The Physics of Detonation Chemistry: A Radical Theory in Predicting the Deagration to Detonation Transition

The theoretical nding of the Sanal-ow-choking [PMCID: PMC7267099] is a methodological advancement in predicting the deagration-to-detonation-transition (DDT) in the real-world-uid ows (continuum/non-continuum) with credibility.[1,2] Herein, we provide a proof of the concept of the Sanal-ow-choking and streamtube-ow-choking causing DDT in wall-bounded and free-external ows. Once the streamlines compacted, the considerable pressure difference attains inside the streamtube and the ow gets accelerated to the constricted region for satisfying the continuity condition set by the conservation law of nature. If the shape of the streamtube in the internal/external ow is similar to the convergent-divergent (CD) duct the phenomenon of the Sanal-ow-choking and supersonic ow development occurs at a critical-total-to-static pressure ratio (CPR) in yocto to yotta scale systems and beyond, which leads to shock wave generation or detonation as the case may me. At the lower critical detonation or hemorrhage index, the CPR of the reacting ow and the critical blood-pressure-ratio (BPR) of the subjects (human being/animal) are unique functions of the heat-capacity-ratio (HCR) of the evolved gas in the CD duct. In silico results are presented herein to establish the proof of the concept of the Sanal-ow-choking and streamtube-ow-choking causing shock-wave/detonation in diabatic ow systems and asymptomatic-hemorrhagic-stroke in biological systems. The physics of detonation chemistry presented herein sheds light for exploring supernova explosions.[107]


Introduction
Although the underlying knowledge in advanced science of real-world ows (continuum / non-continuum) with the multi-disciplinary focus has been evolved over the centuries there are still many unresolved problems due to the lack of fundamental understanding of physics and chemistry of diabatic uid ows ( ow involves transfer of heat). [1] Such problems of urgency to the scienti c communities are the prediction and attenuation of detonation in reacting uid ow systems and that of asymptomatic stroke (AS) in the human circulatory system (HCS). Note that the de agration to detonation transition (DDT) in reacting uid ow systems and the creeping ow to asymptomatic hemorrhagic stroke (AHS) in biological systems could happen due to the consequence of the Sanal ow choking. [1][2][3][4][5][6][7][8][9] Over the decades several in vitro and in silico studies were reported on DDT in various energy systems from yocto to yotta scales but there were no authentic answers on the fundamental cause of DDT in real-world uid ow systems. [10][11][12][13][14][15][16][17][18][19][20] Modeling and simulation of nanoscale uid ow is truly intricate, because in the contrary to milli-scale or macroscale uid ow, the governing-equations capturing exact ow physics and chemistry are not well delineated. [21][22][23][24][25][26] Hence, even if the in silico method is well suited for the solution of considered problem, in vitro methods in nanoscale are having inherent inaccuracy for generating benchmark data for in silico code veri cation. Therefore, one should rely up on the exact solution for generating benchmark data for solving unresolved problems carried forward over the centuries with credibility. Such models should scrupulously satisfy the conservation laws as imposed by our nature. Therefore, the Sanal ow choking models [1] should be invoked for in silico model validation, veri cation and calibration before featuring uid ow characteristics of yocto to yotta scale diabatic uid ow systems and beyond with reliability.
Of late, small scale systems have got signi cant attention in the industry because mostly micro/nanoelectromechanical systems (MEMS/NEMS) are based on the uid motion. [21] This is particularly true in the nano medicine for drug discovery and nano/micro thrusters for aerospace systems design. Obviously, the nano scale uid ow system development in microgravity aerospace application is a challenging research topic. Furthermore, such systems in atmospheric conditions applicable to physical, chemical, and biological sciences are also challenging areas for research due to the pragmatic di culties to perform in vitro and in silico studies and in addition the lack of closed-form analytical models for benchmarking. Various researchers reported through in vitro and molecular dynamics simulations that the surface friction compared to the uid ow is very low for carbon nanotubes (CNT). [26][27][28][29] The fact is that the reported results were not supported with benchmark data generated from any exact solution for meeting all the conservation laws of nature.
Qi-Long Yan et al. [30] reported (2016) that encapsulation of energetic molecules into CNTs is extremely challenging and still demanding additional analytical and in vitro studies to understand its sensitivity and performances [31][32][33][34] having with highly sensitive energetic material (EMs). Gunpowder, a rearm propellant, invented in ancient China is believed as the earliest energetic material, [30] which generally does not detonate but rather de agrates. The de agration and detonation properties of black powder however differ signi cantly from new generation high energetic solid propellants [35,36] and there are no authentic predictive models available as on the date to forecast these properties at nanoscale. Therefore, in silico simulation of DDT in the real-world nano uid ow system is the need of the 21st century; and it must be veri ed with an exact solution for a credible decision making. [36][37][38] Admittedly, there are no literature available on in silico simulation of DDT in milli-scale or nanoscale systems having port with the sudden expansion/divergence region. [39][40][41][42][43][44][45] The Sanal ow choking, a compressible uid ow effect, is a radical theory in advanced science of real-world uid ow systems, [1] which is capable to provide solutions to many unanswered research questions in the continuum and non-continuum uid ows moved ahead over the centuries. [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] Note that the non-continuum or nanoscale uid ows obey all conservation laws of nature. Indeed, all uids available in our nature are compressible. [1] In the case of nanoscale uid ows, when pressure increases the Knudsen number reduces causing the compressible viscous ow effect due to the decrease in the average mean free path heading to zero-slip wall boundary condition. All these deliberations corroborate that the Sanal ow choking model puts a focal role in interdisciplinary science for performing in-silico experiments with credibility in the continuum and non-continuum uid ows in yocto to yotta scale systems. Certainly, at the Sanal ow choking condition for diabatic ows ( ow involves transfer of heat) all conservation laws of nature are contented. Any uid ow solver calibrated with the Sanal ow choking condition of diabatic ow could be capable to predict a priori the risk of DDT in chemical energy systems and AHS in biological systems. [1] It could be achieved by predicting the lower critical detonation index (LCDI) and the lower critical hemorrhage index (LCHI) as the case may be. It is pertinent to note that both the LCDI and the LCHI are representing the critical pressure ratio of the respective systems. These indexes are regulated by the heat-capacity-ratio (HCR) of the evolved gas with the lowest HCR.
In this article we are primarily focusing on analytical modeling and in silico simulation of a diabatic uid ow system aiming to demonstrate the Sanal ow choking, streamtube ow choking, shock wave generation and pressure overshoot for proving the concept of the occurrence of DDT in a classical straight-tube ending with a divergent port geometry at the subsonic in ow condition. This physical situation is analogous to the creeping ow to the choked ow condition in an artery with the divergent/bifurcation/vasospasam region causing AHS (see Figure 1(a-h) as the central illustration). Herein, we made an effort to correlate the radical theory of the Sanal ow choking in the human circulatory system (HCS) because blood is a compressible uid. [1] Furthermore, in vitro study shows (see Fig.2) that carbon dioxide (CO 2 ) gas is predominant in fresh-blood samples of the healthy human-being than Guinea-pig at a temperature range of 37-40 0 C (98.6-104 0 F), which increases the risk of owchoking leading to AHS. It is an admitted fact that the Sanal ow choking steers to the shock-wave generation in viscoelastic tubes with vasospasm (see the attached in vitro results as movie S1 and S2) like blood vessels, which create memory effect leading to AHS in the later stage.
Over the decades many blood ow simulation studies have been carried out with the incompressible uid ow assumption [63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78], which are useful only for simulating the creeping ow conditions in HCS. Herein, we established the proof of the concept of DDT and AHS at the creeping in ow condition in an internal diabatic ow system (see Figure 3) through in silico modeling at a critical total-to-static pressure ratio (CPR) where the compressibility effect is signi cant. The importance of this interdisciplinary study design is succinctly reviewed in the subsequent background section for highlighting the research question pertaining to an authentic prediction of LCDI and LCHI.

Background
Of late many in silico studies have been reported in base uids and nano uids for various industrial applications without an authentic validation of the results with benchmark data. As the pressure of the nano uid rises, average-mean-free-path diminishes and thus, the Knudsen number lowers heading to a zero-slip wall-boundary condition with compressible viscous (CV) ow regime. [2] V.R.S.Kumar et al. [1][2][3] presented an exact analytical solution, which is capable to predict precisely the three-dimensional boundary-layer blockage factor (named herein as blockage factor) of diabatic uid ow systems at the zero-slip-length. The innovation of the Sanal ow choking model was established through the entropy relation, as it meets all the conservation laws of nature. [1] The physical insight of the Sanal ow choking and streamtube ow choking demonstrated herein sheds light on getting answers of several unanswered research questions in advanced science.
V.R.S.Kumar et al. [1][2][3][4][5][6][7][8][9] established that there are likelihoods of Sanal ow choking in HCS (see Figure 1(ah) as the central illustration), after attaining the critical blood pressure ratio. [1,7] The experiences gained from the theoretical and in vitro ndings (see Figure 2) prompted us for the internal ow simulation of the straight duct ending with a divergent port for examining Sanal ow choking and streamtube ow choking (see Figure 3 and Figure 4(a-b)) through the reliable in silico simulation. It is a well-recognized fact that, the entire governing equations for viscous ows are extremely challenging to solve analytically using the existing mathematical tools. Using the developing system of non-linear equations, the in silico simulation with multi-phase and multi-species composite uid ow with oscillating boundary wall is also a challenging task. It is because of the fact that an accurate, strong and competent solution with the super ne grid system is critical for the high reliability in silico modelling. [1][2][3] Physics of Sanal ow-choking received signi cant attention in the global scienti c community for solving various research problems of topical interest. [1,2,7,8] Certainly, using the Sanal ow choking model to predict the 3D blockage factor, the chemical rocket motor designer could optimize the grain port geometry with the maximum possible propellant loading density with the allied igniter, without inviting DDT and without any costly empirical design technique or in silico simulation. [2] Of late (2020) V.R.S.Kumar et al. [2] highlighted the physical signi cance of the detonation kernel associated with the 3D blockage factor and the critical pressure ratio (CPR) causing the phenomenon of Sanal ow choking in a constant area duct ending with a divergent port. Through this study, [2] the fundamental cause of DDT in the chemical rocket has come to the foreground. Over the centuries the scienti c communities under the strong impression that at the creeping in ow condition DDT won't occur in a straight duct ending with a divergent region. We could authentically disprove this wrong notion on DDT through a closed-form analytical model, in silico results [3] and the full motor static test results. [1] Thereby, a popular research question revolving through the globe over the centuries has been settled with a cogent answer. In brevity, it says that due to the Sanal ow choking the creeping or low subsonic ow (continuum or noncontinuum) will get augmented to the supersonic ow condition in a straight duct ending with a divergent port and create possible shock waves and shock diamonds due to streamtube ow choking (see Figure 4 (a-b)). Note that the Sanal ow choking and the streamtube ow choking are new theoretical concepts applicable to both the continuum and non-continuum uid ows. Once the streamlines compacted, the considerable pressure difference attains within the streamtube and the ow within the streamtube gets enhanced to the constricted section for satisfying the continuity condition set up the conservation law of nature, which leads to the Sanal ow choking and supersonic ow development at a CPR due to the convergent-divergent (CD) shape of the streamtube (see Figure 4(a-b)). For authenticating the proof of the concept the analytical and in silico methodologies are presented in the subsequent section.

Methodology
Analytical and in silico methodologies are invoked herein for establishing the proof of the concept of the occurrence of DDT and AHS at the creeping in ow condition in a constant area duct ending with a divergence/bifurcation region (see Figure 3). Figure 3 is highlighting the Sanal ow choking condition in such a classical model of a real-world uid ow system and Figure 4(a) is depicting the Sanal ow choking and streamtube ow choking corresponding to Figure 3. Figure 4(b) shows the enlarged view of streamline pattern and the streamtube ow choking in yocto to yotta scale internal and external ow systems. It is highlighting the CD duct ow effect in a streamtube leading to detonation in the chemical energy and environmental systems at a CPR. Physical situations of ow choking depicted in Figure 3 and Figure 4(a-b) are meeting the conditions set by the conservation laws of nature. This is a remarkable nding for solving various unresolved problems in aerospace, biomedical, chemical, environmental, material, mechanical and nanotechnology, oil and natural gas industries. [1] At the unchoked ow condition pressure in the constricted region of the streamtube will be lower than the wider region and this physical situation leads to choked ow condition at the CPR. Note that CPR is governed by HCR. When the streamtube is compressed, the reduction in internal energy is transformed into an accelerated uid ow motion to satisfy the law of conservation of mass, which leads to the Sanal ow choking in CD shaped streamtube heading to the generation of supersonic ow causing shock waves, pressure-overshoot and detonation in the downstream region of the streamtube. These analytical ndings are corroborated with the in silico results presented in the subsequent section.
The uid-throat induced internal ow choking in real-world uid ow systems at the creeping in ow condition is a new concept, which is de ned as Sanal ow choking, [1] a phenomenon occurs due to the boundary layer blockage. [1][2][3][4][5][6][7][8][9] The exact solution of the 3D boundary layer blockage (BLB), corresponding to LCDI (i.e., considering the lowest value of HCR (γ lowest ) of the evolved gases), at the Sanal ow choking for diabatic ows (continuum / non-continuum) with respect to Figure 3 is given in Equation 1. M i is the subsonic upstream in ow Mach number. Figure 5 is the solution curve of Equation 1. Note that irrespective of the magnitude of the BLB factor, the Sanal ow choking occurs anywhere in the circulatory circuit once the ow attains the critical pressure ratio (see Figure 5). The critical pressure ratio is dictated by the heat capacity ratio (HCR or γ ) of the evolved gas with the lowest HCR (see Equation 2 and 3). Note that BLB will never be zero in any real-world uid ow system. [1,82] Equation 2 represents the LCDI, which is estimated based on the γ lowest for attaining the Sanal ow choking condition. Equation 2 reveals that in any ow system, the total-to-static pressure ratio (P total /P static ), should at all times be lesser than the LCDI for negating the undesirable detonation. In the case of biological ows Equation 2 is re-cast with respect to the blood pressure ratio (BPR) and the blood/bio uid heat capacity ratio (BHCR) for estimating the LCHI, which is presented herein as Equation 3. It is evident from Equation 3 that for negating AHS, the BPR should maintain always lesser than LCHI, which is governed by the lowest HCR of the evolved gas in the vessel. In the HCS the total pressure indicates the systolic blood pressure (SBP) and the static pressure shows the diastolic blood pressure (DBP).
Equation 4 shows the inlet Mach number estimation for getting diabatic ow choking in a straight duct. [1] Equation 5 is a remarkable closed-form analytical model capable to predict the average friction coe cient, of any wall-bounded ow system, without any empiricism, for an authentic in silico simulation. [3] If we know and the length-to-diameter (l/d i ) ratio we could x the in ow Mach number for prohibiting DDT. Equation 5 will enable us for getting a choked ow condition at station 2 (see Figure 3) for the calibration of various in silico ow solvers by matching the numerically predicted blockage factor and the exact analytical solution.
The Sanal ow choking and streamtube ow choking are regulated by the physical situations set by Equations 1-6. It is a well known fact that for negating the ow choking Mach number should always be less than one in the system (see Equation 6). Equations 6(a-d) are the corollary of Equation 6. The selfexplanatory Equations 6(a-d) derived from the compressible ow theory [1,4,83] are representing Mach number, which are complimenting with Equation 2 and Equation 3. All these equations set the conditions for prohibiting Sanal ow choking and streamtube ow choking in any real-world uid ow system. The individual or coupled effects of vessel geometry (stenosis) and the thermo-physical properties on ow choking can be easily discerned from Equations 6(a-d). These equations (Equations 6(a-d)) are well correlated with the clinical ndings. [5][6][7][8] It is evident from Equation 6(a,c,d) that an increase in blockage factor (i.e., a decrease in the port-cross-sectional-area), in any vessel due to plaque and/or boundary layer induced blockage, could increase the risk of Sanal ow choking in the creeping in ow condition. As directly evidenced from Equations 2, 3 and 6(b-d), the risk of Sanal ow choking could be negated by increasing the HCR of the evolved gas in the vessel. Note that the left hand side of Equations 6(a-d) are representing the magnitude of Mach number, which could be estimated from the bio uid properties and the vessel port area for estimating the risk of internal ow choking (see Figure 5). It is important to note that the ow Mach number must always be less than one in the circulatory circuit including the vasa vasorum for retaining the unchoked ow condition. In a nutshell, Equations 6(a-d) are the useful tools, highlighting the geometric and thermo-uid dynamics parameters, for maintaining an unchoked ow condition in the circulatory circuit for negating the risk of AHS. It is important to note that an overdose of blood-thinning drug for reducing the blood-viscosity augments Reynolds number leading to highturbulence and enhanced boundary-layer-blockage (BLB), which increases the chances of cavitation and the Sanal-ow-choking leading to the shock wave and pressure-overshoot causing memory effect (stroke history) in viscoelastic vessels. Therefore, designing the precise blood-thinning regimen is vital for attaining the desired therapeutic e cacy and negating undesirable ow-choking leading to AHS. Brie y, the analytical models reveal that the relatively high and low blood viscosity are risk factors of AHS.
It is a well ascertained physical condition in the compressible ow theory that supersonic ow will be developed in the divergent region of a choked CD duct ow passage similar to an artery with divergent or bifurcation or vasospasm regions (see Figure 1 as the central illustration). At this physical situation [1,84] there is a possibility of shock wave generation and pressure-overshoot, causation of asymptomatic aneurysm and/or AHS as the case may be. [1,37] Largely, in the HCS the ow is laminar and it becomes turbulent due to blood thinners and/or due to local or seasonal effects. Note that the over dose of anticoagulant drugs decrease the dynamic viscosity of blood dramatically and as a result Reynolds number increases leading to enhanced BLB causing the Sanal ow choking. The ow turbulence increases the loss of energy in the form of friction, which augments the blockage factor in the vessels and generates heat and enhance the internal energy resulting a reduction in the blood/bio uid heat capacity ratio (BHCR). The ow turbulence augments the perfusion pressure vital to push the ow of blood, leading to internal ow choking and shock wave generation. It leads to establish that at a CPR in any straight duct ending with the sudden expansion / divergent / bifurcation region could lead to detonation at a low subsonic in ow condition.
It is crystal clear from the SANAL chart given in Figure 5 (the solution curve of Equation 1) that, irrespective of the percentage of blockage factor, the risk of detonation could be negated by retaining the total-to-static pressure rato in a uid ow system always lower than LCDI. Similarly, irrespective of the percentage blockage of any artery, the risk of AHS could be reduced by maintaining the SBP/DBP ratio lower than LCHI, which is a unique function of HCR. For instance, if an internal ow system is having 50 % port area blockage, there will NOT be any possibilities of the Sanal ow choking leading to detonation or hemorrhage provided the system maintains a ow Mach number lower than 0.3 or BPR < LCHI. The upper critical hemorrhage index (UCHI) could be estimated from the HCR of blood. At a CPR, the Sanal ow choking would occur in a vessel with gas embolism (i.e., when BPR > LCHI) or without gas embolism (i.e., whwn BPR > UCHI) irrespective of the blockage factor (plaque and/or boundary layer blockage). In a nutshell, Figure 5 is explicitly showing the condition of DDT and ASH in an internal uid ow system of any scale at the Sanal ow choking condition.

In Silico Results
For demonstrating the proof of the concept of the Sanal ow choking and streamtube ow choking in a classical uid ow system in silico studies have been conducted using a validated ow solver. [3,4,85] The results generated from the in silico modeling (see Figure 6(a-c) and Figure 7(a-f)) are conveying the message to the scienti c community on the occurrence of the Sanal ow choking and streamtube ow choking in a diabatic uid ow system leading to detonation and asymptomatic stroke. Please see movie S3 containing the in silico results.
It is appropriate to mention here that, the simulation of chemical reaction mechanisms containing shock waves and detonation reported in the open literature are not unique. [2] Therefore, we deliberately set aside the reacting ow simulation in this fundamental pilot study for establishing one of the basic causes of DDT in the internal ow system. Figure 6(a-c) and Figure 7(a-f) show the in silico result highlighting the axial Mach number variations, sharp pressure spike and diminishing shock waves at the downstream region of the duct with bifurcation due to the Sanal ow choking and streamtube ow choking. Note that in the HCS, the large BPR oscillations could lead to the choking and unchoking phenomena creating high risk to the subjects (human being / animal) leading to an arrhythmia. Due to the periodic Sanal ow choking any valve, including heart valve, with CD duct shaped ow passage will get more defects than convergent type valves as time advances in any ow circuit. This is corroborated with the clinical ndings. [1,7,8] The fact is that during the Sanal ow choking the divergent region of the valve will experience the shock wave and pressure overshoot causing damage. Most heart valve problems involve the aortic and mitral valves, possibly because of its geometric shape similar to CD duct ow passage.
The valve defects can happen in water pipe line due to cavitation and shock waves. [1] Further discussion on the defects of various types of valves is beyond the scope of this article. Figures 7(a-f) are showing the enlarged view of the streamtube, demonstrating the shape of the streamtube and the Mach number contours at different time intervals before and after the Sanal ow choking. It is crystal clear from Figure 6 and Figure 7 that the streamlines are compressed and the pressure differences are signi cant within the streamtube and as a result the ow gets enhanced to the narrow region of the streamtube for satisfying the conservation law, which leads to Sanal ow choking and detonation due to the convergent-divergent (CD) shape of the streamtube. Normal shock and oblique shock waves are evidenced in the in silico results. The Sanal ow choking location, the strength of shock, and shock diamonds can be observed in Figure 6(a-c). Packed streamlines could be discerned in the constricted area of the streamtube (see Figure 6(a-b) and Figure 7(a-f)) where low pressure is evident. In the case of biological ows, the sonic-uid throat location discerned in Figure 6(a-c) could alter due to the BPR oscillation, wall exibility of the viscoelastic blood vessel, chemistry of multi-species and multiphase uid ow, and pathophysiological conditions.
The objective of this study was to establish the phenomenon of the Sanal ow choking and streamtube ow choking through the analytical and in silico modeling of diabatic uid ows, which we could achieve herein. In the case of HCS, the blood and/or bio uid could get evaporated at the higher temperature creating an undesirable formation of gases within the duct creating a detrimental ow choking due to low HCR of the evolved gas leading to gas embolism. [1][2][3][4][5][6][7][8][9] Figure 6(a-c) and Figure 7(a-f) are analogous to bio uid choking effect in the circulatory circuit due to gas embolism. Brie y analytical and in silico results established that predicting the conditions of LCDI and LCHI, based on the lowest HCR of evolved gas, are inevitable for negating the undesirable DDT and ASH in any uid ow system with credibility.

Discussion
Despite 40 years of study (Hoyle & Fowler 1960), the mechanism whereby a degenerate carbon-oxygen white dwarf explodes, producing a Type Ia supernova (SN Ia), remains poorly understood. Early calculations assumed that central carbon ignition would lead to a detonation (Arnett 1969) that would incinerate the star entirely to iron. This proved inconsistent both with observations of features in the supernova spectrum from intermediate-mass elements and with detailed calculations of isotopic nucleosynthesis. Nowadays it is understood that prompt detonation does not occur because the core at ignition time is insu ciently isothermal.
Although it is controversial whether the de agration will later make a transition to a detonation (Niemeyer & Woosley 1997;Khokhlov et al. 1997;Niemeyer 1999), it is universally assumed that the runaway begins as a de agration (Nomoto et al. 1976).
Indeed, there may be great di culty getting a viable supernova explosion if all the ignition occurs on one side (Niemeyer et al. 1996). Unless a transition to detonation occurs, or pulsational oscillations, it will be di cult to ever burn the other side. The explosion will then be subenergetic and produce too little 56Ni.
We do not know whether the burning wave propagates through the white dwarf as a supersonic detonation or as a subsonic de agration. We do not understand the details of initial ignition and runaway. We do not know the nature of the binary companion that feeds the white dwarf-whether it is a main sequence star, a subgiant star, a giant star, or another white dwarf. All these types of companions might occur with some frequency.
The result of all this ignorance is that theorists cannot predict-from rst principles and with su cient precision-the 56Ni yields, explosion energies, light curves, and spectra of type Ia supernovae to justify them as cosmological theodolites

Concluding Remarks
The theoretical discovery of Sanal ow choking received considerable attention in the central science for resolving centuries long unresolved problems. Understanding ow physics and the transport of uid from creeping in ow to the supersonic ow at the yocto to yotta scale systems are of signi cant interest for testing classical theories of the continuum and non-continuum uid ows for solving varieties of industrial problems with credibility. Gotthard Seifert [102] reported ab initio in silico simulations, which provide a sign of the development of the molecular and electronic structure of an explosive undergoing detonation. Moseler and Landman [103] used molecular dynamics (MD) simulations of nanoscale jets to encounter a rupture pro le not illustrated by macroscopic theory. Of late (2020), Chengxi Zhao [104] reported that the soundness of the traditional theories at the microscale and nanoscale has been taken into question. Authors reported that the thermal uctuations are spontaneously occurring within molecular dynamics (MD) simulations. D.M.Holland et al. [105] further reported that the time dependent mass ow rate predicted using their enhanced in silico simulation matches well with full molecular dynamics (MD) simulation and highlighted that the traditional in silico results of such cases are incompetent. It leads to say that in real world scienti c experiments of complex nano-microscale systems the robustness of in silico model needs to be tested to featuring the actual uid characteristics in a nontrivial geometry at the nanoscale. Singh and Myong [106] reported that for improved modeling efforts, the joint effect of material properties, the scale and shape of the flowing medium on fluid flow must be taken into account, which we conclusively addressed herein through the closed-form analytical models capable to solve real-world uid ow (continuum / non-continuum) problems experiencing de agration to detonation transition of any scale.
The physics of detonation chemistry presented herein through the Sanal ow choking/ streamtube ow choking phenomenon is a pointer for prediting detonation in yocto to yotta scale systems and beyond, which includes supernova explosion. [107] Note that the mechanism whereby a degenerate carbon-oxygen white dwarf explodes, producing a Type Ia supernova (SN Ia), still remains poorly understood. [108] Earlier researchers do not know whether the burning wave propagates through the white dwarf as a supersonic detonation or as a subsonic de agration. [107][108][109][110][111][112][113][114][115][116][117][118][119][120][121]. Herein, we provide the proof of the concept of the Sanal ow choking and streamtube ow choking causing the sharp pressure spike due to shock wave formation. The streamtube ow choking is a radical theory in predicting the de agration to detonation transition in both internal and external ows. At the low subsonic inlet conditions, the realworld uid ow (continuum / non-continuum) system with the divergent/bifurcation duct could incline to de agration-to-detonation-transition (DDT) due to the phenomenon of the boundary-layer-blockage (BLB) factor induced the Sanal ow choking in a wall-bounded or streamline bounded ows at a critical pressure ratio. The Sanal ow choking is vulnerable to catastrophic failures of reacting and non-reacting uid ow systems with sudden expansion/divergent port due to the cavitation, shock wave and detonation as the case may be. At the lower critical detonation or hemorrhage index, the critical pressure ratio of the chemical energy system and the blood pressure ratio (BPR) of the subjects (human being / animal) are unique functions of the heat capacity ratio (HCR) of the gas in the duct. Numerical simulations are carried out with creeping in ow conditions using a calibrated viscous ow solver [3] for demonstrating the novel concept of the uid-throat induced Sanal ow choking followed by the shock wave generation and pressure overshoot in a straight-tube ending with a divergent port, similar to an artery with the divergent / bifurcation region. We concluded that the detonation kernel is more sensitive in the reacting ows generating the leading species with low HCR. We also concluded from the analytical solution that the bio uid / blood with low HCR is more susceptible to asymptomatic hemorrhagic stroke (AHS) in the circulatory circuit of all subjects due to an early ow choking. The risk of Sanal ow choking and streamtube ow choking could be negated by breaking the blockage and/or increasing the HCR of the evolved gases in the tube for keeping the total-to-static pressure ratio always lower than the lower critical detonation / hemorrhage index in any uid ow system. In silico results reported herein shed light for the biological, chemical, energy, environmental, material and aerospace systems design and drug discovery. The result of this study is a strong exposition to the industry for the elimination of the detonation in any energy system with con dence, which was an unknown fact to the scienti c communities for several decades. [1][2][3][4][86][87][88][89][90][91] Using the exact solution reported herein a detonation free energy system could be devised authoritatively by regulating the in ow condition, selecting the uid viscosity, HCR and the average wallfriction coe cient based on the upstream length-to-diameter ratio of the ow system for achieving the condition LCDI > (P total /P static ) uid-throat . In other words, we can reduce the risk of DDT by increasing the HCR. In the case of biological systems by keeping BPR < LCHI, we could reduce the risk of AHS. [1][2][3][4][5][6][7][8][9] It can be achieved by increasing the BHCR, which could simultaneously reduce blood viscosity and turbulence.
A uid-structural simulation could be useful to offer cogent answers to clinical questions pertaining to AHS and aneurysm, which are beyond the scope of this manuscript. In a nutshell, this basic research article sheds light for discovering the likelihoods of bio uid ow choking, Sanal ow choking and Streamtube ow choking in real-world uid ow system. Brie y, analytical, and in silico results highlighted in this article will complement preclinical in vivo assessments in mega and nanotubes and can ne-tune decision making steps in biomaterial design and drug discovery through the nanotechnology. [89][90][91][92][93][94][95][96][97][98][99][100][101] This article is a part of the scienti c odyssey that resulted from a collaboration among members from various research groups, viz., rocket propulsion, physical and material science, chemical science, environmental science, biomaterials, biomedical, cardiology, nanotechnology and nanomedicine.

Supplementary Materials
Movie S1: In vitro result demonstrating the shock wave generation in a viscoelastic tube with vasospasm at a critical pressure ratio: https://youtu.be/59E6pI3L5Rc Movie S2: In vitro result demonstrating the internal ow choking and the shock wave generation in a viscoelastic tube with vasospasm at different locations at a different pressure ratio: https://youtu.be/UQqtpQaUVHg Movie S3: In silico result demonstrating the boundary layer blockage induced the Sanal ow choking at a critical pressure ratio: https://youtu.be/eFndUAU_m5I Declarations