What effect would a crystalline material that is inert under ordinary environmental conditions have on someone if it was injected into their bloodstream? Examples materials include finely pulverized silica or alumina, and the quantities under consideration are at the gram level.
They would clog up the capillaries at the end of where they were injected. Effect depends on the place of injection.
If they were injected into a vein, they would clog up capillaries in lungs, essentially leading to the person efficiently suffocating due to reduced oxygen absorption.
If they were injected into any of arteries that branches off into brain, they would clog up brain blood flow, causing effects equivalent to a serious stroke, and likely death or at least serious brain damage from lack of oxygen.
The least serious effects would be if they were injected into a vein leading to a limb. They would clog up capillaries of that limb, incapacitating it, and eventually leading to necrosis (and death) unless treated (amputated) before that happens (a couple days of gradually worsening conditions as the concentration of anaerobic bacteria developing in the limb increases, causing organism-wide infection).
apaul34208's examples unfortunately shows crystalline material outside bloodstream. In the bloodstream, yes, it will be excruciatingly painful, but unless it dissolves, it will stop somewhere, and where is matter of the grain sizes; fine dust will end up in capillaries.
A lot of the things that can crystallize inside the human body can cause excruciating pain if they crystallize in the right spot, or if you eventually need to pass or excrete the crystal at some point.
Think of things like:
The body will pass an awful lot of contaminates, we consume them all the time, so I'm not too sure about specific doses. I'm sure for common dangerous contaminates you could some info or at least anecdotes.
Lets say it does absorb and the initial injection doesn't cause death:
Aluminum is considered toxic in high amounts...there really isn't much for biological processes that make use of Aluminum and it tends to gather in the brain and bones. It gets compared to mercury poisoning (though mercury is far more toxic). In high enough concentrations, it will result in general confusion, speech problems, and potentially seizures...brain lesions is a potential as well. Bone issues (spurs, deformations, and brittleness) can also be an issue. Lung and nervous system issues can be linked to Aluminum as well and it can interfere with the bodies ability to absorb iron. There appears to be a link between aluminum toxicity and Alzheimer as well, but thats a long term effect.
However it should be noted that most of these concerns are from long term high volume exposure (a child's development can be adversely effected, especially bones and brain function). Short term exposure doesn't quite have the same effect, however the body can hold on to aluminum for a significant amount of time. (incidentally, there is a movement against the amount of aluminum we ingest. It's in a significant amount of drugs...after birth vaccines given to children contain disolved aluminum. If we are injecting it into newborns, adults can handle it).
Silica is a bit different and our body can make a bit more use of it...infact it's usually included within dietary supplements and I believe you can outright find silica supplement pills. There are some warnings in Silica's ability to break down certain vitamins such as B1 which can cause a vitamin B1 deficiency, but that is a long term and high volume exposure before that occurs...not a single injection. High enough volumes could lead to issues where the substance is crystallizing joints and on bones, which would be gout like I'd imagine, potential for kidney stones?...but for the most case, silica is dissolved within blood stream and comes out in our urine.
From a body harm standpoint...one injection isn't going to do much if the substance is able to dissolve into the blood. The aluminum and silica examples you give here would only start to see health issues through prolonged injections...risk would be higher in a developing human as opposed to a full grown adult.
The issue that I'm less sure on here is the substances ability to dissolve into the blood stream. If the substance only partially dissolved, then you are getting into issues around clogged veins and arteries...the risk here is significantly higher than what the substance could do had it simply dissolved.
Edit: Alum (aluminum and sulphur or potassium) apparently acts as quite the blood coagulant...injecting a strong coagulant into someones blood stream can't be a good thing.
SiO2, and Al2O3 are both chemically inert, water insoluble and can only be reduced by strong as acids. In the body, they will not participate in any chemical reactions. However, the body will recognize them as alien objects and seek to seal them off with antibodies and plaque.
They will very quickly be coated with antibodies and white blood cells eventually forming a protein shell. This is the same effect that happens when a bullet or flint arrowhead is stuck in the body. It gets "walled off".
If the particles are mostly microscopic, They will be engulfed by white blood cells, carried to the lymph system and from their eventually pumped through the lymph system and dumped in the lower large intestine.
If larger, say a normal grain of sand, they will likely be adhered to the side of major blood vessels and then walled off under a shell of protein, fats and cholesterol.
If they wedge in capillaries in any layer of the skin, they will be pushed out of the skin out of few months.
I can say all this confidently because quite some while ago I read a book on military medicine. One of the injuries that occurred fairly often was personal being penetrated by grains of sand accelerated by explosions. In most cases, the sand is pushed out of the skin over a period of weeks or months. However, autopsies on soldier who died much later of other causes found what first appeared as cholesterol plaque in the blood vessels but upon examination contained grains of sand inside.
You couldn't actually inject inert substances without making a suspension of them in water, either mechanically, or by attaching them some sticky protein like albumin (found in egg whites.) They'd have to be injected slowly or they would simply block, rupture or implode the view or artery.