance of a yield stress. The competition between the adhesion of the gel onto the substrate and the increasing internal stresses caused by evaporation leads to the formation of a different final pattern made up of cracks in order to release the excess of stored elastic energy [12,13]. Concentration, ionic strength, the presence of surfactant, the thickness of the system, deformability, and the size of particles are many parameters influencing this nonequilibrium pattern formation. The formation of cracks has mainly been studied in physical systems (polymeric and colloidal suspensions) but this mechanism has also been observed during the drying of biological fluids [14,15]. A regularly radial fracture structure is observed during the drying of bovine serum. A similar pattern has recently been observed for the first time with whole blood [16]. The flow motion induced by the evaporative solvent has been investigated. A capillary flow segregates and transports the cellular matter to the edge leading to a final half-doughnut shape.

In this article, we focus on the dynamics of evaporation and
crack formation. Two main types of kinetics of evaporation

are reported due to the competition between evaporation and
gelation. The transition of the evaporative kinetics is well
predicted using a diffusion model. Finally, by observing the
concentration of solid mass in the drop during the evaporative
process, we demonstrate that crack nucleation is driven by a
critical mass concentration of solid.

II. MATERIALS AND METHODS

An experimental setup was designed to provide a charac-
terization of both the mass and geometry of a drop of whole
blood deposited onto a microscope glass substrate during its
evaporation. Environmental conditions (temperature, pressure,
humidity) were recorded using a weather station. Evaporation
took place in a parallelepipedic box measuring 100 × 100 ×
150 mm³ designed to avoid external flow perturbations. The
volume was sufficient to preclude saturation of the atmosphere
with the vapor generated. To monitor the drying process, the
mass of the drop m(t) was recorded using a digital high-
precision balance with a resolution of 10 µg at 10 Hz (Mettler
Toledo XS 205). Moreover, a simultaneous visualization from
above was performed using a Canon EOS 7D digital camera
fitted with a macro lens in order to follow the morphological
evolution of the drop. The blood used in this study was human
blood and came from the same donor. The fibrinogen protein
was neutralized to avoid coagulation during the process. Blood
is a complex fluid made up of a liquid phase (plasma) and
of the cellular matter (red blood cells, white blood cells,
platelets). The whole of these biocolloids are described in
Table I in terms of quantities, sizes, and volumes. These
components account for 43.9% of the drop volume based on
a hematology analysis and 23.9% of the mass according to
the mass of the deposit on the substrate at the end of the
drying process. Physical properties of blood such as viscosity
and surface tension had been determined previously [16]. A
full cell numeration and biochemistry characterization were
performed. Experiments for the set of drops presented here
were performed within a period of 48 hours. The solid mass
fraction φ<sub>S</sub>(t) was deduced from the measurement of the mass
using a biphasic constituent model. At a given time t, the total
sample mass m(t) is the sum of the solid m<sub>S</sub> and the water m<sub>w</sub>
masses: m(t) = m<sub>S</sub> + m<sub>w</sub>(t). The solid mass concentration
is thus the ratio between the final dried mass m<sub>S</sub> and the

<footnote>*benjamin.sobac@polytech.univ-mrs.fr</footnote>
<table><caption>TABLE I. Distribution of biocolloids inside the cellular component of blood [17].</caption><thead><tr><th>Biocolloids</th><th>Typical quantity (units/mm³)</th><th>Typical size (µm)</th><th>Volumic % of colloids</th></tr></thead><tbody><tr><td>Red blood cells</td><td>4.9 × 10⁶</td><td>8</td><td>97</td></tr><tr><td>White blood cells</td><td>4.3 × 10³</td><td>15</td><td>2</td></tr><tr><td>Platelets</td><td>2.4 × 10⁵</td><td>3</td><td>1</td></tr></tbody></table>

mass at a given time $m(t): \phi_S(t) = m_S/m(t)$. The volumetric concentration cannot be used in the case of blood since blood cells are shells containing water which will be released during the drying.

### III. RESULTS AND DISCUSSION

The morphological evolution of a drying drop of blood is provided in Fig. 1. The drop was deposited onto the substrate and the edge was pinned throughout the drying process as shown by the constant wetting diameter. Indeed, in the case of biological fluids, proteins are adsorbed on the substrate leading to an anchoring of the triple line [18]. The evolutions of the drop mass and drying rate are presented in Fig. 2. An analysis of the kinetics of the drying rate reveals three different regimes, which are linked to physical processes. During the first regime, an outward flow induced by solvent evaporation is observed, which displaces biocolloids toward the edge of the drop [16]. This leads to a typical cross section of the deposit in the shape of a half-doughnut. Simultaneously, a gel-like skin phase forms at the edge and a gelation front moves inwards (see Fig. 1 at time $\tau_{C1}$). This mechanism is clearly shown both in Fig. 2, with the nonlinear decrease of the mass indicating that another process (gelation) disturbs the pure evaporation of the liquid phase (see the dashed line, which refers to the drying time of a pinned drop of pure liquid $\tau_D$), and in Fig. 1 at time $\tau_{C1}$ with the color contrast between the solid ring-like area (light red) and the fluid area (dark red). Considering the time for a red blood cell to radially move to the edge $t_f$ and the time to sediment across the thickness $t_s$, the sedimentation process is negligible in this problem since $t_f/t_s \approx 0.2$ [16]. At the end of this first regime, the central area of the drop is still liquid while the drop edge is gellified. Then a transition regime is observed which is characterized by a sharp decrease in the drying rate and a rapid gelation of the center as shown by the shrinking of the fluid part between the $\tau_{C2}$ and $\tau_G$ images of Fig. 1. Similar transition behavior is usually observed during phase change transitions such as solidification. The last regime of drying is characterized by a very slow drying rate, which is explained by the evaporation of the remaining liquid in the gellified cellular matter.

The typical drying rates extracted from Fig. 2 are, respectively, 5.2 µg/s (12.3 mg in 2300 sec) for the first regime of evaporation and 0.092 µg/s (0.25 mg in 2700 sec) for the last regime of drying. The kinetics of evaporation of the last regime is about 56 times slower than the first, indicating a process that is only related to the evaporation of the liquid phase diffusing through the gellified porous media. Indeed, during the drying process, these biocolloids accumulate and are compacted, which traps liquid inside the solid matrix. Similar kinetics of evaporation has been revealed in suspension

<figure><img src="image_122.png" /><figcaption>FIG. 1. (Color online) Structural evolution of the drop of blood: pictures taken simultaneously with the drop mass signal presented in Fig. 2 and showing the different stages of the drying of the drop of blood (initial drop mass $m_0$: 17.30 mg, final dried drop mass $m_S$: 3.51 mg, wetting diameter $d_0$: 8.60 mm, room temperature: 22.0 °C, humidity: 42%). The different times presented are defined, respectively, as follows: $\tau_0$ deposit time, $\tau_{C1}$ first time of nucleation of radial cracks at the periphery, $\tau_{C2}$ time of nucleation of radial cracks at the center, $\tau_G$ gelation time, and $\tau_F$ total drying time.</figcaption></figure>

films [13]. Our process clearly reveals a competition between evaporation and gelation. Considering the characteristic times of the problem, one can notice that the desiccation time $\tau_D$ is the same order of magnitude as the gelation time $\tau_G$ since the ratio $\tau_G/\tau_D \approx 1.25$. This is in agreement with the fact that a gelled foot builds up near the drop edge while the central part stays fluid at first and then recedes [2]. In the work of Pauchard et al. [2], with the same ratio of $\tau_G/\tau_D$, the authors evidence a buckling instability, as in their case the buckling time is shorter than the gelation time. For our situation, gelation continues in the central area of the drop, avoiding the development of buckling instability. The gelation time $\tau_G$ has been taken as the time at the end of the sol-gel transition. The desiccation time $\tau_D$ can be evaluated using the mean water flux evaporated per surface unit $w_E = -\frac{1}{S} \frac{dV}{dt}$, where S and V, respectively, are the free surface and the volume of the drop at a time t. In the situation where the wetting radius remains constant during the drying and considering a
<figure><img src="image_123.png" /><figcaption>FIG. 2. (Color online) Evolution of mass *m*, drying rate $|dm/dt|$, and solid mass concentration $\phi_S$ (inset) for an drying drop of blood (same conditions as Fig. 1). Regime I: drying regime driven by convection, diffusion, and gelation. Regime II: drying regime only driven by diffusion.</figcaption></figure>

spherical cap shape, the desiccation time is expressed: $\tau_D = \frac{V_0}{S_0} \frac{1}{w_E} = \frac{1}{6} \frac{(1-\cos\theta_0)(2+\cos\theta_0)}{\sin\theta_0} \frac{R_0}{w_E}$, where the subscript 0 specifies that parameters are considered at the initial time. With the approximation of weak contact angles ($\theta_0 \approx 14.8^\circ$ [16]), the expression of the desiccation time can be simplified $\tau_D \approx \frac{\theta_0 R_0}{4 w_E}$ and finally written

$$ \tau_D \approx \frac{\theta_0}{4} \frac{\rho R_0 S_0}{\left(\frac{dm}{dt}\right)_{t=0}} \quad (1) $$

with $\rho$ the density of the fluid. The obtained numerical value $\tau_D = 2.5 \times 10^3$ s fits with the experimental value extracted from Fig. 2 where $\tau_D = 2.3 \times 10^3$ s. As for the total time of evaporation $\tau_F$, it is defined by a constant signal of the mass along with a null mean signal of the drying rate.

The influence of the drop mass on the evaporation process was investigated. Figure 3 provides dimensionless evolutions of the liquid mass evaporated $[m_0 - m(t)]/[m_0 - m_S]$ as a function of the dimensionless time $t/\tau_F$ for different initial drop masses. The proportion of the second regime of drying becomes bigger at the expense of the first regime with the increase of the drop mass. This can be explained by the increase of the gel deposit thickness, the wetting diameter evolving with the drop mass to the power of 1/3 [see Eq. (2)]. Consequently, more water is trapped in the gellified cellular matter and the diffusion time through this porous media becomes longer.

In our experimental situations using a low-volatility fluid drying under natural conditions without heating, evaporation is limited by diffusion of water into air. Thus, a diffusion model was used to predict the time of drying transition, which also

corresponds to the gelation time $\tau_G$. For blood as a working fluid and for the range of drop diameters, the contact angle is assumed to be constant at $\theta = 14.8^\circ$ [16]. Using the spherical cap shape assumption, it is thus possible theoretically to relate the drop diameter to the drop mass by

$$ d_0 = K(\theta)m_0^{1/3} \quad (2) $$

with $K(\theta) = (\frac{24}{\rho\pi} \frac{\sin^3\theta}{(1-\cos\theta)^2(2+\cos\theta)})^{1/3} = 0.331 \text{ m}^2 \text{ s}^{-1} \text{ kg}^{-1/3}$ (the fit of experimental data gives $0.323 \text{ m}^2 \text{ s}^{-1} \text{ kg}^{-1/3} \pm 0.75\%$). From the simplified version of Stefan's law, the total time of

<figure><img src="image_124.png" /><figcaption>FIG. 3. (Color online) Evolution of the dimensionless liquid mass evaporated $[m_0 - m(t)]/[m_0 - m_S]$ for a range of drop masses: an indication of the proportion of each of the two evaporation regimes in the drying time.</figcaption></figure>
<figure><img src="image_125.png" /><figcaption>FIG. 4. (Color online) Variation of the gelation time $\tau_G$ and the wetting diameter of the drop of blood $d_0$ as a function of the initial blood drop mass $m_0$: experimental results (points) and theoretical models (dashed lines) (room temperature = 23.1 $^{\circ}$C $\pm$ 0.1 $^{\circ}$C, humidity varying between 7.0% and 26.5%).</figcaption></figure>

evaporation (in seconds) based on the first regime driven by a convection, diffusion, and gelation mode is expressed by

$$ \tau \approx \frac{4RT}{\pi \Delta P d_0} \frac{m_0}{D} \approx \frac{4RT}{\pi \Delta P K(\theta)} \frac{m_0^{2/3}}{D} \approx \left(\frac{2.036}{D}\right) m_0^{2/3} \quad (3) $$

with D the coefficient of diffusion, T the air temperature, R the gas constant, and $\Delta P$ the difference between the saturated pressure and the air pressure. The solute phase diffuses into the air during the first regime of evaporation with a diffusion coefficient that is extracted from our experimental results with the previous relation: $D_{C1} = 5.5 \times 10^{-7} \text{ m}^2/\text{s}$. This is in agreement with the two extreme cases: pure water diffusion into air ($D_{wa} = 2.19 \times 10^{-5} \text{ m}^2/\text{s}$) and diffusion through a colloidal gel made of stacked spheres ($D_{cg} = 5.0 \times 10^{-10} \text{ m}^2/\text{s}$ [19]). Figure 4 summarizes both these experimental results and models. A good agreement is found with the experimental observations made for whole blood, which was shown to behave like a colloidal suspension. The last drying regime previously described can be clearly observed for heavy drops. However, for small drops this stage of evaporation is not easily noticeable although it does exit. Water diffuses through the desiccated cellular components at an evaporation rate that is 56 times slower during the second regime than during the first regime. Consequently, the diffusion coefficient for the second regime is $D_{C2} = D_{C1}/56 = 9.8 \times 10^{-9} \text{ m}^2/\text{s}$. This second regime diffusion coefficient is in good agreement with the values obtained in the situation of colloidal gel diffusion into air [19] where the value is between $10^{-9}$ and $10^{-10} \text{ m}^2/\text{s}$.

The structural evolution of a drying drop of blood is shown in Fig. 1 with a set of pictures. Several stages are observed and are described here for the case presented. As previously described, a gelled part builds up at the edge and extends inwards while the central fluid part shrinks progressively. Because of the competition between the ad-

hesion of the deposit onto the substrate, which limits the reorganization of the solid phase, and the evaporation of solvent, the internal stresses increase inside the matter. At a certain moment, this internal stress is too great and regularly spaced radial fractures appear so as to release mechanical energy. The first cracks form at the gel periphery after 25% of the total time of evaporation $\tau_{C1}$. Then, secondary radial cracks appears at the center at 44% of the evaporation time $\tau_{C2}$. During the drying, cracks propagate toward the center and become wider. At the time $\tau_G$, the drop is almost dried. This pattern is explained by the presence of orthoradial stress, which is a consequence of the adhering ring of gelled blood around the fluid central area [2].

Considering the solid mass fraction during desiccation, experiments reveal that crack formation, as other steps, appears at a critical mass concentration of solid whatever the initial drop mass. The results are summarized in Table II. The first mechanical crack of the dried cellular matter at the periphery is observed at 29.6%, while the other central radial cracks nucleate at 65.4%. These cracks propagate inward as stretch by the motion of the gelation front. The transition to the last regime of evaporation occurs at a critical concentration of 88.3%. At this time, almost all the liquid has been evaporated. The remaining 11.7% is trapped inside the cellular components

<table><caption>TABLE II. Solid mass concentration threshold $\phi_S^*$ observed for different events for the same blood (17 drops studied ranging from 1.9 to 24.3 mg).</caption><thead><tr><th>Event</th><th>t</th><th>φ<sup>*</sup><sub>S</sub></th><th>Δφ<sup>*</sup><sub>S</sub></th></tr></thead><tbody><tr><td>Appearance of 1st radial cracks (periphery)</td><td>τ<sub>C1</sub></td><td>29.6%</td><td>3.4%</td></tr><tr><td>Appearance of central radial cracks</td><td>τ<sub>C2</sub></td><td>65.4%</td><td>5.0%</td></tr><tr><td>Drying regime transition</td><td>τ<sub>G</sub></td><td>88.3%</td><td>4.8%</td></tr></tbody></table>
gellified onto the substrate and dries slowly until the end of
the evaporation.

IV. CONCLUSION

Two regimes of evaporation are clearly evidenced during
the drying of drops of blood. After a first stage mainly driven by
convection, diffusion, and gelation, a transition phase occurs
with the complete gelation of the system. Then, a second
regime appears, which is only diffusive. The transition is
correctly predicted by means of a model of diffusion through

the liquid evaporating into the air. Finally, during the drying,
cracks nucleate and propagate, leading to the formation of
a typical regularly spaced radial pattern. By observing the
concentration of solid mass in the drop during drying, we
observe that fractures' formation occurs at a critical mass
concentration of solid.

ACKNOWLEDGMENTS

We would like to thank F. Boyer, B. Loquet, and J. Sampol
for useful discussions.

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# Annexe G

## Influence of substrate nature on the evaporation of a sessile drop of blood

David Brutin, Benjamin Sobac & Céline Nicloux

*Journal of Heat Transfer 134, 061101 (2012).*
Influence of Substrate Nature
on the Evaporation of a
Sessile Drop of Blood

David Brutin<fnref n="1" />

e-mail: david.brutin@polytech.univ-mrs.fr

Benjamin Sobac

Aix-Marseille University,
IUSTI UMR 7343 CNRS,
Marseilles 13013, France

Céline Nicloux

Institut de Recherche Criminelle
de la Gendarmerie Nationale,
IRCGN-DCIH-DATO,
Rosny sous Bois 93110, France

We fully characterize the natural evaporation of human drops of blood from substrates and substrate-dependent behavior. The heat flux adsorbed by the drops for evaporation is measured by means of a heat flux meter. A side-view measurement enables access to the drop contact angle, wetting diameter, and initial height. A top-view camera allows for the monitoring of the drying regime (deposition, gelation, and fracturation). This directly measured heat flux is related to the evaporative mass flux obtained from the mass of the drop, and the two show good agreement. Both types of measurements indicate that regardless of the substrate type, there is first a linearly decreasing regime of evaporation when the drop is mostly liquid and a second regime characterized by a sharp decrease. We show that the evaporation dynamics are influenced by the substrate's wettability but not by the substrate's thermal diffusivity. The different regimes of evaporation exhibited by glass and metallic substrates are explained in terms of evaporation fluxes at the drop surface. In the case of wetting drops (below 40 deg), the evaporation flux is very important along the drop periphery and decreases across the interface, whereas in the case of nonwetting drops (about 90 deg), the evaporation flux is almost uniform across the droplet's surface. We show that these different evaporation fluxes strongly influence the drying behavior. In the case of metallic substrates, this enables the formation of a uniform "glassy skin" around the droplet surface and, in the case of glass substrates, the formation a skin along the drop periphery with an inward gelation front. This behavior is analyzed in terms of the competition between the drying time and the gel formation time. Unstable drop surfaces were observed at high initial contact angles and are very similar to those of polymer drops. [DOI: 10.1115/1.4006033]

Keywords: bloodstain, wettability, phase change, forensic investigations

# 1 Introduction

Sessile drop evaporation is currently a widely researched field in the scientific community. The numerous applications for cooling, combustion, fire safety, paintings, coatings, printings, microelectronics, DNA analysis, disease diagnosis, and even forensic investigation are well documented. The scientific community has naturally divided the subject into several topics depending on the target fluid's nature-pure fluid, nanofluid, complex fluid or biological fluid, or the type of evaporation exhibited by the fluid-natural or forced. For colloidal drops, pattern formation after evaporation is also of great interest. Depending on a colloid's particle size (microparticles or nanoparticles), the observations and the droplet evaporation dynamics are different.

There are only a few papers in the literature that address the evaporation of sessile drops of biological fluids. See Table 1 for papers about colloidal sessile drop evaporation. Whole blood has rarely been studied as the target fluid for sessile drop evaporation, though drops of serum have generated several publications [1]. The studies on drops of serum mainly focus on pattern formation rather than heat transfer. The literature reveals that drops of biological fluids can be understood within the framework of natural evaporation. Few authors record the ambient temperature and moisture level during evaporation. These two parameters are fundamental in studying biological fluids because the fluid phase that evaporates is water. Experiments performed under ambient hu-

midity levels of 10% or 40% will completely change the rate of evaporation. With a room temperature of 23°C and atmospheric pressure of 1013.25 hPa, Stefan's law can be simplified and indicates that the rate of evaporation by diffusion is proportional to the difference between the associated saturation and vapor pressures. At 10% humidity, the evaporation rate is 50% higher than that at 40% humidity. Consequently, the time of evaporation will decrease sharply, and the flow motion inside the drop will certainly be modified as well. This is a critical point that needs to be addressed by researchers in the future to allow for quantitative comparisons.

To understand the evaporation of drops of biological fluids, studying drops of colloids composed of either microparticles or nanoparticles is a good way to begin distinguishing the role of biology from the roles of other physical mechanisms that are potentially involved, such as fluid mechanics, solid mechanics, and chemistry. The pattern formation observed for drops of blood is very similar to that observed by Pauchard et al. [2] for colloidal drop evaporation, regardless of the fracturation of cracks or evaporation dynamics. The authors studied the crack patterns formed by the desiccation of a colloidal suspension in a sessile drop placed on a glass surface. They show that crack formation is related to the salt concentration of the suspension and explain that for large drops, the patterns can be attributed to buckling instability. The experimental observations of mica-colloids in deionized water made by Deegan in 2000 [3] were theoretically confirmed by Popov in 2005 [4].

The drying mechanics of drops of whole blood are of interest for forensic investigation. Several substrates are encountered, and gravitational droplets induce different wettabilities depending on the nature and roughness of a given substrate. Figure 1 shows

<footnote n="1">¹Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 21, 2011; final manuscript received December 6, 2011; published online May 8, 2012. Assoc. Editor: Franz-Josef Kahlen.</footnote>
<table><caption>Table 1 Literature concerning the evaporation of drops of blood and drops of colloids</caption><thead><tr><td>References</td><td>Fluid used</td><td>Substrate</td><td>Comment</td></tr></thead><tbody><tr><td>Zhuang et al. [11]</td><td>Blood serum</td><td>Filter paper</td><td>Use of dried serum on paper substrates</td></tr><tr><td>Pauchard et al. [2]</td><td>Silica sols of 15 nm</td><td>–</td><td>Influence of salt content on crack patterns</td></tr><tr><td>Deegan [3]</td><td>Mica-colloids in water</td><td>Glass</td><td>Colloid accumulation at the edge of the droplet</td></tr><tr><td>Popov [4]</td><td>0.1 to 1 µm colloids</td><td>–</td><td>Model to create controlled deposition patterns</td></tr><tr><td>Pauchard [12]</td><td>Colloidal gel</td><td>Glass</td><td>Adhering region circular for thick gel layers</td></tr><tr><td>Yakhno [13]</td><td>Blood serum</td><td>Glass</td><td>Salt crystallization and protein glass transition</td></tr><tr><td>Tarasevich and Pravoslavnova [14]</td><td>Biological fluids</td><td>–</td><td>Modeling with diffusion and convection</td></tr><tr><td>Pauchard et al. [15]</td><td>Nanolatex spheres of 30 nm</td><td>Glass</td><td>Evaporation of gel layers evidence three regimes</td></tr><tr><td>Brutin et al. [1]</td><td>Whole blood</td><td>Glass</td><td>Pattern formation in drying drops of blood</td></tr></tbody></table>

examples of drops of blood deposited on different substrates, demonstrating the different possible droplet shapes encountered. Of course, forensics is mostly concerned with drop impact rather than deposition; however, the wettability issues associated with the two are the same. Even in the case of drop impact, a hydrophobic or super-hydrophobic substrate will modify the drop shape and thus the final dried pattern. From a general forensics point of view, this work can help to determine several parameters that are presently unknown in crime scenes. It may also enable us to obtain more precise results in investigating a bloody scene featuring drying drops or layers of blood, given the ambient temperature and humidity.

The transfer of heat from a substrate to a biological or colloidal drop has never been studied. The evaporation of a drop requires energy for the phase change, which is pumped into the substrate or into the surrounding air. Depending on the substrate's thermal properties, the evaporation dynamics could be different. This is the main topic of this study. We want to investigate this point and establish the difference between the role of drop wettability on the substrate and the role of the thermal diffusivity of the substrate. To this end, we will use different substrate types and perform a full geometric and thermal characterization of drops during evaporation.

## 2 Materials and Methods

**2.1 Mass Evolution Measurements.** An experimental setup was designed to provide the complete geometric characterization of a drop of blood during its evaporation. Drops were deposited on Bioblock glass substrates. The environmental conditions (temperature, pressure, and humidity) were recorded using a meteorological station. Evaporation took place in a parallelepiped box measuring 100 × 100 × 150 mm³, which remained covered during the experiment to avoid external flow perturbation. The evaporation box was partially opened on the top and the sides were not hermetically sealed to allow the humidity to equilibrate between the inside and outside of the box. This configuration protected the drying drop from surrounding convection.

Visual monitoring was performed using a Canon EOS 7D digital camera coupled with a 1 × −5 × macrolens. This camera enabled us to obtain images measuring 5184 × 3456 pixels on a chip area measuring 22.3 × 14.9 mm². At a magnification of 1 ×, the resolution was 4.30 µm, and with the greatest magnification of 5 ×, the resolution was 0.86 µm. To film at 30 images per second,

the spatial resolution had to be reduced to 1920 × 1080 pixels (full high definition) with a pixel size of 2.30 µm (at 1 ×). This allowed for the visualization of drops from above with sufficient detail for further analysis of specific areas.

Drops were illuminated by a cold cathode backlight at 5000 K ± 270 K (StockerYale ML-0405) without any surrounding light to avoid reflection at the blood drop surface. The cold light provided homogeneous illumination without heating the drop and was placed 100 mm from the drop. The effect of the light intensity on the drying process was studied to avoid any biological or chemical disturbance of the phenomenon. To follow the drying process, the experiment was performed on a digital weighing balance with a resolution ranging from 10 µg to 81 g (Mettler Toledo XS 205). Drops were deposited on a microscope glass substrate (5 g); then, the total mass of the setup was recorded on a computer at 1 Hz. The detailed explanations of all data/characteristics which can be obtained doing the experiments (drop base diameter, drop wet diameter over time, drop mass evolution, drop initial and final mass, drop diffusing drying time, etc.), are fully detailed in recent publications [1].

**2.2 Heat Flux Measurements.** The entire experimental setup is presented in Fig. 2. It includes a heating control support where the drop was placed. The entire device was placed in an experimental test cell to avoid perturbation from natural convection. The test cell contained instrumentation dedicated to thermal measurements (temperature and heat flux). For all experiments presented in the manuscript, evaporation occurred under atmospheric conditions (P = 1005 hPa ± 3 hPa, T = 24.5 °C ± 1.2 °C and 26% ± 2%), and the drops were observed using digital cameras. The environmental conditions (temperature, pressure, and humidity) were recorded.

The uncertainty on the heat flux due to the voltage measurement and the calibration method is 0.5 mW. The calibration of the heat flux measurement is done by studying the evaporation of an ethanol droplet on a rough substrate to pine the triple line. Thus, the drop diameter is constant, the height decreases linearly, and consequently the mass decreases linearly too. The mass flow rate is the slope of the mass evolution. By multiplying the mass flow rate by the phase-change enthalpy, we find the power pumped by the drop. This method is used as a calibration of the heat flux meter [5]. Since all drops of blood evaporate at ambient conditions, the diffusion is the limit phenomena driving the evaporation [6].

The substrate was a complex sandwich composed mainly of a cylindrical block of aluminum 10 mm in diameter by 8 mm in length. A heat flux meter located above the aluminum cylinder allowed us to determine the power absorbed by the drops from the substrate during evaporation. The latter was covered with a sheet of glass, aluminum, or gold nanocoated glass. More details about the heat flux meter can be obtained in Brutin et al. [7]

**2.3 Blood Biological and Physical Properties.** Blood samples were taken in a nearby medical laboratory and stored in their original 10-µl sterile tubes (BD Vacutainer 9NC 0.109M) in a refrigerator at +4 °C so that several experiments could be

<figure><img src="image_126.png" /><figcaption>Fig. 1 Drops of blood on different substrate types</figcaption></figure>
<figure><img src="image_127.png" /><figcaption>Fig. 2 Schematic of the experimental setup used for heat transfer measurements</figcaption></figure>

conducted at different times. Experiments were performed for 1 h to 6 days after the samples were taken and show the same results for the same person. Thus, the storage conditions did not influence the main drying process. The blood used in this paper was taken from a volunteer in good health (33 years old, male, blood type AB+). The experiments have been repeated at least ten times. The curves are presented for one single droplet, since the averaging of the heat flux measurements or evaporation mass flux is not possible.

The biological fluid properties were determined to correctly analyze the flow behavior and the patterns observed. The whole blood was analyzed in terms of fluid viscosity using a Rheometer Physica MCR 501 “Anton Paar,” and the surface tension was determined using the pendant drop method. At the same time, a full haematological and biochemical analyses of the blood were performed to determine the blood characteristics in terms of composition (haematocrit, lipidemic balance, and so on). In this study, the whole blood density was assumed to be 1040 kg m⁻³.

The blood rheology for a shear stress range of 1–100 s⁻¹ revealed nonlinear behavior (τ = kγⁿ) between the stress and the strain with a coefficient *n* equal to 0.822 ± 0.001, with *k* being constant. This is in agreement with typical results obtained, indicating that the whole blood viscosity is driven by the RBC concentration (the haematocrit) [8] and that the blood behaves as a non-Newtonian fluid. The whole blood drops were initially composed of 43.9% cellular components by volume based on haematological analysis. By mass, it was composed of 23.9% colloids, which remained on the glass substrate at the end of the drying process. The blood's main colloid distribution is given in Table 2.

For our analysis, we assumed that the fluid was mainly composed of a high concentration of 8 µm-diameter colloidal particles. The whole blood also contained ions and proteins, which represented 11.6% of the final dried deposit by mass (statistical value obtained for all experiments performed with the same blood sample).

The blood surface tension measurements using the pendant drop method were performed using a capillary tube of 1 mm in diameter.

The exact capillary tube diameter was measured to an accuracy of ± 0.02 mm, and the blood drop mass was weighed using an electronic balance with an error of ± 10 µg. The results for the surface tension of over 72 drops gave a statistical value of 69.8 mN/m ± 4.6% for the full blood. This is in accordance with the theoretical value found in the literature and indicates that the surface tension of full blood is very close to that of water [8].

## 3 Experiments

The evaporation of whole blood drops on glass has been previously reported from a fluid mechanics point of view [1]. The authors presented the different stages leading to the final pattern observed and analyzed the competition between gelation and evaporation [9]. Several physical mechanisms involved were pointed out, including Marangoni convection, crack formation, gelation, and adhesion. Heat and mass transfer were investigated in this paper with respect to wettability aspects.

Three different types of substrates were chosen to investigate the influence of wettability and substrate diffusivity. The drop of blood placed on the metallic substrate exhibited almost the same contact angle as that placed on glass, though the roughnesses of the two substrates are different (a few nanometers for gold and a few micrometers for aluminum). Indeed, as summarized in Table 3, the glass and gold-coated glass substrates have the same thermal properties but different surface energies. In contrast, the aluminum and gold-coated glass substrates have very similar surface energies, but their thermal properties are different. For all experiments, the conduction time was calculated for a Fourier number of 1, which indicated a conductive time of 1.5 s, while the typical drying time was 1080 s on glass and 3600 s on gold. Thus, the heat flux measured by the heat flux meter is the representative of quasi-static heat flux.

### 3.1 Blood Drop Evaporation on Glass
Blood drop evaporation on a glass microscope plate has been previously studied [1]. The pattern formed at the end of the drying phase has been

<table><caption>Table 2 Distribution of biocolloids inside the cellular component of whole blood [8]</caption><thead><tr><th>Colloid</th><th>Quantity (units/mm³)</th><th>Size (µm)</th><th>Volumetric %</th></tr></thead><tbody><tr><td>Erythrocytes (RBCs)</td><td>4.9 × 10⁶</td><td>8</td><td>97</td></tr><tr><td>Leukocytes (WBCs)</td><td>4.3 × 10³</td><td>15</td><td>2</td></tr><tr><td>Platelets</td><td>2.4 × 10⁵</td><td>3</td><td>1</td></tr></tbody></table>

<table><caption>Table 3 Substrates' thermal properties</caption><thead><tr><th>Substrate</th><th>E<br>mm</th><th>κ<br>m² s⁻¹</th><th>R<sub>th</sub><br>W⁻¹ m² K</th><th>t<sub>cond</sub> (F<sub>o</sub> = 1)<br>s</th></tr></thead><tbody><tr><td>Glass</td><td>1</td><td>6.6 × 10<sup>-5</sup></td><td>8.3 × 10<sup>-4</sup></td><td>1.5</td></tr><tr><td>Gold-coated</td><td>1</td><td>6.6 × 10<sup>-5</sup></td><td>8.3 × 10<sup>-4</sup></td><td>1.5</td></tr><tr><td>Aluminum</td><td>0.5</td><td>9.5 × 10<sup>-5</sup></td><td>2.2 × 10<sup>-6</sup></td><td>0.003</td></tr></tbody></table>
<figure><img src="image_128.png" /><figcaption>Fig. 3 Initial and final drop shapes on glass (initial drop mass: 5.67 mg, initial drop diameter: 4.79 mm, initial drop height: 0.41 mm, initial drop contact angle: 20.5 deg)</figcaption></figure>

<figure><img src="image_129.png" /><figcaption>Fig. 4 Heat and mass transfer during blood drop evaporation on glass: heat flux, evaporative mass flow rate, and image at specific time steps (initial drop mass: 5.67 mg, initial drop diameter: 4.79 mm, initial drop height: 0.41 mm, initial drop contact angle: 20.5 deg, drop interface sequence from 0 to 12 min in steps of 2 min)</figcaption></figure>

explained, but the heat flux removed by the drop has not been investigated. Due to the very low roughness and wettability of the glass substrate, the drops wet the surface with an initial contact angle of 20.5 deg (angle is measured from the inside of the drop). The initial and final drop images are presented in Fig. 3. The final average drop thickness was less than 50 µm, which is very small compared to the initial drop thickness of 410 µm. The side view of this situation is difficult to use for quantitative measurements, and thus, the average thickness was determined by weight.

The total heat transfer required by a blood drop on the 1-mm-thick glass microscope plate is plotted in Fig. 4. The total heat transfer decreases linearly during the first step of drop evaporation, which is mainly driven by internal drop convection and the diffusion of water into the air [1]. The linear decrease is consistent with the receding gelation front observed at the bottom of the figure. Because the evaporation diameter decreases, the heat flux coming from the substrate also decreases. This is in agreement with the observation of pure fluids' evaporation flux for natural evaporation with a decreasing triple-line perimeter.

In the second stage, the heat flux sharply decreases when most of the water has been evaporated. After a time step of 13 min, the drop is almost completely dried, and the changes observed are those of the fracturation and color. The remaining water is trapped between the red blood cells deposited on the substrate. This sharp decrease is consistent with a slow heat transfer rate due to a slower evaporation rate of water through gelified matter.

The mass was recorded using an electronic balance; the mass was used to obtain the evaporative mass flux plotted in Fig. 4. The behavior of two curves is consistent with a linearly decreasing trend followed by a sharp decrease. The good agreement between the two curves confirms that the total heat transfer withdrawn from the substrate is used for heat transfer associated with phase transformation. The phase-change enthalpy is not taken from the surrounding air. The heat flux withdrawn is thus the product of the phase-change enthalpy and the evaporative mass flux. Because the mass must be calculated to determine the evaporative mass flux, the use of the heat flux provided by the heat flux sensor provides a real-time measurement that is related to the evaporative mass flux through a proportionality coefficient. The total time required to evaporate 4.31 mg of fluid (76.1% of the initial drop mass of 5.67 mg) was 15 min; thus, the average evaporative mass flux was 4.80 µg/s. This value will be compared to the values of the other two cases.

## 3.2 Blood Drop Evaporation on Gold.
Coating the substrate with gold can change the wettability of a 1-mm-thick glass substrate. Thus, only the blood drop wettability and not the thermal properties of the substrate is altered. The initial and final drop images are presented in Fig. 5. The initial contact angle on gold was 91.9 deg. The drop shape was hemispherical with a radius of 1.72 mm and a height of 1.53 mm.

At the end of the evaporation, the drop dewets the substrate and develops a hole at its center. The change in the color of the gold substrate along the edges is due to the chemical reaction between blood proteins and gold, which is called “proteinization” (see Fig. 5). The final deposit appears to be thicker compared to the gelified deposit on glass because the area of the deposit has been reduced by a factor 2.

Some characteristic aspects of the pattern are not observed in this case, even though a few axisymmetric cracks are observed around the drop. The main difference between the initial and final drop is the formation of a central hole during drying. This point will require more investigation from a soft matter and shell mechanics point of view. The total time of evaporation is 60 min.

Figure 6 shows the heat transfer required by a blood drop on a 1-mm-thick glass microscope plate covered with a nanolayer of 14-k gold and the rate of fluid mass evaporated. Again, both curves show good agreement. However, the variation in the heat flux provides a better reflection of the heat transfer, which is indicated using a red dashed line, compared to the mass derivative,
<figure><img src="image_130.png" /><figcaption>Fig. 5 Initial and final drop shapes on gold (initial drop mass: 9.53 mg, initial drop diameter: 3.45 mm, initial drop height: 1.53 mm, initial drop contact angle: 91.9 deg, drop interface sequence from 0 to 36 min in steps of 6 min)</figcaption></figure>

<figure><img src="image_131.png" /><figcaption>Fig. 6 Heat and mass transfer during the blood drop evaporation on gold: heat flux, evaporative mass flow rate, and image at specific time steps (initial drop mass: 9.53 mg, initial drop diameter: 3.45 mm, initial drop height: 1.53 mm, initial drop contact angle: 91.9 deg)</figcaption></figure>

which is noisy. The total time required to evaporate 7.25 mg of fluid (76.1% of the initial drop mass 9.53 mg) was 55 min. Thus, average evaporative flux is 2.20 µg/s.

During the first half of the evaporation process, the evaporative mass flux decreases linearly, which corresponds to the stage during which the main part of the drop is still liquid and no receding of the triple line is observed. The decrease in the heat flux is thus related to a parameter other than the diameter, which is fixed. Because no gelation front is clearly visible, the same analysis as that for the glass case cannot be performed here. However, the side view of the drop clearly indicates a continuous decrease in the drop volume (see Fig. 5).

The transition period was documented by taking three images at times of 30, 35, and 40 min. The drop of blood, which was initially a clear red and almost transparent, becomes darker due to gelation. The wetting diameter clearly decreases and fracturation

appears; nine cracks can be observed around the drop periphery starting at 30 min. The 3D shape of the drop is clearly much more complex and will require 3D visualization using dedicated equipment (i.e., numerical microscope).

During the second half of the drop evaporation process, the heat flux suddenly decreases. This corresponds to the end of the main evaporation phase. The drop's liquid phase is almost evaporated, as evidenced by the change in drop color in the last few images. Also, some area of the drop in contact with the substrate dewets. The contact area with the substrate, and thus, the heat transferred is reduced. The dewetting process in enhanced, while the heat flux decreases. At the end of the drying period, the drop is almost completely dewetted from the substrate. Experimental observations indicate that the dried drop does not adhere to the substrate at all.

### 3.3 Blood Drop Evaporation on Aluminum.
With the same substrate thermal properties, different heat transfer behavior during the second stage of evaporation has been observed. We switched the substrate to aluminum, which does not change the drop wettability but only the substrate's thermal properties. The drop's initial contact angle on aluminum was 95.7 deg. As in the case of the gold substrate, the drop was hemispherical in shape with a radius of 1.69 mm and a height of 1.66 mm. The initial and final drop images are presented in Fig. 7. Under drying stresses, the droplet clearly dewets from the aluminum substrate and recedes, as indicated by the fact that the final perimeter is smaller than the initial one. On the gold substrate, the dried matter does not stick at all.

The transfer of heat to the blood drop from the 0.5-mm-thick aluminum disk as well as the evaporative mass flux are provided in Fig. 8. Again, the heat flux is a better indicator of heat transfer compared to the mass flux, which clearly shows fluctuations. Despite the high thermal diffusivity of the aluminum substrate, the drop required the same drying time as the drop on the gold substrate (57 min to dry 7.24 mg (76% of the initial drop mass 9.51 mg): A drying rate of 2.12 µg/s). Even with a high thermal conductivity, the evaporation time is not reduced. The evaporation dynamics are also nearly identical to those of the previous cases, exhibiting two distinct stages.

The first stage of evaporation shows a drop that is almost completely liquid with a constant wetting diameter. The change in evaporation dynamics is characterized by a sudden change in the blood color from clear to dark red. The same transition can be traced along the heat transfer profile due to dewetting during the
<figure><img src="image_132.png" /><figcaption>Fig. 7 Initial and final drop shapes on aluminum (initial drop mass: 9.51 mg, initial drop diameter: 3.39 mm, initial drop height: 1.66 mm, initial drop contact angle: 95.7 deg, drop interface sequence from 0 to 36 min in steps of 6 min)</figcaption></figure>

<figure><img src="image_133.png" /><figcaption>Fig. 8 Heat and mass transfer during blood drop evaporation on aluminum: heat flux, evaporative mass flow rate and image at specific time steps (initial drop mass: 9.51 mg, initial drop diameter: 3.39 mm, initial drop height: 1.66 mm, initial drop contact angle: 95.7 deg)</figcaption></figure>

second stage of the drying process. Again, the gelified deposit did not wet the substrate at the end of the drying process, and only the receding of the drop was observed during this second stage. Hole formation was also observed during the transition.

**3.4 Discussion.** To compare the three cases, we have summarized the heat transfer parameters in Table 4. The initial contact area with the substrate (S) and the initial interface area with the surround air (A) have been added. For the three cases, the drop evaporated with almost the same dynamics. In the first stage, there is a linear decrease in the heat flux released by the drop that is associated with internal flow motion. The second stage shows a sharp decrease associated with the end of gelation for all cases and partial dewetting for the metallic cases.

<table><caption>Table 4 Summary of the three drops' evaporation parameters</caption><thead><tr><th>Substrate</th><th>m<sub>0</sub><br>mg</th><th>m<sub>F</sub><br>mg</th><th>θ<br>deg</th><th>t<sub>evap</sub><br>min</th><th>ṁ<sub>evap</sub><br>µg/s</th><th>d<br>mm</th><th>h<br>mm</th><th>S<br>mm<sup>2</sup></th><th>A<br>mm<sup>2</sup></th></tr></thead><tbody><tr><td>Glass</td><td>5.67</td><td>4.31</td><td>20.5</td><td>15</td><td>5.65</td><td>5.51</td><td>0.41</td><td>18.0</td><td>18.5</td></tr><tr><td>Gold</td><td>9.53</td><td>7.25</td><td>91.9</td><td>55</td><td>2.65</td><td>3.45</td><td>1.53</td><td>9.3</td><td>16.6</td></tr><tr><td>Aluminum</td><td>9.51</td><td>7.24</td><td>95.7</td><td>57</td><td>2.64</td><td>3.39</td><td>1.66</td><td>9.0</td><td>17.7</td></tr></tbody></table>

For all three cases, the evaporation dynamics should have been the same because the limiting factor is the solvent vapor's diffusion to the surrounding air. However, we observed different dynamics depending on the wettability. When the initial contact angle was low, we observed the formation of a skin with an inward motion of the gelation front. When the contact angle was high, we observed the formation of a glassy skin at the drop/air interface. Because the drop was still evaporating, this elastic shell was deforming and led to the observed patterns. Assuming the gelation was due to particle accumulation, we attribute these observations to the evaporation flux at the drop/air interface as a function of the initial contact angle. Indeed, according to Hu and Larson, 2002 [6], for a contact angle of about 90 deg, the evaporation flux is uniform (see page 1340), while that for a sessile drop with a low contact angle (below 40 deg) is nonuniform with a diverging flux at the drop's periphery. For drops on the glass substrate, the initial contact angle was far below 40 deg. Thus, evaporation occurred mainly along the drop's periphery. The particles were transported by outward flow along the drop's periphery. We confirmed this with the visualization of the receding gelation front. For drops on gold or aluminum, the initial contact angle was approximately 90 deg; thus, the evaporation was almost homogeneous around the drops' interface. This is also in agreement with our observation of gelation at the drop/air interface during the first stage of evaporation with the formation of a glassy skin.

Regarding the final patterns obtained for nonwetting situations (such as those for drops on a gold substrate), similar patterns were obtained by Pauchard and Allain in 2003 [10]. The authors investigated the surface evolution of drying drops of polymer solution. They showed that the two parameters used to predict the surface stability are the initial drop contact angle and the room humidity. In our study, the room humidity was held constant. However, a change in humidity would affect the competition between the evaporation time and the gelation time. The experimental results provided by the authors were compared to a model that was based
<figure><img src="image_134.png" /></figure>

Pauchard et Allain, 2003, Fig. 3

Complex fluid: solutions of hydrosoluble polysaccharide dextran.

Initial contact angle of 70°
Humidity: 30%

<figure><img src="image_135.png" /></figure>

Present study

Complex fluid: whole blood

Initial contact angle: 92°
Humidity: 26%

<caption>Fig. 9 Comparison with experiments by Pauchard and Alain [10] performed using a polymer drop; the two dried drops had almost the same contact angle and evaporated at the same room humidity. The initial diameter was also almost the same.</caption>

on the competition between the drying process and the formation of a glassy skin. They observed different shapes depending on the two parameters. We compare one of their unstable surfaces to a dried drop of whole blood on gold in Fig. 9. The two images were obtained for similar drop diameters, room humidity levels, and initial contact angles.

In the polymer drop solution observed at a humidity level of 30% and an initial contact angle of 70 deg, Pauchard and Allain reported that "a complex pattern progressively builds up involving a cascade of buckling, and in the final state the drop axisymmetry is broken." In our experiments, we studied whole blood; the polymerization of the polymer solution in Pauchard and Allain's study is analogous to the gelation in our experiments. The surface stability of blood drops can thus be explained by the competition between the uniform drying around the drop surface and the formation of a glassy skin. A more precise model must be developed, and more experimental situations need to be realized to compare our stability map to that for polymer solutions.

## 4 Conclusion and On-Going Work

The drying of a drop of whole blood under room conditions is influenced by substrate wettability and not at all by the substrate's thermal diffusivity. The surrounding air temperature and humidity are important because the diffusion of vapor to the surrounding air is driven by the difference between the saturation pressure and the vapor pressure. Because the limiting process is diffusion, the evaporation time is relatively long compared to the time required for conduction or thermal diffusion through the substrate. The change in substrate thermal diffusivity does not influence the total time of evaporation, though the substrate wettability has a direct influence on the drying process. We explain the different final patterns observed based on the substrate wettability. For a wetting drop (on glass for example), the contact angle is very small, and according to the Hu and Larson model [6], the evaporative flux occurs mainly at the drop's periphery; however, for a drop with a contact angle of 90 deg (on gold or aluminum), the evaporative flux occurs uniformly around the drop's surface. This explains the initial inward motion of the gelation front that is then followed by fracturation. For a drop on a metal substrate, the formation of a uniform glassy skin was observed and is in agreement with a uniform evaporative flux at the drop's interface. This situation also shows the formation of unstable surfaces that were very similar to

those observed by Pauchard and Allain [10] for drying polymer drops. The polymerization observed by Pauchard and Allain is the equivalent of the gelation observed in our experiments.

## Nomenclature

### Roman Letters

A = initial drop interface area with air (mm²)

C = colloids mass concentration (%)

d = drop diameter (mm)

e = substrate thickness (mm)

Fo = Fourier number

H = haematocritis (volumetric % of cellular component)

h = drop height (mm)

k = proportionality coefficient

m₀ = initial drop mass (mg)

ṁ<sub>evap</sub> = evaporation mass flux (µg/s)

R<sub>th</sub> = thermal resistance (W⁻¹ m² K)

S = initial drop contact area with the substrate (mm²)

t<sub>evap</sub> = total time of evaporation (s)

t<sub>cond</sub> = conduction time (s)

T = room temperature (°C)

### Greek Letters

Δ = uncertainty

κ = thermal diffusivity (m²/s)

θ = contact angle (deg)

τ = shear stress (Pa s⁻²)

γ = shear rate (s⁻¹)

## Acknowledgment

The authors gratefully acknowledge the help and the fruitful discussions raised with B. Loquet.

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